CN109919791A - Method and system for analyzing cooperation level in prisoner predicament network game based on betweenness - Google Patents
Method and system for analyzing cooperation level in prisoner predicament network game based on betweenness Download PDFInfo
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Abstract
A method and a system for analyzing cooperation level in prisoner trapping situation network game based on betweenness are provided. The method comprises the steps of calculating the strategy diffusion probability q corresponding to each node by calculating the profit after each node and a neighbor node in the network are played in the whole evolutionary game process by utilizing the betweenness of all nodes in the network, determining the strategy adopted by each node in the next step according to the probability, updating the strategy, further forming a state matrix of the whole network, and finally determining the partner proportion in a stable state. And obtaining the cooperation level in the prisoner predicament network game. Because the betweenness is introduced in the calculation process, the specific characteristics of the network can be converted into the calculable parameters, the method has calculability, and can reflect the influence of the specific characteristics of the network on the game process more accurately. The calculation result of the method is more accurate, and the method can be more fit with the actual network to reflect the cooperation level in the prisoner predicament network game.
Description
Technical field
The present invention relates to complex network and network games, analyze prisoner net based on betweenness in particular to one kind
The method and system of cooperative level in network game.
Background technique
Complex network is a kind of network model for being used to analyze for being abstracted system in the real world and obtaining.Its
To be able to be by being abstracted to systems such as social relation network in the real world, power network, bio-networks, transportation networks
Independent individual is abstracted as the node in complex network in system, and the relationship in system between Different Individual is abstracted as in complex network
Corresponding complex network model is constructed on side between node, to analyze system performance.
Cooperative level is to study a key factor of evolutionary Game on complex network.In prisoner research, wherein
One level is exactly the cooperation behavior found between nodes is that how to occur and consolidate maintenance.
In response to this problem, in existing much researchs, the phase of Evolutionary Game and manifold structure has all been laid stress on
In interaction, for example prisoner is introduced into space structure, observes the variation of cooperative level.But in existing research simultaneously
Not the concrete property of network in view of during entire evolutionary Game.Existing research can not obtain the concrete property pair of network
The influence of cooperative level in prisoner network game.
Summary of the invention
It is analyzed in the game of prisoner network in view of the deficiencies of the prior art, the present invention provides one kind based on betweenness and cooperates water
The concrete property of network is introduced entire evolutionary Game process by the betweenness of nodes by flat method and system, the present invention
In, so as to obtain influence of the concrete property of network to cooperative level in prisoner network game.The present invention specifically adopts
With following technical solution.
Firstly, to achieve the above object, proposing a kind of method for analyzing cooperative level in the game of prisoner network, packet
Include: the first step determines number N >=2 of network model and network model interior joint, constructs complex network, in the complex network
Node be expressed as zx, N >=x >=2；Prisoners' dilemma game model is constructed, gain matrix therein, which is arranged, is
Each node includes two kinds of strategies of betrayal and cooperation, is expressed as node wherein betrayingCooperation is expressed as nodeB indicates that it betrays bring income for the node of cooperation；Second step calculates each node zxReceipts
BenefitWherein, zyIndicate node zxA neighbor node, Ω x indicate node zxWhole neighbours section
Set composed by point；Remember node zxNeighbor node in possessed maximum value be PY；Third step calculates each section
Point zxCorresponding betweenness Bx；4th step calculates each node zxCorresponding tactful diffusivity is the leading factorWherein, α indicates Dynamic gene, and the value range of α is [- 3,3]；5th step calculates each node zx
Corresponding tactful spreading probabilityWherein, k indicates the noise factor of broad sense, is decimal；The
Six steps, to each node zxPolicy update is carried out according to the tactful spreading probability q corresponding to it respectively, with each node z of determinationx
Corresponding next step strategy；7th step, according to node z each in the complex networkxCorresponding strategy generating state matrix；
8th step repeats the above-mentioned first step to the 7th step, until each node zxCorresponding strategy tends towards stability；It obtains under stable state
Each node z in complex networkxIt is middle that c is denoted as using the ratio of cooperation policy；9th step changes the gain matrixIn for the node of cooperation its betray bring income b, repeat above-mentioned second step to the 8th step, obtain b
The corresponding ratio c using cooperation policy when taking different value；Tenth step, respectively to betray bring income b and using cooperation
The ratio c of strategy establishes b-c figure as two reference axis, obtains the cooperative level in the game of prisoner network.
