CN111245857B

CN111245857B - Channel network steady state evolution game method in block link environment

Info

Publication number: CN111245857B
Application number: CN202010053929.6A
Authority: CN
Inventors: 张佩云; 李晨曦; 汪丽翠; 章一磊; 张捷
Original assignee: Anhui Normal University
Current assignee: Anhui Normal University
Priority date: 2020-01-17
Filing date: 2020-01-17
Publication date: 2021-11-26
Anticipated expiration: 2040-01-17
Also published as: CN111245857A

Abstract

The invention discloses a channel network steady-state evolution game method in a block link environment, which is characterized in that node transaction in a channel network is modeled into a dynamic evolution game model based on a replication dynamic mechanism of a limited theory and a biological evolution process, the model designs a channel network dynamic defense mechanism based on an evolution game, the mechanism adds a defense strategy on a strategy space of a type I node, and considers the cost and success rate of attack of a type II node under the condition of deploying the defense strategy, and the defense mechanism can help the type I node resist the attack behavior of the type II node with a certain probability. The nodes of the model have the finite evolutionary learning capacity, and can dynamically adjust respective strategies according to different attack strategies of attackers to achieve effective defense.

Description

Channel network steady state evolution game method in block link environment

Technical Field

The invention belongs to the technical field of block chains, and particularly relates to a steady-state evolution game method of a channel network in a block chain environment.

Background

The security of blockchain based cryptocurrency (e.g., bitcoin, etherhouse) comes in part from the extensive replication of the block data, at the cost of limited scalability. One of the primary methods of increasing cryptocurrency size is to focus on moving transactions from blockchain to subchain by using point-to-point payment channels through which transaction parties can make a large number of transaction transfers and ultimately settle the net revenue on the blockchain to reduce transaction validation delays. Although the off-chain payment based on the channel network is fast, if one party exits the transaction and closes the channel, the two parties need to submit each operation of the transaction to the chain for processing, and the transaction on the chain not only needs a large transaction fee, but also needs a long transaction confirmation time (sometimes possibly several hours). The huge economic expenditure and the time cost make the channel an attack target of an attacker.

The channels are linked to form a channel network, and the transactions between two parties can be transmitted through the channel network. An attacker may launch an attack, such as a routing attack, on the channel network. In addition, nodes in the channel network can also become targets of attacks and be captured by attackers, and the internal nodes can launch attacks from the interior of the channel, can seriously affect the performance of the channel network, and even cause the whole network to be paralyzed. Therefore, the attack behavior of the internal node is effectively prevented, the stability and the safety of the channel network can be improved, and the transaction in the channel can be completed quickly and smoothly. Based on the idea of evolutionary game, the motivation of profit of the nodes in the channel network is deeply analyzed from the economic perspective, and the attack and defense strategies are designed on the strategy space of the nodes so as to effectively improve the stability and the safety of the channel network.

Giulio Malavolta and Pedro Moreno-Sanchez et al propose the concept of channels, and a large number of transactions can be carried out under a chain, so that the dependence on the existing channels on block chain transactions is reduced and the existing channels are mainly divided into two categories: a payment channel and a status channel, having respective transaction types.

(1) And (3) payment channel: the payment channel is intended to establish direct point-to-point payment, allowing both parties to maintain and update both parties' accounts privately. Each transaction need not be written on a blockchain account, and legitimate funds can be withdrawn from its blockchain at any time. The payment channel comprises a Spilman payment channel, a Lightning network, a duplex micro-payment channel and the like.

1) Spilman payment channel: jeremy Spilman first proposed a channel payment protocol based on the bitcoin system. The protocol realizes the instant confirmation of the transaction, and is characterized in that the sum of a transaction receiver is always increased in the payment process of a channel. The receiver only publishes the latest status in the channel to the blockchain, otherwise the receiver's money is lost. The channel payment protocol only supports one-way payment, and meets the situation that a single user pays a merchant.

2) Lightning network: the channel network is the earliest to form a payment network through a payment channel so as to improve the block chain transaction throughput. Lightning networks mainly contain two contracts: two new transaction types, the Sequence due revocable Contract (RSMC) and the Hash Time Lock Contract (HTLC). The RSMC mainly implements a two-person, two-way payment channel, so that both parties of the channel can confirm the transaction in real time without chaining the transaction. The HTLC realizes that the transfer of any two nodes in the system can be realized through a bidirectional payment channel. The Lightning network scheme has the defects of insufficient efficiency and usability, particularly, in the two-way payment channel protocol, limited by bitcoin system scripts, in order to prevent one party from doing harm, the other party needs to store punished transactions of each previous round of interaction, and along with the continuous occurrence of high-frequency transactions, the cost for storing the transactions is increased, and great burden is brought to users.

3) Duplex micropayment channel: the channel network solves the problems of the two channel networks and realizes high expansibility for digital payment based on the bitcoin. Due to the use of the HTLC of the Lightning network, it is ensured that the transmission over the duplex micropayment channel network is secure and the payment cannot be restored. But only the security of the transmission process is ensured, and whether the participant has a malicious behavior cannot be ensured.

(2) A state channel: unlike payment tunnel networks that only support user-away-chain payments, state tunnel networks also allow for arbitrarily complex intelligent contracts to be executed. Status channels include Sprites channels and Revive channels.

1) Sprites channel: miller et al proposed Sprites' solution that improves the efficiency of Lightning networking solutions and solves the problem of excessive time cost for the user when cross-channel payment is unsuccessful.

2) Revive channel: the Revive channel is proposed by Rami Khalil and Arthur Gervais, a persistence mechanism in a channel payment network is realized, and a transaction participant in the payment network can safely transfer balance among the payment channels. However, in the security analysis of the Revive channel, only honest participants are considered not to lose any funds in the process of Rebalancing (Rebalancing) channel funds, but malicious behaviors of dishonest participants are not considered.

The channel network processes a large amount of transactions offline, and simultaneously uses the block chain as an arbitration platform to process abnormal conditions in the channel transaction process, such as the situation that two parties have a divergence in the channel state, and the like, thereby indirectly improving the transaction throughput of the system. With channel technologies such as payment channel and status channel, the number of interconnected nodes in the channel network may reach tens of thousands or even millions, and therefore, a transaction path from a transaction sender to a transaction receiver, which can realize stable and fast transaction, needs to be found in the decentralized channel network. The scheme of selecting working Flare, Landmark Routing and the like from the existing channel path can find that: the nodes need to obtain all information in the routing process, if all the nodes are willing to cooperate, a payment path can be found but cannot be determined as an optimal path through a routing algorithm under the condition of not considering dynamic joining or quitting of the nodes in the network. However, in practical applications, the tunnel network has a problem of being attacked, especially, an attack behavior is initiated from a node inside the tunnel, an internal attack usually seriously affects the performance of the tunnel network, and even the whole network is paralyzed, and an attack of an internal node is more difficult to prevent than an attack of an external node, and meanwhile, a traditional signature verification faces a failure problem in the internal attack. Therefore, it is necessary to analyze the stability and security of the channel network in the case where an internal attack occurs.

The relevant settings of the channel network are as follows: the channel is composed of a plurality of channels and nodes, each node has a transaction forwarding function, the nodes in the channel network are classified according to the behaviors, and the nodes are divided into I-type nodes and II-type nodes, which are defined as follows: the type I node is composed of participants with defense behaviors in the channel network; the type II node is composed of participants with attack behaviors in the channel network. Note that: both type I and type II nodes have cooperative and uncooperative behavior. Multiple channels may be established between two nodes by means of other nodes.

The usual channel transaction process can be divided into 3 phases: 1) in the initial stage, both sides establish a channel; 2) in the payment stage, both channel parties complete the transaction and update the channel state; 3) and in the channel closing stage, the two sides close the channel and redeem the own funds in the channel. An overview of the channel network is shown in figure 1.

