CN106953879A - The cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model - Google Patents
The cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model Download PDFInfo
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Abstract
The invention belongs to computer network security defense technique field, being specifically related to a kind of cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model includes：Based on bounded rationality condition, using best response dynamics study mechanism, the attacking and defending Evolutionary Game Model based on best response dynamics is built；Dynamic Evolution and defence Evolutionary Equilibrium point are chosen using defender's strategy, defence policies On The Choice between different defenders is studied；On the basis of the best response dynamics Evolutionary Game Model of foundation, the model is analyzed and solved by specific example, promote Evolutionary Game Model.The present invention establishes the non-cooperative network attacking and defending Evolutionary Game Model under the conditions of bounded rationality, original state is chosen by arranging defender's strategy, by constantly evolution, best response dynamics will eventually make game playing system reach some stable state, so as to obtain optimal defence policies, method proposed by the present invention can be good at being applied to network security defence policies On The Choice, can provide network security research certain directive significance.
Description
Technical field
The invention belongs to computer network security defense technique field, a kind of best response dynamics evolution is specifically related to rich
Play chess the cyber-defence strategy choosing method of model.
Background technology
In recent years, the social life that the fast development of internet gives people brings huge change, particularly " internet
+ " strategy push the development of internet to a new climax.With the fast development of internet, cyberspace safety problem
Become increasingly conspicuous.Network security problem is very severe, and for local and overseas disparate networks attacks, how Strengthens network is pacified
The problem of full defence turns into current era urgent need to resolve, needing badly can be analyzed and be predicted to network-combination yarn behavior, Jin Ershi
Alms giver moves the new technology of Prevention-Security.Because network safe state is determined by the agonistic behavior and its result of attacking and defending both sides in itself
It is fixed, and target antagonism, tactful interdependence and the relation Non-synergic exactly game theory having in network-combination yarn confrontation
Essential characteristic, therefore game theory increasingly rises in the research and application of network safety filed, and with using classical traditional game
Based on model is analyzed network security behavior.
But, existing achievement in research sets up what is assumed in participant's rational mostly based on traditional game is theoretical
Under the premise of, and such hypothesis is not consistent with actual conditions.Its betting model and real deviation are larger, so as to reduce safety
The accuracy and directive significance of defence policies choosing method.For problem above, some scholars are used premised on bounded rationality
Evolutionary game theory is analyzed applied to network-combination yarn.By analysis, evolutionary Game more conforms to network-combination yarn confrontation dynamic evolution
Reality, turns to the gradual evolution process with certain adaptability learning ability, using typical by the behavior model of attacking and defending both sides
Replicator dynamics equation is solved and analyzed.But it is low that replica locating study mechanism has that pace of learning is slow, strategy chooses efficiency
Problem.
The content of the invention
The present invention mostly based on traditional game is theoretical, sets up false in participant's rational for existing achievement in research
If on the premise of, and such hypothesis is not consistent with actual conditions, is drilled if existing and being directly applied to network-combination yarn confrontation
Change game theory analysis, it will have that learning cycle is long, learning efficiency is not high, this is suitable by largely reduction model and method
With sex chromosome mosaicism, a kind of cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model is proposed.
The technical scheme is that：A kind of cyber-defence strategy selection side of best response dynamics Evolutionary Game Model
Method, comprises the following steps：
Step 1：Based on bounded rationality condition, using best response dynamics study mechanism, build and be based on best response dynamics
Attacking and defending Evolutionary Game Model；
Step 2：Dynamic Evolution and defence Evolutionary Equilibrium point are chosen using defender's strategy, between different defenders
Defence policies On The Choice is studied；
Step 3：On the basis of the best response dynamics Evolutionary Game Model of foundation, the model is entered by specific example
Row analysis promotes Evolutionary Game Model with solving.
It is optimal in the cyber-defence strategy choosing method of described best response dynamics Evolutionary Game Model, the step 1
Reaction dynamic evolution betting model is represented by four-tuple, BRDEGM=(D, DS, P, U)
D={ d1,d2,…dnDefence participant space is represented, wherein, diRepresent defender i, different defender can be with
Choose different defence policies；
DS={ DS1,DS2,…DSmDefender's policy space is represented, different defenders enjoy the defence policies jointly
Collection；
P={ p1,p2,…pmDefender's conviction set is represented, wherein, piRepresent that defender chooses defence policies DSiIt is general
Rate；
U={ U1,U2,…UmRevenue function set is represented, wherein, UiRepresent that defender chooses defence policies DSiIt is acquired
Income.