Optionally, in above-mentioned method, in the first step, the initial policy of each node is determined by following steps: step
A1, the initial value for obtaining partner's ratio in the complex network is C；Step a2 is randomly choosed wherein in whole nodes
'sIts initial policy is arranged as cooperation in a node, is somebody's turn to doA nodeThe initial policy of remaining node is set
It, should to betrayA node
Optionally, in above-mentioned method, in the third step, the node zxCorresponding betweenness BxFor the complex network
In shortest path pass through node zxQuantity.
Optionally, in above-mentioned method, the noise factor k of the broad sense takes 0.1.
Optionally, in above-mentioned method, the 6th step specifically: step 601, the node zxIt is corresponding generate one with
Machine number, the random number are uniformly distributed between [0,1]；Step 602, by the random number and node zxCorresponding strategy diffusion
Probability q compares size；By node z if being no more than qxIt is updated to opposite strategy；Otherwise, node z is keptxStrategy not
Become；Step 603, to each node zxAbove-mentioned steps 601 are carried out to step 602, until determining all each node zxCorresponding
Strategy in next step.
Optionally, in above-mentioned method, in the 8th step, the above-mentioned first step is repeated to the 7th step 1000 times so that each
Node zxCorresponding strategy tends towards stability.
Meanwhile to achieve the above object, the present invention also provides cooperative levels in a kind of analysis prisoner network game
System, comprising: original state module, for determining number N >=2 of network model and network model interior joint, building is complicated
Network, the node in the complex network are expressed as zx, N >=x >=2；Prisoners' dilemma game model is constructed, income square therein is set
Battle array beEach node includes two kinds of strategies of betrayal and cooperation, is expressed as node wherein betraying
Cooperation is expressed as nodeB indicates that it betrays bring income for the node of cooperation.Calculative strategy updates general
Rate module calculates each node z according to the gain matrix A firstxIncome Px, then calculate each node zxInstitute
Corresponding betweenness Bx, to obtain each node zxCorresponding tactful diffusivity is denoted as leading factor θx, and then according to institute
State leading factor θx, node zxNeighbor node in possessed maximum value be PYObtain each node zxCorresponding
Tactful spreading probability Wherein, k indicates the noise factor of broad sense, takes 0.1.It determines one under node
Policy module is walked, for each node zxPolicy update is carried out according to the tactful spreading probability q corresponding to it respectively, with true
Fixed each node zxCorresponding next step strategy, then according to node z each in the complex networkxCorresponding strategy generating shape
State matrix repeats the above steps to each node zxAt least 1000 policy updates are carried out to obtain complex web under stable state
Each node z in networkxUsing the ratio of cooperation policy, it is denoted as c.Output module, for changing being betrayed in above-mentioned original state module
Bring income b obtains the corresponding ratio c using cooperation policy when b takes different value by above-mentioned calculating process, respectively
To betray bring income b and establish b-c figure as two reference axis using the ratio c of cooperation policy, prisoner network is exported
The schematic diagram of cooperative level in game.
Optionally, in above-mentioned system, each node zxIncome Wherein, zyTable
Show node zxA neighbor node, Ω x indicate node zxWhole neighbor nodes composed by set.
Optionally, in above-mentioned system, each node zxCorresponding betweenness BxIt is most short in the complex network
Node z is passed through in pathxQuantity.
Optionally, in above-mentioned system, each node zxCorresponding tactful diffusivity is the leading factorWherein, α indicates Dynamic gene, and the value range of α is [- 3,3].