As can be seen from fig. 1, the tunnel network enables the transaction initiator to perform transactions via intermediate nodes, e.g., node b may send a transaction to node f via node d and node e. Where the path from node b to node d, the path from node d to node e, and the path from node e to node f all have sufficient funds to forward the transaction. Node b may also reach node f through nodes c and e or through nodes a, d and e. These nodes may be type II nodes with aggressive behavior, adversely affecting the forwarding and completion of transactions in the tunnel. Therefore, it is necessary to analyze the steady state evolution of the channel network to improve the stability and security of the network. Analyzing the stability and safety of the channel faces the following problems:

(1) in a channel network, a central node does not exist generally, so that centralized control and supervision are difficult to realize;

(2) channel creation requires that transaction parties respectively deposit collateral articles with a certain amount of money to a multi-signature address, the amount of money is locked during transaction, and how to maximize the success rate of channel transaction is particularly important;

(3) due to the characteristics of the channel network, the network may be sparse, and there is little chance to complete transactions through direct connection, so the method of isolating the type II nodes alone is not suitable, and the type II nodes need to be fully utilized;

(4) and the nodes in the channel network are added and withdrawn, so that the topological structure of the channel network is changed continuously.

Disclosure of Invention

The invention provides a block chain lower channel network steady state evolution game method, which analyzes the channel network steady state evolution to improve the stability and the safety of a network.

In order to achieve the above object, a steady state evolution game method for a channel network under a block chain specifically includes the following steps:

s1, the two parties of the transaction initiate the transaction T and broadcast the transaction T to the channel network;

s2, carrying out strategy selection on the nodes in the channel network respectively, obtaining the initial strategy selection proportion of the nodes, and inputting the initial strategy selection proportion into the channel network to copy the dynamic model;

the nodes are divided into I-type nodes and II-type nodes, the I-type nodes comprise three strategies of cooperation, non-cooperation and defense, and the II-type nodes comprise three strategies of cooperation, attack and non-cooperation;

s3, carrying out an evolutionary game based on the network replication dynamic model, and outputting equilibrium points corresponding to the stable state of the evolutionary game, namely ESS points;

when C is present_D>C_RWhen, the combination policy ((1,0,0), (1,0,0)) is an ESS of the channel network replication dynamic model; when C is present_D<C_RWhen, the combination policy ((0,0,1), (1,0,0)) is an ESS of the channel network replication dynamic model;

wherein, C_DRepresents the cost required for the type I node to adopt the defense strategy, C_RRepresents the cost required by the node to make a transaction;

s4, the nodes in the channel network and the combined strategy reselection strategy corresponding to the equilibrium point, namely determining the strategy adopted by the nodes in the channel network for the transaction T;

the combination strategy ((1,0,0), (1,0,0)) represents that both type I and type II nodes will adopt a cooperative strategy to process the transaction T; the combination policy ((0,0,1), (1,0,0)) represents that type I nodes will adopt a defensive policy and type II nodes will adopt a cooperative policy to process transaction T.

Further, the network replication dynamic model comprises: the replication dynamic equation of the type I node and the replication dynamic equation of the type II node,

constructing a replication dynamic equation of the type I node based on the expected income of the type I node selection strategy and the product of the average income difference value of the type I node population and the strategy proportion;

constructing a replication dynamic equation of the type II node based on the expected income of the type II node selection strategy and the product of the average income difference value of the type II node population and the strategy proportion;

the expected yield of the type I node selection strategy I is:

the average benefit of the type I node population is as follows:

the replication dynamic equation for type I nodes is:

the expected yield of the type II node selection strategy j is:

the average benefit of the type II node population is as follows:

the replication dynamic equation for type II nodes is:

wherein, a_ijMatrix elements in the revenue matrix A being type I nodes, b_ijMatrix elements, x, in the revenue matrix B for type II nodes_iRepresents the proportion of the type I node selection strategy I, y_jRepresenting the proportion of type II node selection policy j.

Further, the revenue matrix A for type I nodes and the revenue matrix B for type II nodes are represented as follows:

wherein R represents the income obtained by the two parties in one game, C_DRepresents the cost, R, required by the type I node to adopt the defense strategy_ARepresents the gain obtained by successful attack activity of the type II node, C_ARepresents the cost of a type II node for an attack activity, C_RThe cost required by the node for one transaction is shown, L shows the loss of the I-type node when the I-type node is attacked, and P shows the success rate of attack success of an attack party under the condition that the I-type node adopts a defense strategy.

Further, the replication dynamic equation of the type I node includes: x is the number of₁，x₂，x₃The replication dynamics equation for the type II node comprises: y is₁，y₂，y₃Respectively, as follows:

representing the change rate of participant proportion with time when the class I node adopts a strategy I, I belongs to S₁，S₁∈{1,2,3}，

Representing the change rate of participant proportion with time when the class II node adopts a strategy j, j belongs to S₂，S₂∈{1,2,3}，x₁，x₂，x₃Respectively representing the proportion of cooperation, non-cooperation and defense strategies adopted by the class I node; y is₁，y₂，y₃Respectively representing the proportion of cooperative, aggressive and unworkable strategies adopted by class II nodes.

The channel network dynamic defense mechanism based on the evolutionary game adds a defense strategy on the strategy space of the type I node, considers the cost and success rate of attack of the type II node under the condition of deploying the defense strategy, and can help the type I node resist the attack behavior of the type II node with a certain probability. The nodes of the model have the finite evolutionary learning capacity, and can dynamically adjust respective strategies according to different attack strategies of attackers to achieve effective defense.

Drawings

Fig. 1 is a schematic structural diagram of a channel network arrangement according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a system C according to an embodiment of the present invention_D>C_RWhen the I-type nodes do not adopt the defense strategy, the model stability analysis graph is obtained;

FIG. 3 is a block diagram of a system C according to an embodiment of the present invention_D>C_RWhen the I-type node part adopts a defense strategy, the model stability analysis graph is obtained;

FIG. 4 is a graph illustrating the effect of initial scaling on model convergence, where (a) is strategy 3, (b) is strategy 4, and (c) is strategy 5;

FIG. 5 is a graph illustrating the effect of cost on model convergence provided by an embodiment of the present invention;

FIG. 6 is a diagram illustrating the effect of attack success rate on model convergence according to an embodiment of the present invention;

FIG. 7 shows a block diagram C according to an embodiment of the present invention_D<C_RWhen the I-type nodes do not adopt the defense strategy, the model stability analysis graph is obtained;

FIG. 8 is C_D<C_RWhen the I-type node part adopts a defense strategy, the model stability analysis graph is obtained;

FIG. 9 is a graph illustrating the effect of initial scaling on model convergence, where (a) is strategy 3, (b) is strategy 6, and (c) is strategy 7;

FIG. 10 is a graph illustrating the effect of cost on model convergence provided by an embodiment of the present invention;

FIG. 11 is a diagram illustrating the effect of attack success rate on model convergence according to an embodiment of the present invention;

FIG. 12 is a diagram illustrating the impact of uncooperative behavior of nodes on transaction success rate provided by an embodiment of the present invention;

fig. 13 is a diagram illustrating an influence of an uncooperative behavior of nodes on a transaction transmission delay according to an embodiment of the present invention.

Detailed Description

The following detailed description of the embodiments of the present invention will be given in order to provide those skilled in the art with a more complete, accurate and thorough understanding of the inventive concept and technical solutions of the present invention.

The method comprises the following steps of constructing a dynamic evolution game model based on a channel network, wherein three basic elements of game analysis need to be considered: participants, policy space, and revenue matrix.

The participants of the game are respectively composed of two different node sets: one is a node set composed of type I nodes, and benefits can be obtained by forwarding a transaction; the other is a set of nodes consisting of type II nodes that can gain revenue by launching an attack or forwarding a transaction.

For the type I node, three strategies of cooperation, non-cooperation and defense are available, and the strategy space of the type I node is recorded as:

S₁∈{1,2,3} (1)

wherein, 1 represents that the type I node adopts a cooperation strategy, and the node adopting the cooperation strategy transmits the agreement to the transaction; 2, adopting a misaction strategy, and refusing to forward the transaction by adopting the misaction strategy; 3, adopting a defense strategy; the nodes adopting the defense strategy will defend against malicious uncooperative and offensive actions implemented by type II nodes.