The cyber-defence strategy choosing method of described best response dynamics Evolutionary Game Model, the best response dynamics
Equation isWherein NtRepresent Selection Strategy DS in n defender1Number, DS1It is optional
Any one defence policies in set of strategies.
Defendd in the cyber-defence strategy choosing method of described best response dynamics Evolutionary Game Model, the step 2
Strategy slightly chooses Dynamic Evolution：There is a kind of competition in network-combination yarn antagonistic process, between different defence policies to close
System, the defence policies of high yield will eliminate the relatively low strategy of income.
The cyber-defence strategy choosing method of described best response dynamics Evolutionary Game Model, the defence of the high yield
Strategy will be eliminated in the relatively low strategy of income, and gain matrix is：Wherein, u1、u2Point
Wei not strategy DS1、DS2Income, a is u1、u2Difference.
Promoted in the cyber-defence strategy choosing method of described best response dynamics Evolutionary Game Model, the step 3
Evolutionary Game Model is mainly, when defender has any n defender, based on best response dynamics Evolutionary Game Model,
To any two defence policies DSiAnd DSjCarry out evolutionary Game Analysis, it is assumed that DSiIt is relative to DSjDominating stragegy, and i ≠
J, over time, finally gives certain Evolution.
The cyber-defence strategy choosing method of described best response dynamics Evolutionary Game Model, the Evolution is：
For there is the defender of n defender, when all defenders choose defence policies DS in first gameiOr strategy DSj
When, using best response dynamics study mechanism, it is then institute that the strategy of whole network defender, which chooses the stable state being finally reached,
Some equal Selection Strategy DS of defenderiOr strategy DSj。
The cyber-defence strategy choosing method of described best response dynamics Evolutionary Game Model, the Evolution is：
For there is the defender of n defender, when n is odd number, in first game, as long as there is a defender to have chosen strategy
DSi, institute finally can all be converged on by the adjustment repeatedly in multiple periods to itself strategy by best response dynamics study mechanism
There is defender's Selection Strategy DSiStable state.
The cyber-defence strategy choosing method of described best response dynamics Evolutionary Game Model, the Evolution is：
For there is the defender of n defender, when n is even number, in first game, there is a defender to have chosen defence policies
DSi, the equal Selection Strategy DS of other defendersj, then, best response dynamics can not make all defenders converge on some stable shape
State, evolution over time, adjustment of each defender to strategy can only be absorbed in loop cycle and change.
The cyber-defence strategy choosing method of described best response dynamics Evolutionary Game Model, the Evolution is：
For there is the defender of n defender, in first game, strategy is have chosen simultaneously simply by the presence of two adjacent defenders
DSi, under best response dynamics study mechanism, evolution over time eventually converges on all defenders and all chooses plan
Slightly DSiStable state.
The beneficial effects of the invention are as follows：The present invention establishes the non-cooperative network attacking and defending evolutionary Game under the conditions of bounded rationality
Model, and computable general equilibrium has been carried out with solving to the model.On this basis, from defender's angle, for different defence
Policy learning adjustment process between person, using best response dynamics study mechanism, establishes the multistage weight between defender
Double action state Evolutionary Game Model, is studied defence policies On The Choice between different defenders.In the optimal anti-of foundation
Answer on the basis of dynamic evolution betting model, the model is analyzed and solved by specific example, and the model is made
Further genralrlization, improves the versatility of model.Chosen just for the difference of defender's number parity, and defender's strategy
The difference of beginning state, can all influence the final evolution result of whole game playing system.Initial shape is chosen by arranging defender's strategy
State, by constantly evolution, best response dynamics will eventually make game playing system reach some stable state, so as to obtain optimal anti-
Imperial strategy.Illustrate that method proposed by the present invention can be good at being applied to network security defence policies On The Choice, network is pacified
Full research can provide certain directive significance.
Brief description of the drawings
Fig. 1 method of the present invention step schematic block diagrams；
Fig. 2 cyber-defence person's game theory schematic diagrames；
1 DS of the first games of Fig. 31Best response dynamics schematic diagram；
Two DS of the first games of Fig. 41Best response dynamics Developing Tactics process schematic；
Three DS of the first games of Fig. 51Best response dynamics Developing Tactics process schematic；
Fig. 6 is odd number as n, and original state only one of which selects DS1Simulated effect schematic diagram；
Fig. 7 is odd number as n, and original state selects DS in the presence of two adjacent defenders1Simulated effect schematic diagram.