Beneficial effect
The concrete property of network is considered the mistake of entire evolutionary Game using the betweenness of all nodes in network by the present invention
Cheng Zhong calculates plan corresponding to each node by calculating each node and the income size after neighbor node game in network
Slightly spreading probability q carries out policy update according to the strategy that each node of the determine the probability is taken in next step, and then is formed entire
The state matrix of network, the final partner's ratio determined under stable state.Obtain the cooperation water in the game of prisoner network
It is flat.Since the present invention introduces betweenness in calculating process, the concrete property of network can be converted to computable parameter, had
Have a computability, and can be more accurate reaction network influence of the concrete property to gambling process.Calculating of the invention
As a result more accurate, it is also better able to fitting real network and reacts cooperative level in its prisoner network game.
Other features and advantages of the present invention will be illustrated in the following description, also, partly becomes from specification
It obtains it is clear that understand through the implementation of the invention.
Detailed description of the invention
Attached drawing is used to provide further understanding of the present invention, and constitutes part of specification, and with it is of the invention
Embodiment together, is used to explain the present invention, and is not construed as limiting the invention.In the accompanying drawings:
Fig. 1 is the process signal of the invention based on the method for cooperative level in betweenness analysis prisoner network game
Figure；
Fig. 2 is the specific steps schematic diagram that original state is determined in the above method；
Fig. 3 is the full mistake calculated in the system of the invention based on cooperative level in betweenness analysis prisoner network game
The schematic diagram of journey.
Specific embodiment
To keep purpose and the technical solution of the embodiment of the present invention clearer, below in conjunction with the attached of the embodiment of the present invention
Figure, is clearly and completely described the technical solution of the embodiment of the present invention.Obviously, described embodiment is of the invention
A part of the embodiment, instead of all the embodiments.Based on described the embodiment of the present invention, those of ordinary skill in the art
Every other embodiment obtained, shall fall within the protection scope of the present invention under the premise of being not necessarily to creative work.
Those skilled in the art of the present technique are appreciated that unless otherwise defined, all terms used herein (including technology art
Language and scientific term) there is meaning identical with the general understanding of those of ordinary skill in fields of the present invention.Should also
Understand, those terms such as defined in the general dictionary, which should be understood that, to be had and the meaning in the context of the prior art
The consistent meaning of justice, and unless defined as here, it will not be explained in an idealized or overly formal meaning.
Fig. 1 is a kind of method for analyzing cooperative level in the game of prisoner network based on betweenness according to the present invention.It 3
A key step can be realized by following several modules: original state module, determines node at calculative strategy update probability module
Next step policy module:
With reference to Fig. 2, above-mentioned original state module determines original state especially by following step: 204, pass through selection net
Network type determines that network node number constructs network, and 203 by selecting prisoner model to determine earnings pattern, and 202 by true
Determine partner's scale, determines node initial policy state.Specifically, its step comprises determining that network model and net
Number N >=2 of network model interior joint, construct complex network, and the node in the complex network is expressed as zx, N >=x >=2；Construct prisoner
Empty predicament betting model, gain matrix therein, which is arranged, is Each node includes two kinds of plans of betrayal and cooperation
Slightly, node is expressed as wherein betrayingCooperation is expressed as nodeB is indicated for the node of cooperation
It betrays bring income.In gain matrix A, we use the simplified model of prisoners' dilemma game, select R=1, P=S=0,
T=b (1≤b≤2), b represents the benefit betrayed for partner here.Wherein, by selecting network type, net is determined
Network node number constructs the step of network, and by taking the network of communication lines of Beijing is network model as an example, intersection number therein is pair
It should be node number.
The calculative strategy update probability module.The income for calculating all nodes passes through Income Maximum in selection neighbours
Person is compared, calculate node strategy diffusivity, uses for reference Fermi's formula, finally obtains policy update rule, i.e., corresponding plan
Slightly spreading probability q.Specifically, it calculates each node z according to the gain matrix A firstxIncome Px, then calculate
Each node zxCorresponding betweenness Bx, to obtain each node zxCorresponding tactful diffusivity be denoted as it is leading because
Sub- θx, and then according to the leading factor θx, node zxNeighbor node in possessed maximum value be PYObtain each
Node zxCorresponding tactful spreading probabilityWherein, k indicates the noise factor of broad sense, takes
0.1。
The determination node next step policy module determines node strategy in next step, is generated at random by being uniformly distributed
Number small determines whether to update with determining that numerical value is bigger.Specifically, it is to each node zxRespectively according to corresponding to it
Tactful spreading probability q carries out policy update, with each node z of determinationxCorresponding next step strategy, then according to the complex web
Each node z in networkxCorresponding strategy generating state matrix repeats the above steps to each node zxIt carries out at least 1000 times
Policy update is to obtain under stable state each node z in complex networkxUsing the ratio of cooperation policy, it is denoted as c.