For type II nodes, there are three strategies of cooperation, attack and non-cooperation, and the strategy space of type I nodes of type II nodes is recorded as:

S₂∈{1,2,3} (2)

wherein, 1 represents that the II type node adopts a cooperation strategy, and the node adopting the cooperation strategy transmits the agreement to the transaction; 2, adopting an attack strategy, and implementing malicious uncooperative and attack behaviors on the type I node by the node adopting the attack strategy to obtain a profit; and 3 denotes taking the uncooperative strategy. Nodes adopting the non-operating strategy refuse to forward the transaction.

According to the characteristics of the channel network, the income parameters of the type I node and the type II node are defined as follows: r (reward): the income obtained by the two parties in one game can be the income obtained by the node successfully forwarding one transaction; c_D(Cost of decay): the cost required by the type I node for adopting the defense strategy can be the consumption of funds; r_A(Reward of attack): the gain obtained by the successful attack activity of the II type node can be the gain of funds, and the R is assumed>R_A；C_A(Cost of attack): the cost required by the type II node for attack activity can be the fund consumed in attack, the related legal sanctions when the type II node is found and the like; c_R(Cost of relay): represents the cost required by the node to conduct a transaction, and can be the consumption of funds; l (loss): representing type I nodesLoss when under attack; p (Proavailability): the success rate of attack success of an attack party is shown under the condition that the I-type node adopts a defense strategy; in the yield parameters of both type I and type II nodes, R>C_D>C_A，R>C_R>C_A。

The premise of the evolutionary game is that each participant in the game is rationalized in the decision phase, i.e., the participant makes a strategy selection in pursuit of maximum profit. The selfish or proficient nature of the game participants in a limited sense maximizes the benefits of the gaming pool. That is, if only selfish behavior or only interested behavior is not the optimal strategy for maximizing profit among a participant group or different participant groups, the maximization of group profit can be achieved only when selfish is achieved in some aspects and interested behavior is achieved in some aspects, that is, selfish behavior and interested behavior reach a certain proportion, which is also called the optimal strategy. The premise assumption of this patent is therefore that each node is required to make policy selections with the goal of maximizing the expected revenue given the respective policy space. Under the condition that the nodes of the two parties of the game do not know the strategies of each other, the income analysis of the two parties of the game is divided into the following three main conditions according to the II-type node strategy.

When the II-type node adopts a cooperation strategy and the I-type node adopts a cooperation, non-cooperation and defense strategy, the game combination strategy between the I-type node and the II-type node comprises the following steps: three cases (cooperative ), (uncooperative, cooperative) and (defensive, cooperative). The profit analysis of the two parties to the game is shown in table 4.1.

TABLE 4.1 revenue analysis of both parties in a game when a type II node takes a cooperation strategy

(collaboration ): the two parties agree to carry out the transaction, and the profits of the parties are the profits obtained by the game or the profits R of the transaction successfully forwarded by the node minus the cost C required by forwarding the transaction_R. The final benefit of the type I node is R-C_RThe final yield of the type II node is R-C_R(ii) a (uncooperative, cooperative): the I-type nodes are not cooperated, the I-type nodes have no loss or gain, and the final gain is 0. The type II node can not successfully complete the forwarding operation because the type I node does not cooperate with the type I node to forward the transaction, so the successful benefit of forwarding is not obtained, and only the fund C consumed by one transaction is carried out_R. The final yield of the type II node is recorded as-C_R(ii) a (defense, collaboration): the type I node performs transaction due to the adoption of defense measures, and the two parties cooperate. The profits of all parties are profits obtained by the game or profits R successfully forwarded, and only the cost of the consumed funds is different. I-type node cost C consumed by deploying defensive measures_DAnd the final profit of the type I node is recorded as R-C_D. Type II node consumes capital C for performing one transaction_R. The final profit of the type II node is recorded as R-C_R。

When the type II node adopts a cooperation strategy and the type I node respectively adopts cooperation, non-cooperation and defense strategies, the type I node respectively obtains R-C _R0 and R-C_D(ii) a The type II node gains are R-C_R、-C_R、R-C_R. Because it is assumed that R>C_D>C_A，R>C_R>C_ASo that R-C_R>0，R-C_D>0, the maximum income of both parties is larger than 0, and the income maximization requirement is met.

And secondly, when the II type node adopts an attack strategy, the income analysis of both game parties is shown in the table 4.2.

TABLE 4.2 revenue analysis of both parties in the game when the type II node takes the attack strategy

(collaboration, attack): the type I node cannot successfully complete the transaction forwarding operation because the selected cooperation strategy is successfully attacked by the type II node. The type I node has no successfully forwarded profit, only has the loss L when being attacked, and the final profit is-L. The II type node obtains the income R due to successful attack_AFurthermore, a certain cost C is required for forwarding the transaction_RThus the final benefit is R_A-C_R。

(uncooperative, aggressive): the type I node cannot successfully complete the transaction forwarding operation because it is not collaborated and successfully attacked by the type II node. The type I node has no success forwarding profit, only has the loss L when being attacked, and the final profit is-L. Attack of type II nodes is not successful for uncooperative type I nodes, and yield R of attack success cannot be obtained_AAnd the attack activity requires a certain cost C_AThus, the final yield of the type II node and the type I node is-C_A。

(defense, attack): the I type node adopts a defense strategy, so that the II type node only has P success rate attack success. Under the condition that the attack is successful, the I-type node obtains the profit R of successful forwarding, but the defense cost C is needed for deploying the defense measures_DAnd the I type node has loss L when the II type node is successfully attacked, the I type node has loss capital of P multiplied by L under the condition that the attack success rate is P, and therefore the final yield is R-C_D-P × L. Attack of type II nodes is unsuccessful on type I nodes adopting defense strategies and can not obtain the successful gain R of attack_AAnd the attack activity requires a certain cost C_AThus the final yield of the type II node is-C_A。

When the type II node adopts an attack strategy and the type I node respectively adopts a cooperation strategy, a non-cooperation strategy and a defense strategy, the income of the type I node is respectively-L, -L and R-C_D-P × L. According to the maximum income requirement, the defense strategy adopted by the type I node is effective, and the R-C is required_D-PxL ≧ 0, i.e.:

R≥C_D+P×L (3)

and thirdly, when the II type node adopts the non-cooperative strategy, the income analysis of both sides of the game is shown in the table 4.3.

TABLE 4.3 revenue analysis of both parties in a game when a type II node takes a misbehaving policy

(cooperative, uncooperative): type I nodes are not cooperative with type II nodesAnd forwarding cannot be smoothly completed. Type I nodes do not forward successful proceeds, only the funds C consumed to make a transaction_RThus, the final yield is-C_R. The II type nodes are not cooperated, so that no loss or gain is generated, and the final gain of the II type nodes is 0; (uncooperative ): the two parties do not agree to carry out transaction forwarding, and the income of the two parties is 0; (defense, uncooperative): although the type I node adopts a defense strategy, the type II node does not cooperate, the type I node does not have the benefit of successful forwarding, and only the cost C required by deploying defense measures_DThus, the final yield is-C_D. The type II nodes are not cooperative, so that no loss or no profit is caused, and the final profit of the type II nodes is 0.

When the II type node adopts the non-cooperative strategy and the I type node respectively adopts the cooperative, non-cooperative and defense strategies, the income of the I type node is-C_R、0、-C_D(ii) a Type II node earnings were 0,0 and 0. The maximum benefit of table 4.3 is 0.

As can be seen from tables 4.1 to 4.3, since there are three policy spaces for the type I node and the type II node, in order to balance the interest relationship between the type I node and the type II node, a 3 × 3 revenue matrix is respectively constructed for both game parties, and the revenue matrix of the type I node is denoted as a ═ a_ij]_3×3The type II node profit matrix is denoted as B ═ B_ij]_3×3Where i is equal to {1,2,3}, j is equal to {1,2,3}, a_ijRepresenting the gain obtained by a type I node when the type I node adopting the I strategy plays games with a type II node adopting the j strategy, b_ijRepresenting the earnings obtained by the type II nodes when the type I node adopting the I policy is playing the game with the type II node adopting the j policy.