Embodiment
Embodiment 1, with reference to Fig. 1-Fig. 7, a kind of cyber-defence strategy selection side of best response dynamics Evolutionary Game Model
Method, comprises the following steps：
Step 1：Based on bounded rationality condition, using best response dynamics study mechanism, build and be based on best response dynamics
Attacking and defending Evolutionary Game Model；
Best response dynamics Evolutionary Game Model is represented by four-tuple, BRDEGM=(D, DS, P, U) in step 1
D={ d1,d2,…dnDefence participant space is represented, wherein, diRepresent defender i, different defender can be with
Choose different defence policies；
DS={ DS1,DS2,…DSmDefender's policy space is represented, different defenders enjoy the defence policies jointly
Collection；
P={ p1,p2,…pmDefender's conviction set is represented, wherein, piRepresent that defender chooses defence policies DSiIt is general
Rate；
U={ U1,U2,…UmRevenue function set is represented, wherein, UiRepresent that defender chooses defence policies DSiIt is acquired
Income.
Best response dynamics equation isWherein NtRepresent to choose plan in n defender
Slightly DS1Number, DS1It is any one defence policies in optional set of strategies.
Step 2：Dynamic Evolution and defence Evolutionary Equilibrium point are chosen using defender's strategy, between different defenders
Defence policies On The Choice is studied；
Defender's strategy selection Dynamic Evolution is in step 2：In network-combination yarn antagonistic process, different defence policies
Between there is a kind of competitive relation, the defence policies of high yield will eliminate the relatively low strategy of income；The defence plan of high yield
Summary will be eliminated in the relatively low strategy of income, and gain matrix is：Wherein, u1、u2Respectively
For tactful DS1、DS2Income, a is u1、u2Difference.
Step 3：On the basis of the best response dynamics Evolutionary Game Model of foundation, the model is entered by specific example
Row analysis promotes Evolutionary Game Model with solving.
Evolutionary Game Model is promoted in step 3 is mainly, when defender has any n defender, based on optimal anti-
Dynamic evolution betting model is answered, to any two defence policies DSiAnd DSjCarry out evolutionary Game Analysis, it is assumed that DSiBe relative to
DSjDominating stragegy, and i ≠ j over time, finally gives certain Evolution.
Further：Evolution is：For there is the defender of n defender, when all defenders are in first game
In all choose defence policies DSiOr strategy DSjWhen, using best response dynamics study mechanism, the strategy of whole network defender
It is then all equal Selection Strategy DS of defender to choose the stable state being finally reachediOr strategy DSj。
Further, Evolution is：For there is the defender of n defender, when n is odd number, in first game
In, as long as there is a defender to have chosen tactful DSi, when passing through multiple to itself strategy by best response dynamics study mechanism
The adjustment repeatedly of phase, finally can all converge on all defender's Selection Strategy DSiStable state.
Further, Evolution is：For there is the defender of n defender, when n is even number, in first game
In, there is a defender to have chosen defence policies DSi, the equal Selection Strategy DS of other defendersj, then, best response dynamics can not
All defenders are made to converge on some stable state, evolution over time, adjustment of each defender to strategy can only be absorbed in week
Phase cyclical variations.
Further, Evolution is：For there is the defender of n defender, in first game, simply by the presence of two
Individual adjacent defender have chosen tactful DS simultaneouslyi, under best response dynamics study mechanism, evolution over time, eventually
Converge on the whole Selection Strategy DS of all defendersiStable state.
Embodiment 2, with reference to Fig. 1-Fig. 7, a kind of cyber-defence strategy selection side of best response dynamics Evolutionary Game Model
Method, for analyzing network-combination yarn evolutionary Game process.Due to conventional replica locating study mechanism, to there is pace of learning slower, learns
The problems such as practising inefficient, the present invention still uses the thought of evolutionary Game, dynamic using peak optimization reaction based on bounded rationality condition
State study mechanism, builds the attacking and defending Evolutionary Game Model based on best response dynamics, and analysis defender's strategy chooses dynamic evolution
Process and defence Evolutionary Equilibrium point, are studied defence policies On The Choice between different defenders.In the optimal of foundation
React on the basis of dynamic evolution betting model, the model is analyzed and solved by specific example, and by the model
Make further genralrlization, improve the versatility of model.Method proposed by the present invention can be good at being applied to network security defence
Tactful On The Choice, can provide network security research certain directive significance.