It is exported after the above process by output module: during output, being changed in above-mentioned original state module first
Bring income b is betrayed, the corresponding ratio c using cooperation policy when b takes different value is obtained, respectively to betray bring receipts
The beneficial b and ratio c of use cooperation policy establishes b-c figure as two reference axis, exports the cooperation water in the game of prisoner network
Flat schematic diagram.
Above-mentioned modules have supporting relation step by step, determine that original state module 104 is calculative strategy update probability
Provide the foundation data, and policy update probability 103 is to determine that strategy 102 provides foundation to node in next step.
The complete calculating process of each module of above system is shown in Fig. 3.Include:
301, it determines number N >=2 of network model and network model interior joint, constructs complex network, the complex network
In node be expressed as zx, N >=x >=2；Prisoners' dilemma game model is constructed, gain matrix therein, which is arranged, isEach node includes two kinds of strategies of betrayal and cooperation, is expressed as node wherein betrayingCooperation
It is expressed as node B indicates that it betrays bring income for the node of cooperation；
302, calculate each node zxIncomeWherein, zyIndicate node zxA neighbour
Node is occupied, Ω x indicates node zxWhole neighbor nodes composed by set；
303, remember node zxNeighbor node in possessed maximum value be PY；
304, calculate each node zxCorresponding betweenness Bx；
305, calculate each node zxCorresponding tactful diffusivity is the leading factor Wherein,
α indicates Dynamic gene, and the value range of α is [- 3,3]；
306, calculate each node zxCorresponding tactful spreading probability Wherein, k table
Show the noise factor of broad sense, is decimal；
307, to each node zxPolicy update is carried out according to the tactful spreading probability q corresponding to it respectively, with determination
Each node zxCorresponding next step strategy；
308, according to node z each in the complex networkxCorresponding strategy generating state matrix；The strategy of each node
After determination, the facility strategy of whole network is state matrix；
309, the above-mentioned first step is repeated to the 7th step, until each node zxCorresponding strategy tends towards stability；Stablized
Each node z in complex network under statexIt is middle that c is denoted as using the ratio of cooperation policy；
310, change the gain matrixIn for the node of cooperation its betray bring income b,
Above-mentioned second step is repeated to the 8th step, obtains the corresponding ratio c using cooperation policy when b takes different value；
Finally, respectively to betray bring income b and establish b-c figure as two reference axis using the ratio c of cooperation policy,
Obtain the cooperative level in the game of prisoner network.Wherein, c represents the ratio of partner, i.e. the number of partner is more total than upper
Node number, the strategy of node is cooperation or betrays that b variation causes c to change.
Wherein, described 301 the step of in, the initial policy of each node is determined by following steps:
Step a1, the initial value for obtaining partner's ratio in the complex network is C；
Step a2 is randomly choosed therein in whole nodesIts initial policy is arranged as cooperation in a node, is somebody's turn to doA nodeThe initial policy of remaining node is set to betray, is somebody's turn to doA node
Wherein 304 the step of in, the node zxCorresponding betweenness BxIt is the shortest path in the complex network by being somebody's turn to do
Node zxQuantity.Shortest path in complex network can by existing algorithm, such as dijkstra's algorithm, Floyd algorithm,
It is obtained according to network structure feature calculation.
The noise factor k of the broad sense takes 0.1.
Described 307 the step of specifically:
Step 601, the node zxCorresponding to generate a random number, which is uniformly distributed between [0,1]；
Step 602, by the random number and node zxCorresponding tactful spreading probability q compares size；If being no more than q
By node zxIt is updated to opposite strategy；Otherwise, node z is keptxStrategy it is constant；
Step 603, to each node zxAbove-mentioned steps 601 are carried out to step 602, until determining all each node zxInstitute
Corresponding next step strategy.
