Research On Equilibrium Solutions In Multi-Scenario Security Games

In recent years,security game model has been widely used in the fields of infrastructure protection,wildlife conservation,and network security.The optimal decision of the security department can be obtained by solving the equilibrium solution ofthe game.However,complex real-life scenarios need to be established as different forms of security game models,which corresponds to different forms of equilibrium solutions.In order to study equilibrium solutions in multi-scenario security games and make it suitable for solving the resource allocation problem of security department in more realistic scenarios,this thesis has done the following work:(1)The SSE(Strong Stackelberg Equilibrium)solution in a single defender vs single attacker security game scenario is studied.Specifically,analyze it in a scenario where the communication system versus active time-varying attacker.First,an attacker-defender security game model between the communication system and the active time-varying attacker is built.Based on the gains and losses of both players in the game,a nonlinear programming model for solving the best artificial noise addition strategy for the defender is proposed.Then the algorithm designed in this thesis transforms a M-dimensional problem into M 1-dimensional problems and obtains a strong Stackelberg equilibrium solution.Finally,this thesis proves that the game-theoretic defense strategy significantly outperforms non-strategic defense strategies in terms of decreasing the total losses for the communication system.(2)The Pareto Equilibrium solutionin a single defender vs multi-attacker repeated security game scenario is studied.Considering the complex behavior of multiple attacker types in repeated security game scenario,this thesis adopts the worst-case analysis to optimize the defender's expected utility assuming all attackers are fully adversarial.First,the problem of maximizing the defender's utility under uncertainty is transformed into a problem of minimizing the defender's regret.At the same time,it is difficult for a defense strategy to achieve the optimal regret value at the same time in response to each attacker's behavior uncertainty,this thesis establishes a multi-objective repeated security game model and computes the Pareto equilibrium solution for the defender.Then,in order to solve the Pareto frontier from the simultaneous guarantee vector set,a Q-value iteration approximation algorithm on a linear programming is proposed.Finally,theoretical analysis obtains the error bound of the approximate algorithm,and the ideal approximate results are obtained through experimental analysis.(3)The LSMDE(Logit Stackelberg Multi-Defender Equilibrium)solution in a multidefender vs single-attacker security game scenario is studied.First,based on the attractiveness value of targets in the attacker's best response set,this thesis defines the logit tie-breaking rule and proposes the LSMDE in this scenario.By splitting the game into several sub-games,LSMDE can be obtained by solving several equilibrium sub-problems with equilibrium constraints.Comparing with the defender's utility under the average tie-breaking rule,the results show that the logit tie-breaking rule describes the attacker s behavior more accurately,thus bringing more benefits to the defender.Next,treating the attacker as an external factor of the game,this thesis considers an equivalent equilibrium solution of LSMDE,that is,the Nash equilibrium solution among multiple defenders.Theoretical analysis shows that LSMDE does not necessarily exist in the game,so the Nash equilibrium solution cannotbe guaranteed either.Finally,an improved exclusion algorithm for solving the approximate Nash equilibrium is proposed.Compared with the IBR(Iterated Best Response)algorithm,the experimental results show that the improved exclusion algorithm not only solves more game instances,but also exhibits faster speed(4)The PBE(Perfect Bayesian Equilibrium)solution in a generalized multi-defender vs single-attacker security game scenario is studied In a scenario where the defender holds real resources and fake resources at the same time,the attacker cannot fully distinguish them due to the asymmetry of information.A weak defender type with fake resources couldbluffas a strong type as if all resources are real.First,this thesis establishes a bluffing security game model based on signaling game model,where the defender sends a fake signal different from her own real type to confuse the attacker's judgment,and the attacker chooses an attack strategy after receiving the signal.Then,a mixed-integer cubic programming model for solving the PBE is built.Through a variable substitution,the mixed integer cubic programming model is reduced to a mixed-integer quadratic programming model.Finally,this thesis theoretically analyzes the reason why the "bluffing" behavior could benefitthe defender.And the simulationresults verify that the bluffing security game model outperforms the traditional security game model in terms of the defender's utility.