In network-combination yarn game playing system, policymaker by continuous trial and error, imitation and Developing Tactics, from original state with
Time constantly develops, and can finally reach that some evolutionarily stable is balanced, and the direct shadow of policy learning method and process of policymaker
Ring and arrive final evolutionarily stable state.For defender, it is assumed that different defenders shares same defence policies collection.Due to not
Same defence policies can bring different incomes to defender, under the traction of yield variance and the driving of study mechanism, low to receive
Beneficial defender constantly learns the strategy of the high defender of income.Evolution over time, the strategy of low income will be by high yield
Strategy eliminate.For the attack of reality, from defence square degree, according to the collaboration between different defenders
Relation, the game that best response dynamics study mechanism is applied between different defence policies is set up multistage peak optimization reaction and moved
State repeats Evolutionary Game Model.Under the promotion of above-mentioned " study-improvement " mechanism, the selection probability of different defence policies is presented
Dynamic evolution trend, may finally analyze and obtain network security defence policies choosing method.
Best response dynamics Evolutionary Game Model
It is dynamic using peak optimization reaction under conditions of bounded rationality based on evolutionary game theory for network defense side
State Fast Learning mechanism, builds the best response dynamics Evolutionary Game Model between different defenders.
Define 1 best response dynamics Evolutionary Game Model BRDEGM (Best-response Dynamics
Evolutionary Game Model) it can be expressed as four-tuple, BRDEGM=(D, DS, P, U), wherein
1. D={ d1,d2,…dnRepresent defence participant space.Wherein, diDefender i is represented, different defenders can
To choose different defence policies.
2. DS={ DS1,DS2,…DSmRepresent defender's policy space.Different defenders enjoys the defence policies jointly
Collection.
3. P={ p1,p2,…pmRepresent defender's conviction set.Wherein, piRepresent that defender chooses defence policies DSi's
Probability.
4. U={ U1,U2,…UmRepresent revenue function set.Wherein, UiRepresent that defender chooses defence policies DSiObtained
The income taken.
In network-combination yarn antagonistic process, there is a kind of competitive relation, the defence plan of high yield between different defence policies
Summary will eliminate the relatively low strategy of income.For any two defender d1And d2, it is assumed that DS1、DS2In being optional set of strategies
Any two defence policies, wherein DS1It is to compare DS2Dominating stragegy, i.e. strategy DS1Compare DS2There is more preferable protection effect,
Higher defence income, but DS can be brought1Corresponding defence cost compares DS2It is high.Using best response dynamics Fast Learning machine
System, the Evolutionary Game Model set up under the conditions of bounded rationality.Game theory is as shown in Figure 2.
As game both sides difference Selection Strategy DS1And DS2When, choose DS1Higher defence income will be obtained, remember high cost
It is α, now, Selection Strategy DS to go out part1Defender obtain income u2- α, and Selection Strategy DS2Defender because hitchhike
Higher income is then obtained Deng behavior, u is designated as2+a.Wherein, u1-u2＞ ＞ a.
From gain matrixAs can be seen that in the game in the presence of two pure strategies receive it is assorted
Weigh (DS1,DS1) and (DS2,DS2), wherein (DS1,DS1) it is that Pareto very wise move is balanced.But if it is also contemplated that between defender
Trusting relationship, or to factors such as Risk Sensitivities, then equilibrium (DS2,DS2) occur possibility can be bigger.
Based on above game condition, it is assumed that all defenders all in a circumference on, each defender with each
Left and right neighbours carry out repeated game, learn than itself high defence policies of tactful income.The income point that note game both sides are obtained
Wei not ∏1And ∏2If, pi(t) it is the Selection Strategy DS in t periods, game person i neighbours1Quantity, the quantity is possible to be taken
Value has 0,1,2 three kind of situation.It can thus be concluded that, game person's Selection Strategy DS1When obtain income for ∏1=u1×pi(t)+(u2-a)×
[2-pi(t)], Selection Strategy DS2When obtain income for ∏2=(u2-a)×pi(t)+u2×[2-pi(t)].According to peak optimization reaction
Dynamic mechanism is understood, works as ∏1>∏2, i.e.,When, game person will be in next game stage Selection Strategy DS2.Thus may be used
To obtain following best response dynamics equation.