In above-mentioned 309 the step of, the above-mentioned first step is repeated to the 7th step 1000 times so that each node zxCorresponding plan
Slightly tend towards stability.
The present invention does not examine the concrete property of network to improve the analysis method of existing network cooperation level as a result,
Consider the problems in policy propagation ability, proposes a kind of tactful diffusivity based on betweenness and prisoner network game is closed
Make horizontal analysis method, by calculating the sum of the income of each node and all neighbours' games in network, calculates each node
Income, by compared with the income of Income Maximum neighbours, calculate facility strategy diffusion probability size, determine each node
The strategy taken in next step, and then the state matrix formed, the final partner's ratio determined under stable state, analyze network
Cooperative level.It has the advantage that
(1) using the betweenness of nodes as data basis, there is computability, it can be straight by the concrete property of network
Tape splicing enters to be calculated；
(2) using prisoner classics betting model as model basis, gambling process is simplified, by income corresponding to game
Matrix A is set as R=1, P=S=0, T=b (1≤b≤2)；Game calculates more easy.
(3) cooperative level is indicated with partner's scale in final network, the relationship by exporting two-dimensional coordinate is shown
It is intended to, the present invention more can intuitively embody the cooperative level of network with data.
(4) betweenness for having fully considered all nodes in network, more accurately represents the characteristic of network.
The above is only embodiments of the present invention, and the description thereof is more specific and detailed, and but it cannot be understood as right
The limitation of the invention patent range.It should be pointed out that for those of ordinary skill in the art, not departing from the present invention
Under the premise of design, various modifications and improvements can be made, these are all belonged to the scope of protection of the present invention.
Claims (10)
1. a kind of method of cooperative level in analysis prisoner network game characterized by comprising
The first step, determines number N >=2 of network model and network model interior joint, constructs complex network, in the complex network
Node be expressed as zx, N >=x >=2；Prisoners' dilemma game model is constructed, gain matrix therein, which is arranged, is
Each node includes two kinds of strategies of betrayal and cooperation, is expressed as node wherein betrayingCooperation is expressed as nodeB indicates that it betrays bring income for the node of cooperation；
Second step calculates each node zxIncomeWherein, zyIndicate node zxA neighbours
Node, Ω x indicate node zxWhole neighbor nodes composed by set；Remember node zxNeighbor node in possessed maximum
Income be PY；
Third step calculates each node zxCorresponding betweenness Bx；
4th step calculates each node zxCorresponding tactful diffusivity is the leading factorWherein,
α indicates Dynamic gene, and the value range of α is [- 3,3]；
5th step calculates each node zxCorresponding tactful spreading probability Wherein, k table
Show the noise factor of broad sense, is decimal；
6th step, to each node zxPolicy update is carried out according to the tactful spreading probability q corresponding to it respectively, it is each to determine
Node zxCorresponding next step strategy；
7th step, according to node z each in the complex networkxCorresponding strategy generating state matrix；
8th step repeats the above-mentioned first step to the 7th step, until each node zxCorresponding strategy tends towards stability；It obtains and stablizes shape
Each node z in complex network under statexIt is middle that c is denoted as using the ratio of cooperation policy；
9th step changes the gain matrixIn for the node of cooperation its betray bring income b,
Above-mentioned second step is repeated to the 8th step, obtains the corresponding ratio c using cooperation policy when b takes different value；
Tenth step obtains respectively to betray bring income b and establish b-c figure as two reference axis using the ratio c of cooperation policy
Obtain the cooperative level in the game of prisoner network.
2. as described in claim 1 in analysis prisoner network game cooperative level method, which is characterized in that described the
In one step, the initial policy of each node is determined by following steps:
Step a1, the initial value for obtaining partner's ratio in the complex network is C；
Step a2 is randomly choosed therein in whole nodesIts initial policy is arranged as cooperation in a node, is somebody's turn to doIt is a
NodeThe initial policy of remaining node is set to betray, is somebody's turn to doA node
3. the method for cooperative level in the analysis prisoner network game as described in claim 1-2, which is characterized in that institute
It states in third step, the node zxCorresponding betweenness BxPass through node z for the shortest path in the complex networkxQuantity.