According to the game two-party income analysis table 4.1, table 4.2 and table 4.3, the income matrixes of the type I node and the type II node are respectively marked as A and B, and can be respectively obtained as follows:

in the channel network, a condition for keeping all nodes in a dynamic equilibrium state should be found; otherwise, if the network is unstable, the normal operation and safety of the network are affected. Therefore, the aim of creating the channel network dynamic evolution game model is to find conditions for keeping dynamic stability and balance.

An Evolution Stable Strategy (ESS) and a replication dynamic state are the most core concepts of the evolution game theory, wherein the ESS indicates a stable state of the evolution game, and the replication dynamic state indicates a convergence process for achieving the stable state. ESS is only a local stability strategy and does not constitute a sufficient condition for judging the stability of evolution in a random environment. In order to better describe the dynamic evolution process, the static concept and the dynamic process in the Evolutionary game theory are unified, and the static concept and the dynamic process in the Evolutionary game theory are unified by utilizing the concept of Evolutionary Equilibrium (Evolutionary Equilibrium). Replicating the dynamic equations may ensure that the ESS is balanced for evolution. The general form of the replication dynamic equation is as follows:

in the formula (6), P_EFor the expected benefit of the strategy, P_AIs the overall average gain in the policy space corresponding to the policy. z is a radical of_kThe proportion of the strategy k selected for the node is:

z_k＝N_k/M (7)

in the formula (7), N_kAnd selecting the number of nodes of the strategy k in the strategy space, wherein M is the total number of the nodes in the strategy space. N is not less than 0_k≤M。N_kWhen 0, it means that there is no node selection policy k. N is a radical of_kWhen M, it means that all nodes select policy k.

The type I node and the type II node in the channel network respectively have respective strategy spaces. Note N_iNumber of nodes selecting policy I in policy space for type I nodeAnd i ∈ {1,2,3},

for the total number of nodes in the type I node policy space,

and is

The proportion of adopting cooperative, uncooperative and defensive strategies by the I-type node is x₁，x₂，x₃：

In the formula (8), it is known

Recording the proportion distribution set of the strategy of the I-type node at a certain moment as X:

X＝{x_i|i∈{1,2,3}} (9)

note N_jSelecting the number of nodes of the strategy j in the strategy space of the II type node and j is equal to {1,2,3},

for the total number of nodes in the type II node policy space,

and is

Noting that the proportion of adopting cooperative, attacking and uncooperative strategies by the II type nodes is y₁，y₂，y₃:

In the formula (10), y is 0. ltoreq. y_jLess than or equal to 1 and

recording that the proportion distribution set of the strategy of the II type node at a certain moment is Y:

Y＝{y_j|j∈{1,2,3}} (11)

according to the replication dynamic theory of the evolutionary game, the replication dynamic equations of the type I node and the type II node can be obtained as follows: the expected yield of the type I node selection strategy I is given by equations (4), (9), (10):

a_ijfor the matrix elements of the type I node profit matrix a, the average profit of the type I node is obtained from equations (8), (9), (12):

the replication dynamic equation for type I nodes is:

the specific form of the replication dynamic equation obtained by substituting equations (12) and (13) into equation (14) is shown in equation (15):

(2) type II nodal replication dynamic equation

The expected yield of the type II node selection strategy j is given by equations (5), (8), (11):

b_ijfor the matrix elements of the type II node profit matrix B, the average profit of the type II nodes is given by equations (10), (11), (16):

the replication dynamics equation for type II nodes is shown in equation (18):

by substituting formulae (16) and (17) for formula (18):

from the expressions (15) and (19), x is calculated₁，x₂，x₃，y₁，y₂，y₃Duplicate dynamic equations.

To be provided with

Representing the rate of change of participant proportion with time when the type I node adopts a strategy I, wherein I belongs to S₁. X is calculated from the revenue matrix of equation (4) and equation (15)₁，x₂，x₃The replication dynamic equation is:

to be provided with

Representing the rate of change of participant proportion with time when the type II node adopts a strategy j, wherein j belongs to S₂. Y is calculated from the revenue matrix of equation (5) and equation (19)₁，y₂，y₃The replication dynamic equation is:

replicating the dynamic equations ensures that an ESS with local dynamic stability exhibits a relationship and convergence process between the selection process of equilibrium and dynamics. But because the replication dynamics are non-linear, it is difficult to find a unique solution. Therefore, the evolutionary game shifts from solving the equilibrium to analyzing the stability of the equilibrium, which is important for prolonging the life cycle of the network.

According to the theory of the evolutionary game, the channel network replication dynamic systems of the type I nodes and the type II nodes are formed by the formulas (20) to (25), so that any point (X, Y) on the solution curves of the channel network replication dynamic systems of the type I nodes and the type II nodes corresponds to a mixed strategy ((X, Y) of the evolutionary game)₁,x₂,x₃),(y₁,y₂,y₃)). For the dynamically evolving game model, the possible equilibrium points can be calculated by equations (20) - (25) ((x)₁,x₂,x₃),(y₁,y₂,y₃) Values) are shown in table 5.1:

TABLE 5.1 dynamic evolutionary Game model equilibrium points

Is proved to be in C_D>C_RUnder the condition, the balance point ((1,0,0), (1,0,0)) is the only ESS, which means that all type I and type II nodes are willing to select a cooperation strategy at this point, as shown in theorem 1. Theorem 1: the only requirement of the ESS for which the equalization points ((1,0,0), (1,0,0)) are channel network replication dynamic system equations (20) - (25) is C_D>C_R。

(1) Proof of Presence

The requirements for the ESS in which the points ((1,0,0), (1,0,0)) are channel system equations (20) to (25) are Trace J <0 and Det J >0[27 ]. Wherein the Matrix J is a Jacobian Matrix (Jacobian Matrix) of the evolutionary game, Trace J is defined as the sum of elements on the main diagonal of the Matrix J, and Det J is defined as the determinant of the Matrix J. Jacobian matrix notation

Equations (20) to (25) are substituted for equation (26), and a jacobian matrix corresponding to the channel system is obtained. Substituting the points ((1,0,0), (1,0,0)) into the system jacobian matrix J yields:

the traces of matrix J are: trace J ═ 5C_R-C_D-5R+R_A，

The determinant of the matrix J is: det J ═ C_R-R)⁴(R-R_A)(C_D-C_R)，

∵R>R_A，

If C_D>C_R，

∴Trace J＝5C_R-C_D-5R+R_A

<5C_R-C_R-5R+R_A

＝4C_R-5R+R_A

<4C_R-5R+R

＝4(C_R-R)<0，

∵R>R_A，

If C_D>C_R，

∴Det J>0，

Note that: when C is present_D＝C_RWhen Det J is 0, Det J in the ESS requirement is not satisfied>0, is required. Therefore C_D≠C_R。

Therefore, when C_D>C_RAt this time, the point ((1,0,0), (1,0,0)) is an ESS of the channel network replication dynamic system.

(2) Proof of uniqueness

The possible equalization points calculated by equations (20) to (25) are shown in Table 5.1 for a total of 9. To prove the uniqueness of the dots ((1,0,0), (1,0,0)), the uniqueness of the dots ((1,0,0), (1,0,0)) can be explained by only proving that 8 dots other than the dots ((1,0,0), (1,0,0)) are not ESS according to the reverse thinking.