Wherein, NtRepresent Selection Strategy DS in n defender1Number.By the game dynamical equation, network is prevented
The final stable state that imperial strategy is chosen will be certain trend for being chosen for defence policies.
Evolutionary Game Model is analyzed with solving
Based on best response dynamics Evolutionary Game Model established above, the policy learning process between defender is carried out
Detailed description and analysis.In network-combination yarn confrontation, because defender is bounded rationality, and with Fast Learning
Ability, can be analyzed and summarized to payoff on last stage, and make corresponding Developing Tactics at once, realize lower single order
The defence maximum revenue of section.Over time, the strategy of whole defender, which is chosen, will reach a stable state.
Below by using from thinking from the particular to the general, using best response dynamics study mechanism, circumference game is carried out
Concrete analysis.
Assuming that defender has 5 defenders, and 5 defenders are distributed in 5 different positions on circumference, such as Fig. 3 institutes
Show, the defender on each position both can be with Selection Strategy DS1, can also Selection Strategy DS2, therefore, the game has at the beginning of 32
Beginning state, including a whole Selection Strategy DS1, a whole Selection Strategy DS2, it is left 30 and includes DS1And DS2
Two kinds of strategies.
pi(t) it is the Selection Strategy DS in t periods, game person i neighbours1Quantity, the possible value of the quantity has 0,1,
2 three kinds of situations.Correspondingly, Selection Strategy DS2Neighbours' quantity be 1-pi(t), equally exist 0,1,2 three kind of value.According to optimal
React dynamic mechanism to understand, work as ∏1>∏2, i.e.,When, game person will be in next game stage Selection Strategy DS2.
Know u1-u2＞ ＞ α, thenDue to pi(t) only exist 0,1,2 three kind of value, if at two of t period game persons i
As long as there is one to have chosen tactful DS in neighbours1, then game person i will choose DS in t+1 periods1Strategy；If two neighbours are
There is no Selection Strategy DS1, then game person i will choose DS in t+1 periods2Strategy.Therefore deduce that, when 5 defenders are first
All choose DS1Strategy (DS2Strategy) when, final stable state chooses DS for all defenders1Strategy (DS2Strategy).
If there is 1 defender to have chosen DS in first game1Strategy, and other defenders use DS2Strategy
When, then this 5 defenders have finally converged to all defenders and have used DS by the Developing Tactics repeatedly in 4 periods1Plan
Stable state slightly.As shown in figure 3, original state (the DS for giving defender1,DS2,DS2,DS2,DS2), by 4 times
Stage evolution, defender has been finally reached stable state (DS1,DS1,DS1,DS1,DS1)。
Two non-conterminous defenders are contained it can be seen from best response dynamics adjustment process in Fig. 3 to adopt
Use DS1, three non-adjacent game persons use DS1, four defenders use DS1The peak optimization reaction of this several first game situation is moved
State adjust process, they be respectively necessary for three, two and one stages adjustment can reach all use DS1The stabilization of strategy
State.Below to thering are two non-adjacent defenders and three adjacent defenders to use DS in first game1Situation analyzed.
As shown in Figure 4, two adjacent defenders use DS1Best response dynamics Developing Tactics process only need two stages
It can reach all defenders and choose DS1The stable state of strategy.As shown in Figure 5, three adjacent defenders use DS1It is optimal
Reaction dynamic strategy adjustment process only needs a stage to can reach all defenders and chooses DS1The stable state of strategy.