4. the method for cooperative level in the analysis prisoner network game as described in claim 1-3, which is characterized in that institute
The noise factor k for stating broad sense takes 0.1.
5. the method for cooperative level in the analysis prisoner network game as described in claim 1-3, which is characterized in that institute
State the 6th step specifically:
Step 601, the node zxCorresponding to generate a random number, which is uniformly distributed between [0,1]；
Step 602, by the random number and node zxCorresponding tactful spreading probability q compares size；It should if being no more than q
Node zxIt is updated to opposite strategy；Otherwise, node z is keptxStrategy it is constant；
Step 603, to each node zxAbove-mentioned steps 601 are carried out to step 602, until determining all each node zxIt is corresponding
Next step strategy.
6. the method for cooperative level in analysis prisoner network game as claimed in claims 1-5, which is characterized in that described
In 8th step, the above-mentioned first step is repeated to the 7th step 1000 times so that each node zxCorresponding strategy tends towards stability.
7. the system of cooperative level in a kind of analysis prisoner network game characterized by comprising
Original state module constructs complex network, is somebody's turn to do for determining number N >=2 of network model and network model interior joint
Node in complex network is expressed as zx, N >=x >=2；Prisoners' dilemma game model is constructed, gain matrix therein, which is arranged, isEach node includes two kinds of strategies of betrayal and cooperation, is expressed as node wherein betrayingCooperation
It is expressed as nodeB indicates that it betrays bring income for the node of cooperation；
Calculative strategy update probability module calculates each node z according to the gain matrix A firstxIncome Px, then
Calculate each node zxCorresponding betweenness Bx, to obtain each node zxBefore corresponding tactful diffusivity is denoted as
Lead factor θx, and then according to the leading factor θx, node zxNeighbor node in possessed maximum value be PYIt obtains every
One node zxCorresponding tactful spreading probability Wherein, k indicates the noise factor of broad sense,
Take 0.1；
Node next step policy module is determined, for each node zxRespectively according to the tactful spreading probability q corresponding to it into
Row policy update, with each node z of determinationxCorresponding next step strategy, then according to node z each in the complex networkxInstitute is right
The strategy generating state matrix answered repeats the above steps to each node zxIt is steady to obtain to carry out at least 1000 policy updates
Determine under state each node z in complex networkxUsing the ratio of cooperation policy, it is denoted as c；
Output module obtains corresponding when b takes different value for changing bring income b is betrayed in above-mentioned original state module
The ratio c using cooperation policy, respectively using betray bring income b and using cooperation policy ratio c as two reference axis
B-c figure is established, the schematic diagram of the cooperative level in the game of prisoner network is exported.
8. analyzing the system of cooperative level in the game of prisoner network as claimed in claim 7, which is characterized in that described every
One node zxIncomeWherein, zyIndicate node zxA neighbor node, Ω x indicate node
zxWhole neighbor nodes composed by set.
9. the system of cooperative level in the analysis prisoner network game as described in claim 7-8, which is characterized in that described
Each node zxCorresponding betweenness BxPass through node z for the shortest path in the complex networkxQuantity.
10. the system of cooperative level in the analysis prisoner network game as described in claim 7-9, which is characterized in that institute
State each node zxCorresponding tactful diffusivity is the leading factorWherein, α indicate adjustment because
Son, the value range of α are [- 3,3].
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| CN114257507A (en) * | 2021-12-22 | 2022-03-29 | 中国人民解放军国防科技大学 | Method for improving network information sharing level based on evolutionary game theory |
| CN114257507B (en) * | 2021-12-22 | 2024-02-13 | 中国人民解放军国防科技大学 | Method for improving network information sharing level based on evolution game theory |
| CN114826917A (en) * | 2022-04-25 | 2022-07-29 | 中国农业银行股份有限公司 | Game-based network resource allocation method and device |
| CN114826917B (en) * | 2022-04-25 | 2023-12-08 | 中国农业银行股份有限公司 | Game-based network resource allocation method and device |
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