Is administered with Ben_D>C_RWhen the temperature of the water is higher than the set temperature,

1) for points ((1,0,0), (0,1,0)), ((1,0,0), (0,0,1)), ((0,1,0), (1,0,0)), ((0,1,0), ((0,1,0)), ((0,1,0), (0,0,1)), ((0,0,1), (0,0,1)), Det J ═ 0, the requirements for ESS, i.e., Trace J <0 and Det J >0, are not met,

the above 6 equalization points are not ESS;

2) for the points ((0,0,1), (1,0,0)),

Trace J＝3C_D+2C_R-C_A-5R，

Det J＝(C_R-R)²(C_R-R)²(R-C_R+C_A)(C_R-C_D) Wherein, in the step (A),

∵R>C_R，C_D>C_R，

∴R-C_R+C_A>0，C_R-C_D<0, then Det J<0, Trace J, which is a sufficient condition for not satisfying the ESS<0 and Det J>0，

Points ((0,0,1), (1,0,0)) are not ESS;

3) for the points ((0,0,1), (0,1,0)),

Trace J＝3C_D-C_R+3C_A-2L-2R+3P×L，

Det J＝C_A ²(C_D–L–R+P×L)²(C_D+P×L-R)(R-C_R+C_A) Wherein, in the step (A),

∵R≥C_D+ P × L is shown in formula (3), and R>C_R，

∴C_D+P×L–R<0，R-C_R+C_A>0, then Det J is less than or equal to 0, and does not satisfy the requirement of ESS, namely Trace J<0 and Det J>0，

Points ((0,0,1,0,1,0)) are not ESS;

therefore, when C_D>C_RAt this time, the points ((1,0,0), (1,0,0)) are ESS unique to the channel network replication dynamic system.

The above proof of existence and uniqueness proves that the sufficient condition of the ESS with the point ((1,0,0), (1,0,0)) being the only of the channel network replication dynamic system equations (20) to (25) is C_D>C_R. To make C_D>C_RThis means that the cost of executing a transaction by a node is reduced or the cost of deploying a defense strategy by a type I node is increased, so that the cost of executing a transaction is greater than the cost of deploying a defense strategy by a type I node. Therefore, the I-type node can reasonably select whether to deploy the defense strategy or not according to the defense cost of different defense strategies, thereby effectively reducing the overhead and prolonging the life cycle of the node in the whole channel network.

Is proved to be in C_D<C_RUnder the conditions, the equalization point ((0,0,1), (1,0,0)) is the only ESS. This point indicates that all type I nodes are willing to choose a defense strategy and all type II nodes are willing to choose a cooperation strategy, as shown in theorem 2.

Theorem 2: ((0,0,1), (1,0,0)) is C is the only ESS of the channel network replication dynamic system_D<C_RAfter the evolution game is finished, all the type I nodes select a defense strategy, and all the type II nodes select a cooperation strategy.

(1) Proof of Presence

The points ((0,0,1), (1,0,0)) are the sufficiency conditions for the channel system ESS, Trace J <0 and Det J > 0. The Jacobian matrix corresponding to the channel system can be obtained by substituting equations (20) to (25) for equation (26). Substituting the points ((0,0,1), (1,0,0)) into the system jacobian matrix J yields:

the traces of matrix J are: trace J ═ 3C_D+2C_R-C_A-5R，

The determinant of the matrix J is: det J ═ C_D-R)²(C_R-R)²(C_R-C_D)(R-C_R+C_A)，

∵R>R_A，R>C_R，

If C_D<C_R，

∴Trace J＝3C_D+2C_R-C_A-5R

<3C_R+2C_R-C_A-5R

＝5C_R-5R-C_A

＝5(C_R-R)-C_A

<0，

Has another radical (R)>C_R，C_A>0，∴R-C_R+C_A>0，Det J>0，

Therefore, when C_D<C_RAt this time, the point ((0,0,1), (1,0,0)) is an ESS of the channel network replication dynamic system.

(2) Proof of uniqueness

The possible equalization points calculated by equations (20) to (25) are shown in Table 5.1 for a total of 9. To prove the uniqueness of the dots ((0,0,1), (1,0,0)), the uniqueness of the dots ((0,0,1), (1,0,0)) can be explained by only proving that 8 dots other than the dots ((0,0,1), (1,0,0)) are not ESS according to the reverse thinking.

Is administered with Ben_D<C_RWhen the temperature of the water is higher than the set temperature,

1) for points ((1,0,0), (0,1,0)), ((1,0,0), (0,0,1)), ((0,1,0), (1,0,0)), ((0,1,0), (0,1,0)), ((0,1,0), (0,0,1)), ((0,0,1), (0,0,1)), Det J ═ 0, the requirements for ESS, i.e., Trace J <0 and Det J >0, are not met,

the above 6 equalization points are not ESS;

2) for the points ((1,0,0), (1,0,0)),

Trace J＝5C_R-C_D-5R+R_A，

Det J＝(C_R-R)⁴(R-R_A)(C_D-C_R) Wherein, in the step (A),

∵R>C_A，C_D>C_R，

det J <0, which does not satisfy the requirements of ESS, i.e., Trace J <0 and Det J >0,

points ((1,0,0), (1,0,0)) are not ESS;

3) for the points ((0,0,1), (0,1,0)),

Trace J＝3C_D-C_R+3C_A-2L-2R+3P×L，

∵R≥C_D+ P × L is shown in formula (3), and R>C_R，

Points ((0,0,1), (0,1,0)) are not ESS;

therefore, when C_D<C_RAt this time, the points ((0,0,1), (1,0,0)) are ESS unique to the channel network replication dynamic system.

The above proof of existence and uniqueness proves that the sufficient condition of the ESS that the point ((0,0,1), (1,0,0)) is the only one of the channel network replication dynamic system equations (20) to (25) is C_D<C_R. To make C_D<C_RThis means that the cost of a node to perform a transaction is increased or the cost of a type I node to deploy a defense strategy is decreased such that the cost of performing a forward transaction is less than the cost of a type I node to deploy a defense strategy. Thereby a type I sectionThe points can reasonably select and deploy different defense strategies according to the defense costs of the different defense strategies, so that the overhead is effectively reduced, and the life cycle of the points in the channel network is longer.

According to theorem 1 and theorem 2, when the cost required by deploying the defense strategy by the type I node is larger than the cost required by the node to perform one-time forwarding transaction, all the type I nodes in the channel network adopt the cooperation strategy and all the type II nodes adopt the cooperation strategy after the evolution game is finished. However, when the cost required by the type I node to deploy the defense strategy is less than the cost required by the node to perform one-time forwarding transaction, after the evolutionary game is finished, all the type I nodes in the channel network adopt the defense strategy and all the type II nodes adopt the cooperation strategy.

In the current channel transaction process of the block chain, the nodes of both parties of the transaction need to cooperate, if one party of the nodes does not want to cooperate, the channel is closed, the nodes of both parties need to be switched to the block chain to realize transaction operation, and long time is spent for completing transaction verification. Therefore, when a transaction is performed in the channel network, the steady state of the channel network needs to be ensured to ensure that the transaction is completed smoothly. The method is characterized in that node transaction in a channel network is modeled into a dynamic evolution game model based on a replication dynamic mechanism with limited rationality and a biological evolution process, the dynamic evolution game model designs a channel network dynamic defense mechanism based on an evolution game, a defense strategy is added to a strategy space of a type I node by the mechanism, the cost and success rate of attack of a type II node under the condition of deploying the defense strategy are considered, and the defense mechanism can help the type I node to resist the attack behavior of the type II node with a certain probability. The nodes of the model have the finite evolutionary learning capacity, and can dynamically adjust respective strategies according to different attack strategies of attackers to achieve effective defense.

Because of the randomness of the uncooperative behavior of the nodes in the real scene, in order to verify the performance advantage of the applied channel network in the real scene, a simulation framework is developed to simulate a lightning network and a dynamic evolution game channel network with an attack and defense strategy, and the result shows that the channel network with a dynamic defense mechanism has a better transaction transmission success rate and a lower time delay, and the simulation process is specifically as follows:

(1) the experimental environment is as follows: 1) computer configuration: the Windows8 sixty-four-bit operating system comprises an Intel Core i5 processor, a CPU2.80GHz and an 8G memory; 2) and (3) environment configuration: and (4) adopting an MTLAB2018b tool to simulate the game process and result of the dynamic evolution game model.