Analyzed more than, in 32 kinds of possible first game situations, only one kind is evolutionarily stable in all defence
Person's Selection Strategy DS2, remaining 31 kinds finally can all converge on all selection DS1State.Illustrate all defender's Selection Strategies
DS1Or DS2The stable state belonged in the gambling process, but converge on DS1Probability to be far longer than DS2。
Above-mentioned two evolutionarily stable state is further understood, if defender is reaching all defender's Selection Strategy DS1
Stable state under, there are a small number of defenders and deviate strategy DS1Situation, best response dynamics can make defender strategy quickly
Converge to and all choose DS1State.Therefore, all defenders choose DS1Stable state be with stability.On the contrary, working as
Reach that all defenders choose DS2Stable state be not but sane, once because some defender deviate DS2, peak optimization reaction
Dynamic can make the state of defender more and more remote from the stable state, therefore the equilibrium is not really stable.With it is long when
Between evolution, defender most at last can Selection Strategy DS1。
The popularization of Evolutionary Game Model
Because during actual cyber-defence, defender is made up of multiple defenders, it is therefore necessary to the game mould
Type makees further genralrlization, i.e., when defender has any n defender, based on above fast reaction dynamic evolution game mould
Type, to any two defence policies DSiAnd DSjEvolutionary Game Analysis is carried out (assuming that DSiIt is relative to DSjDominating stragegy, and i
≠ j), over time, finally give certain Evolution.Evolution for above particular number of networks defender is won
Analysis is played chess, by further analysis and summary, following proposition can be obtained.
Proposition 1：For there is the defender of n defender, when all defenders choose defence plan in first game
Slightly DSi(tactful DSj) when, using best response dynamics study mechanism, whole network defender strategy choose be finally reached it is steady
It is then all equal Selection Strategy DS of defender to determine statei(tactful DSj)。
Proposition 2：For there is the defender of n defender, when n is odd number, in first game, as long as there is one to prevent
Driver have chosen tactful DSi, pass through the adjustment repeatedly in multiple periods to itself strategy by best response dynamics study mechanism, most
It can all converge on all defender's Selection Strategy DS eventuallyiStable state.
Proposition 3：For there is the defender of n defender, when n is even number, in first game, there is a defender
It has chosen defence policies DSi, the equal Selection Strategy DS of other defendersj, then, best response dynamics can not receive all defenders
Hold back in some stable state, evolution over time, adjustment of each defender to strategy can only be absorbed in loop cycle and change.
Proposition 4：It is same simply by the presence of two adjacent defenders in first game for there is the defender of n defender
When have chosen tactful DSi, under best response dynamics study mechanism, evolution over time eventually converges on all defence
Person's whole Selection Strategy DSiStable state.
Proposition 5：For there is the defender of n defender, if by arranging strategy of the defender in first game,
By continuous dynamic evolution so that when the game playing system reaches a certain stage, occur in that some feelings in aforementioned four proposition
Same evolutionary process will occurs in shape, the later stage.
Numerical simulation
Based on network-combination yarn evolutionary Game established above, experiment simulation is carried out using system dynamics, checking network is attacked
The validity and reasonability of anti-Evolutionary Game Model and best response dynamics Evolutionary Game Model.Defender chooses different defence
Original state, whole game playing system will produce different evolution results.Below by for the different defence initial shapes of defender
State, carries out specific numerical simulation.The present invention will be used as simulation object using proposition 2 and proposition 4.
(1) when n be odd number, and defender's original state be only one of which defender's Selection Strategy DS1, other defenders are equal
Selection Strategy DS2When, n=21 is taken, then Selection Strategy DS1Defender's proportion beSelection Strategy DS2Defender institute
Accounting example beNow, there is the power that adjustment changes itself strategy in the game playing system between defender.It is imitative by system
Very, defender's Selection Strategy DS is found1Defender's ratio it is linear increase, and the DS of Selection Strategy2Defender's ratio is linear
Reduce, and just reached in the 10th simulation result final evolutionarily stable state.It is specific as shown in Figure 6.The evolution
As a result can be system stable stateIn one kind, now DS1For optimal defence policies.
(2) there is two adjacent defenders Selection Strategy DS simultaneously in n is odd number, and defender's original state1, other
The equal Selection Strategy DS of defender2When, n=21 is taken, then Selection Strategy DS1Defender's proportion beSelection Strategy DS2's
Defender's proportion isNow, there is the power that adjustment changes itself strategy in the game playing system between defender.Pass through
Constantly develop, defender's Selection Strategy DS1Defender's ratio it is linear increase, and the DS of Selection Strategy2Defender's ratio is into line
Property reduce, and reach in the 10th simulation result final evolutionarily stable state.It is specific as shown in Figure 7.The evolution result can be with
It is system stable stateIn one kind, now DS1For optimal defence policies.
It can be seen from above simulation result, chosen just for the difference of defender's number parity, and defender's strategy
The difference of beginning state, can all influence the final evolution result of whole game playing system.Initial shape is chosen by arranging defender's strategy
State, by constantly evolution, best response dynamics will eventually make game playing system reach some stable state.By experimental result and this
Literary model reasoning is contrasted, it can be seen that the evolution result in experimental system is consistent with the theory analysis in text, explanation
The Evolutionary Game Model meets reality system Evolution, so as to demonstrate the achieved availability of this model.It can be applied
In the network-combination yarn confrontation of reality, the Alliance Defense of defender is made a concrete analysis of and predicted, be the strategy choosing of defender
Take and strong support is provided.
Claims (10)
1. a kind of cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model, it is characterised in that：Including following
Step：
Step 1：Based on bounded rationality condition, using best response dynamics study mechanism, attacking based on best response dynamics is built
Anti- Evolutionary Game Model；
Step 2：Dynamic Evolution and defence Evolutionary Equilibrium point are chosen using defender's strategy, to being defendd between different defenders
Tactful On The Choice is studied；
Step 3：On the basis of the best response dynamics Evolutionary Game Model of foundation, the model is divided by specific example
Analysis promotes Evolutionary Game Model with solving.
2. the cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model according to claim 1, it is special
Levy and be：Best response dynamics Evolutionary Game Model is represented by four-tuple, BRDEGM=(D, DS, P, U) in the step 1
D={ d1,d2,…dnDefence participant space is represented, wherein, diDefender i is represented, different defenders can choose not
Same defence policies；
DS={ DS1,DS2,…DSmDefender's policy space is represented, different defenders enjoys the defence policies collection jointly；
P={ p1,p2,…pmDefender's conviction set is represented, wherein, piRepresent that defender chooses defence policies DSiProbability；
U={ U1,U2,…UmRevenue function set is represented, wherein, UiRepresent that defender chooses defence policies DSiAcquired receipts
Benefit.
3. the cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model according to claim 1, it is special
Levy and be：The best response dynamics equation isWherein NtRepresent to select in n defender
Take tactful DS1Number, DS1It is any one defence policies in optional set of strategies.
4. the cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model according to claim 1, it is special
Levy and be：Defender's strategy selection Dynamic Evolution is in the step 2：In network-combination yarn antagonistic process, difference defence
There is a kind of competitive relation between strategy, the defence policies of high yield will eliminate the relatively low strategy of income.
5. the cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model according to claim 4, it is special
Levy and be：The defence policies of the high yield will be eliminated in the relatively low strategy of income, and gain matrix is：
Wherein, u1、u2Respectively strategy DS1、DS2Income, a is u1、u2Difference.
6. the cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model according to claim 1, it is special
Levy and be：Evolutionary Game Model is promoted in the step 3 is mainly, when defender has any n defender, based on optimal
Dynamic evolution betting model is reacted, to any two defence policies DSiAnd DSjCarry out evolutionary Game Analysis, it is assumed that DSiIt is relative
In DSjDominating stragegy, and i ≠ j over time, finally gives certain Evolution.
7. the cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model according to claim 6, it is special
Levy and be：The Evolution is：For there is the defender of n defender, when all defenders select in first game
Take defence policies DSiOr strategy DSjWhen, using best response dynamics study mechanism, the strategy of whole network defender is chosen most
The stable state reached eventually is then all equal Selection Strategy DS of defenderiOr strategy DSj。
8. the cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model according to claim 6, it is special
Levy and be：The Evolution is：For there is the defender of n defender, when n is odd number, in first game, as long as
There is a defender to have chosen tactful DSi, the anti-of multiple periods is passed through to itself strategy by best response dynamics study mechanism
Polyphony is whole, finally can all converge on all defender's Selection Strategy DSiStable state.
9. the cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model according to claim 6, it is special
Levy and be：The Evolution is：For there is the defender of n defender, when n is even number, in first game, there is one
Individual defender have chosen defence policies DSi, the equal Selection Strategy DS of other defendersj, then, best response dynamics can not make to own
Defender converges on some stable state, evolution over time, and adjustment of each defender to strategy can only be absorbed in loop cycle
Change.
10. the cyber-defence strategy choosing method of best response dynamics Evolutionary Game Model according to claim 6, it is special
Levy and be：The Evolution is：It is adjacent simply by the presence of two in first game for there is the defender of n defender
Defender have chosen tactful DS simultaneouslyi, under best response dynamics study mechanism, evolution over time is eventually converged on
The whole Selection Strategy DS of all defendersiStable state.
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