(2) Experimental parameters: because the measurement standards of parameters such as node transaction income, cost and the like are different, all research parameters are subjected to standardization processing, and the values are within [0,1 ]. The specific experimental parameter design is shown in table 6.1:

TABLE 6.1 Experimental parameters Table

In Table 6.1, to test the effect of different defense costs on the speed of the system to ESS, when C_D>C_RWhen R is more than or equal to C according to formula (3)_D+P×L，C_DValues of 0.42, 0.44 and 0.46 respectively to test the effect of different defense costs on the system's speed to ESS, otherwise C_DThe value is 0.46. When C is present_D<C_RWhen R is more than or equal to C according to formula (3)_D+P×L，C_DThe values are respectively 0.1, 0.2 and 0.3 to test the influence of different defense costs on the speed of the system to reach the ESS, and C is used in other cases_DThe value is 0.3; in addition, R, R in Table 6.1_A、C_R、C_AIs taken to satisfy R>R_A，R>C_D>C_A，R>C_R>C_AThe requirements of (1).

The nodes in the evolutionary game are limited, the loss after the attack is the same as the loss after the successful game is carried out and the transaction income is completed, and therefore L is 1; in order to test the influence of different attack success rates of II-type nodes on the speed of the system reaching the ESS, the requirement that R is more than or equal to C in the formula (3)_DUnder the condition of + P multiplied by L, the values are respectively 0.1, 0.2 and 0.4, and the values are 0.5 in other cases.

(3) Description of other parameters

1) Simulation time (Time (s))

And (4) the simulation time required by the evolutionary game to reach the evolutionary equilibrium, namely the time required by the channel network replication dynamic system to converge to the ESS point.

2) Proportion of strategy selected by Node (Node ratio (%))

On the solution curve of the I-type node and II-type node channel network replication dynamic system, the simulation point (X, Y) corresponds to a combination strategy of the evolutionary game ((X)₁,x₂,x₃),(y₁,y₂,y₃) I.e. the proportional distribution of the strategies adopted by the type I and type II nodes. See equations (8) and (10) for the calculation. In the initial state of the evolution game, according to 7 different combination strategies in the table 6.2, the type I node and the type II node select respective strategies to carry out a game experiment. The settings of the specific combination strategy are shown in table 6.2:

TABLE 6.2 proportion parameter Table for node selected policy

(4) Performance analysis index

1) Stability: the stability of the balance between the type I node and the type II node depends on the comparison of the profit values of the strategy selection of the type I node and the type II node in the evolutionary game, and the individuals in the two parties in the population can still change continuously when the ESS is reached, namely the process that the interior of the two parties changes continuously and the population is not changed.

2) Convergence property: whether the system can reach the ESS and the amount of time required to reach the ESS are indicated by time(s). I.e., the shorter the required time, the better the convergence.

Under the dynamic replication, the achievement of the ESS is evolution equilibrium, and the nodes and channels in the channel network are still constantly changing when the evolution equilibrium is achieved. In order to research the influence process and the influence result of the continuous change in the channel network on the whole channel network, a simulation model is established according to the formulas (20) to (25). According to differentFor experimental purposes, a combination strategy (X, Y) ═ X₁,x₂,x₃),(y₁,y₂,y₃) X) is an initial value of₁，x₂，x₃，y₁，y₂，y₃The game process is reflected on the simulation image as x₁，x₂，x₃，y₁，y₂，y₃The ratio Node ratio (%) of the policy selected by the respective corresponding Node, i.e., the image ordinate. And observing the game process according to the change of the strategy proportion, and analyzing the stability of the channel network dynamic evolution game model. When C is present_D>C_RThe result of the game of the dynamically evolving model of the model is a (cooperation ) combination strategy.

The analysis of the system evolution stability whether a defense strategy is adopted or not in the initial state of the I-type node is specifically as follows:

(1)C _Dtake 0.46. When strategy 1 is selected for evolutionary game, the channel network game process is shown in figure 2, and figure 2 isC _D>C _RWhen the I-type nodes do not adopt the defense strategy, the model evolves a stable state analysis graph; as can be seen from fig. 2, when no defense strategy is adopted for the type I node in the channel network, the type II node selects an attack strategy to maximize its own benefit, the type I node always selects a cooperation strategy, and after several games, the type II node also selects a cooperation strategy to reduce its own loss through evolutionary learning, and the network finally converges to a stable state where both parties cooperate.

(2)C_DTake 0.46. When the strategy 2 is selected for the evolution game, the channel network game process is shown in figure 3, and figure 3 is C_D>C_RAnd when the I-type node part adopts the defense strategy, the system evolves the analysis chart of the stable state, as can be known from fig. 3, when some I-type nodes in the channel network take the defense measure, the I-type nodes adopt the defense strategy, and the II-type nodes are subjected to evolution learning for a period of time, observe that the I-type nodes adopt the defense strategy, and select the cooperation strategy for maximizing the benefits of the nodes. Of type I nodes over timeAnd (3) evolutionary learning, after the II-type nodes adopt cooperation strategies, abandoning the defense strategies to select the cooperation strategies for the maximum benefit of the nodes, and finally converging the network to a stable state in which the nodes cooperate. Is described in C_D>C_RAnd meanwhile, whether the I-type node takes defense measures or not has no influence on the game evolution strategy of the network replication dynamic system.

The influence of the initial ratio on the convergence of the system is specifically explored as follows:

in order to research the influence of the initial proportion of cooperative strategies deployed by the type I node and the type II node on the system convergence, the stability analysis of a dynamic system replicated by theoretical 1 and 6.2.1 node channel networks shows that the combined strategy (cooperation and cooperation) is an ESS of the system. On the basis, whether the two game parties can still maintain a stable state and influence on model convergence is further considered for different initial proportions of the channel network node selection cooperation strategy. C_DTaking 0.46, fig. 4(a) is a graph of the influence of the initial proportion on the system convergence when the strategy 3 is adopted, fig. 4(b) is a graph of the influence of the initial proportion on the system convergence when the strategy 4 is adopted, fig. 4(c) is a graph of the influence of the initial proportion on the system convergence when the strategy 5 is adopted, and as can be seen from fig. 4(a) and fig. 4(b), the higher the initial proportion of the type I node adopting the cooperation strategy is, the faster the model convergence is; as can be seen from fig. 4(b) and 4(c), the higher the initial proportion of the type II nodes that adopt the cooperation strategy, the faster the convergence of the model.

The influence of cost on the convergence of the system is specifically explored as follows:

in order to research the influence of the cost of the type I node deployment defense strategy on the system convergence, the cost C of the type I node deployment defense strategy is changed according to the ESS stability analysis_DThe values of the parameters were subjected to simulation analysis. When C is present_D>C_RIn order to simplify the simulation graph, only the evolution process that the type I node adopts the cooperation strategy and the type II node adopts the cooperation strategy is displayed in the simulation graph. When strategies 2 and C are adopted in the evolutionary game process_D>C _R1/3 the cost of deploying defense strategies for type I nodes is 0.42, 0.44 and 0.46 respectivelyThe effect of cost on the speed of the system to ESS is shown in FIG. 5, from FIG. 5, it can be seen that when C is_D>C_RIn time, under the condition of three different defense cost games, the cost of deploying the defense strategy by the nodes has obvious influence on the system convergence. As the defense cost increases, the speed at which the type I node reaches the stable cooperation state increases, the speed at which the type II node reaches the stable cooperation state does not change, and the speed at which the system as a whole reaches the ESS increases, that is, the system convergence improves. In the game process, part of the type I nodes adopt a defense strategy, and the type II nodes observe that the type I nodes adopt the defense strategy and adopt a cooperation strategy for maximizing the benefits of the type II nodes; and at the moment, the type I node observes that the type II node adopts a cooperation strategy, and in order to maximize the benefit of the type I node, the defense strategy is abandoned and the cooperation strategy is adopted. Through the evolutionary game, the system will eventually converge to a stable state of the ESS. In this state, the type I node and the type II node both adopt a cooperation strategy and can obtain maximized benefits, and no matter one node or a plurality of nodes have no motivation to deviate from the maximized benefits. Therefore, the higher the cost of deploying the defense strategy by the type I node, the faster the system can reach the ESS, i.e., the better the system convergence.

The influence of the attack success rate on the system convergence is specifically explored as follows:

in order to study the influence of different attack success rates of II-type nodes on system convergence, simulation analysis is performed by changing the value of the attack success rate P parameter of the II-type nodes according to ESS stability analysis. C_DTake 0.46. When strategies 2 and C are adopted in the evolutionary game process_D>C_RWhen the success rates of type II node attacks of 1/3 are 0.1, 0.2, and 0.4, respectively, the influence of the attack success rate on the system convergence is shown in fig. 6, and it is clear from fig. 6 that C is the success rate of the attack_D>C_RIn time, under the condition of three different attack success rate games, the attack success rate of the type II node has influence on the system convergence. With the increase of the success rate of the attack, the speed of the type I node reaching the stable cooperation state is increased, the speed of the type II node reaching the stable cooperation state is unchanged, and the speed of the whole system reaching the ESS is increased, namely the convergence of the system is improved. The game process is analyzed in section 6.2.3, and finally, the type I node is "enableSelf-benefit maximization would forego defense strategies and instead take cooperative strategies. In case the defense cost is larger than the transaction cost, the higher the attack success rate, the faster the system reaches the ESS, i.e. the better the system convergence.

Based on the replication dynamic system modeled by the equations (20) to (25), a mixing strategy (X, Y) ((X) is given according to different experimental purposes₁,x₂,x₃),(y₁,y₂,y₃) X) is an initial value of₁，x₂，x₃，y₁，y₂，y₃Substituting and copying the dynamic system expression, wherein the game process is reflected on the simulation image as x₁，x₂，x₃，y₁，y₂，y₃The ratio Node ratio (%) of the policy selected by the respective corresponding Node, i.e., the image ordinate. And observing the game process according to the change of the strategy proportion, and analyzing the stability of the channel network dynamic evolution game model. When C is present_D<C_RMeanwhile, the game result of the dynamic evolution model of the system is a combined strategy (defense and cooperation).

System evolution stability analysis for judging whether defense strategy is adopted or not in initial state of I-type node

(1)C_DTake 0.3. When strategy 1 is selected for the evolutionary game, the channel network game process is shown in FIG. 7, and FIG. 7 is C_D<C_RAnd when the I-type nodes do not adopt the defense strategy, the model evolves to a steady state analysis diagram, as can be seen from fig. 7, when the I-type nodes in the channel network do not adopt the defense strategy, the II-type nodes select the attack strategy in order to maximize their own benefits, and after a period of game, the I-type nodes always select the cooperation strategy, and the II-type nodes further select the cooperation strategy through evolution learning to reduce their own loss, and the network finally converges to the state where both parties cooperate.

(2)C_DTake 0.3. When the strategy 2 is selected for the evolution game, the channel network game process is shown in figure 8, and figure 8 is C_D<C_RAnd when the I-type node part adopts the defense strategy, the model evolves a steady state analysis chart, which can be known from the chart 8, when there is part in the channel networkWhen the type I nodes take defense measures, the type II nodes evolve and learn for a period of time, the fact that the type I nodes take defense strategies is observed, cooperation strategies are selected for maximizing benefits of the type I nodes, and the network finally converges to a stable combination strategy of (defense and cooperation). Is described in C_D<C_RAnd meanwhile, whether the I-type node takes defense measures or not has influence on the game evolution strategy of the network replication dynamic system. In combination with the above analysis, whether it is C_D>C_ROr is C_D<C_RThe following conclusions can be drawn: whether the I-type node takes defense measures or not has influence on the game evolution strategy of the network replication dynamic system.

The influence of the initial proportion of the strategy on the convergence of the system is specifically explored as follows:

in order to research the influence of the initial proportion of the defense strategy and the cooperation strategy respectively deployed by the type I node and the type II node on the convergence of the system, the stability analysis of a theory 2 and a node channel network replication dynamic system is used for obtaining that the combination strategy (defense and cooperation) is an ESS of a model. On the basis, whether the two game parties can still maintain a stable state and influence on the model to reach the ESS speed is further considered for different initial proportions of the channel network type I node selection defense strategy and the type II node selection cooperation strategy. C_DTake 0.3. FIG. 9(a) is the effect of initial scale on model convergence when strategy 3 is used, FIG. 9(b) is the effect of initial scale on model convergence when strategy 6 is used, FIG. 9(c) is the effect of initial scale on model convergence when strategy 7 is used, and it can be seen from FIGS. 9(a) and 9(b) that system convergence is faster as the initial scale of the defense strategy is taken by the type I node is higher; as can be seen from fig. 9(b) and 9(c), the higher the initial proportion of the type II nodes that adopt the cooperation strategy, the faster the system converges. Based on the above analysis, it was found that either C or C is present_D>C_ROr is C_D<C_RThe following conclusions can be drawn: the convergence of the model is influenced by the initial proportion of the two game parties, and the higher the initial proportion is, the better the convergence of the model is.

deploying defenses for studying type I nodesThe influence of the cost of the strategy on the system convergence changes the C of the type I node deployment defense strategy according to the stability analysis of the ESS_DThe values of the parameters are used for simulation analysis. When C is present_D<C_RIn order to simplify the simulation graph, only the evolution process that the type I node adopts the defense strategy and the type II node adopts the cooperation strategy is displayed in the simulation graph. When strategies 2 and C are adopted in the evolutionary game process_D<C_RWhen the costs of the type I node deployment defense strategies of 1/3 are 0.1, 0.2 and 0.3, respectively, the influence of the costs on the system convergence is shown in fig. 10, and it can be seen from fig. 10 that when C is_D<C_RIn time, under three different defense cost game conditions, the cost of deploying the defense strategy by the nodes has an influence on the system convergence. With the increase of the defense cost, the speed of the type I node reaching the stable defense state is slightly reduced, the speed of the type II node reaching the stable cooperation state is reduced, and the speed of the system as a whole reaching the ESS is reduced, that is, the system convergence is reduced. Through the evolutionary game, the system converges to a stable state of the ESS. In this state, both type I nodes adopt a defense strategy, both type II nodes adopt a cooperation strategy, and both nodes can obtain maximized benefits, regardless of whether one or more nodes have no motivation to deviate from the maximized benefits. Therefore, the lower the cost of the type I node deployment strategy, the faster the system can reach the ESS, i.e., the better the system convergence.

Based on the above analysis, it was found that either C or C is present_D>C_ROr is C_D<C_RThe following conclusions can be drawn: under the condition of different defense cost games, the cost of deploying defense strategies by the type I nodes has influence on the convergence of the system.

in order to study the influence of different attack success rates of II-type nodes on system convergence, simulation analysis is performed by changing the value of the attack success rate P parameter of the II-type nodes according to ESS stability analysis. C_DTake 0.3. When strategies 2 and C are adopted in the evolutionary game process_D<C _R1/3 type II node attackThe effect of attack success rate on the system speed to ESS at power of 0.1, 0.2 and 0.4, respectively, is shown in FIG. 11, where it can be seen from FIG. 11 that when C is_D<C_RIn time, under the condition of three different attack success rate games, the attack success rate of the type II node has influence on the system convergence. With the increase of the success rate of the attack, the speed of the type I node reaching the stable cooperation state is reduced, the speed of the type II node reaching the stable cooperation state is unchanged, and the speed of the system reaching the ESS as a whole is reduced, that is, the convergence of the system is reduced. In case the defense cost is less than the transaction cost, the lower the attack success rate, the faster the system reaches the ESS, i.e. the better the system convergence.

Based on the above analysis, it was found that either C or C is present_D>C_ROr is C_D<C_RThe following conclusions can be drawn: under the game condition of three different attack success rates of the type II nodes, the attack success rate of the type II nodes has influence on the system convergence.

From theorem 1, when C is_D>C_RThe equalization point ((1,0,0), (1,0,0)) is an ESS of the channel network replication dynamic system. From theorem 2, when C is_D<C_RThe equalization point ((0,0,1), (1,0,0)) is an ESS of the channel network replication dynamic system. Based on these two ESS under different conditions, the stability and convergence analysis of the channel network is performed, and the conclusion is as follows:

1) and (3) stability analysis: after the channel network passes through an evolutionary game, the II type node with the attack behavior gives up the attack and adopts a cooperation strategy; and the type I node adopts a cooperation strategy (when C is_D>C_RWhen) or defense strategies (when C_D<C_RIn time), the channel network has better stability and convergence, and the network performance is improved. 2) Influence of initial ratio on system convergence: the initial proportion of each strategy (cooperation strategy or defense strategy) adopted by the node has an influence on the system convergence, i.e. the higher the initial proportion is, the better the system convergence is. 3) Cost impact on system convergence: when the cost required by the I-type node for deploying the defense strategy is larger than the cost required by the node for carrying out one-time forwarding transaction, the higher the cost for the node to adopt the defense strategy is, the higher the system convergence isGood; when the cost required by deploying the defense strategy by the type I node is less than the cost required by the node for carrying out one-time forwarding transaction, the lower the cost for adopting the defense strategy by the node is, the better the system convergence is. 4) Impact of attack success rate on system convergence: when the cost required by deploying the defense strategy by the I-type node is more than the cost required by carrying out one-time forwarding transaction by the node, the higher the attack success rate is, the higher the system convergence is; when the cost required by deploying the defense strategy by the I-type node is less than the cost required by the node to carry out one-time forwarding transaction, the lower the attack success rate is, the better the system convergence is.

Due to the randomness of the uncooperative behavior of the nodes in the real scene, the performance advantage of the channel network of the patent in the real scene, particularly in the case of the uncooperative behavior of the nodes, needs to be further verified. To this end, a simulation framework was developed to simulate Lightning networks and evolving game channel networks with defense strategies. The specific network configuration is as follows:

(1) network topology: generating a random undirected topological graph consisting of 1000 nodes; wherein, 100 II type nodes are randomly extracted from 1000 nodes, and the whole simulation time is 40000 seconds;

(2) routing protocol: the routing protocol mainly comprises 2 types: based on the maximum flow algorithm and based on the Landmark algorithm. Based on a maximum flow algorithm, requiring nodes to store a channel map of the whole network, and finding a feasible payment path of a target point by using a classic maximum flow algorithm, such as Push-Relay and the like; the Landmark-based algorithm mainly comprises a Flare scheme, a Landmark Routing scheme and the like. In the current 2-class schemes, the storage overhead and the running cost based on the maximum flow scheme are too high, and in the scheme based on the Landmark, although the node is not required to store the whole network graph, the success rate of the path searching depends on the mode and the size of the selected beacon point set, and whether the searched path is the optimal path or not cannot be ensured, and more importantly, a solution for bearing malicious behaviors is not provided. For each transaction request, a Flooding (Flooding) mechanism is adopted by using an Epidemic routing protocol, and the message is transmitted to the neighbor nodes as long as the opportunity exists, namely all the nodes transmit the message to all the neighbor nodes. The buffer area of the nodes in the model is set to be large enough, the Epidemic routing protocol can ensure the fairness of the node routing information in the dynamic evolution game model of the channel network, the probability of each node being selected is high, the influence of the nodes with low utilization rate on the network performance is reduced, and the experimental analysis is as follows.

(1) Transaction success rate (abbreviated as T)_R)

The transaction average transmission success rate is the number of transaction messages successfully sent to the target node and the total number of transaction messages: t is_R＝R_M/T_MWherein R is_MNumber of transaction messages successfully sent to target node, T_MIs the total transaction message quantity.

Fig. 12 shows the influence of the uncooperative behavior of the node on the transaction success rate, and fig. 12 reflects the influence of the uncooperative behavior of the node on the transaction average transmission rate under different channel network configurations when the policy 2 and the attack success rate P are 0.5. In Lightning networks, the uncooperative behavior causes the trade mean transmission success rate to decrease due to the presence of type II nodes in the network and the lack of security measures in the network. For the evolutionary game channel network with a defense strategy, the I-type node can resist different attack behaviors at a certain probability, so that the network reaches a stable cooperation state, and the average transaction transmission rate in the network is increased.

(2) Average message transmission delay (abbreviated as T)_D)

T_DThe average time from the generation of the transaction request message for the root node (transaction requester) to the reception of the message by the target node, i.e. the difference between the transaction completion time and the transaction initiation time: t is_D＝T_C-T_SWherein, T_CFor transaction completion time, T_SIs the transaction start time. Fig. 13 shows the influence of the uncooperative behavior of the node on the average message transmission delay, and fig. 13 reflects the influence of the uncooperative behavior of the node on the average transaction transmission delay under different channel network configurations when the policy 2 and the attack success rate P are 0.5. In a channel network, there will always be transactions including type II nodes, in which case the routing of the transactions will result in longer transactionsDelaying; for the evolutionary game channel network with the defense strategy, the network can reach a stable cooperation state through a defense mechanism and an evolutionary game process, and therefore the influence of uncooperative nodes on transaction time delay is relieved.

The invention has been described above with reference to the accompanying drawings, it is obvious that the invention is not limited to the specific implementation in the above-described manner, and it is within the scope of the invention to apply the inventive concept and solution to other applications without substantial modification.

Claims

1. A steady state evolution game method of a channel network under a block chain is characterized by comprising the following steps:

s3, carrying out an evolutionary game based on the network replication dynamic model, and outputting a balance point corresponding to the stable state of the evolutionary game, namely an ESS;

s4, the nodes in the channel network reselect the strategy according to the combination strategy corresponding to the equilibrium point, namely the strategy adopted by the nodes in the channel network for the transaction T is determined;

the combination strategy ((1,0,0), (1,0,0)) represents that both type I and type II nodes will adopt a cooperative strategy to process the transaction T; the combination policy ((0,0,1), (1,0,0)) represents that type I nodes will adopt a defense policy, type II nodes will adopt a cooperation policy to process transaction T;

the network replication dynamic model comprises: the replication dynamic equation of the type I node and the replication dynamic equation of the type II node,

the expected yield of the type I node selection strategy I is:

the average benefit of the type I node population is as follows:

the replication dynamic equation for type I nodes is:

the expected yield of the type II node selection strategy j is:

the average benefit of the type II node population is as follows:

the replication dynamic equation for type II nodes is:

wherein, a_ijFor the matrix element in the income matrix A of the type I node, the I node adopting the I strategy is representedThe income obtained by the type I node when the type II node of the j strategy is taken to carry out game, b_ijIs a matrix element in the income matrix B of the type II node and represents the income obtained by the type II node when the type I node adopting the strategy I plays games with the type II node adopting the strategy j, x_iRepresents the proportion of the type I node selection strategy I, y_jRepresents the proportion of type II node selection strategy j, S₁Representing the policy space of type I nodes, S₂Representing a policy space for type II nodes;

the revenue matrix A for type I nodes and the revenue matrix B for type II nodes are represented as follows:

2. The method for steady-state evolution gaming of the channel network under the blockchain as claimed in claim 1, wherein the replication dynamic equation of the type I node comprises: x is the number of₁，x₂，x₃The replication dynamics equation for the type II node comprises: y is₁，y₂，y₃Respectively, as follows:

representing the rate of change of participant proportion with time when the type I node adopts a strategy I, I belongs to S₁，S₁∈{1,2,3}，

Representing the change rate of participant proportion with time when the II type node adopts a strategy j, j belongs to S₂，S₂∈{1,2,3}，x₁，x₂，x₃Respectively representing the proportion of cooperation, non-cooperation and defense strategies adopted by the type I node; y is₁，y₂，y₃Respectively representing the proportion of cooperation, attack and non-operation strategies adopted by the class II nodes;

r represents the profit obtained by the two parties in a game, C_DIndicating the need for a type I node to adopt a defensive strategyCost, R_ARepresents the gain obtained by successful attack activity of the type II node, C_ARepresents the cost of a type II node for an attack activity, C_RThe cost required by the node for one transaction is shown, L shows the loss of the I-type node when the I-type node is attacked, and P shows the success rate of attack success of an attack party under the condition that the I-type node adopts a defense strategy.