This paper focuses on the performance of equalizer zero-determinant(ZD)strategies in discounted repeated Stackelberg asymmetric games.In the leader-follower adversarial scenario,the strong Stackelberg equilibrium(SSE)...This paper focuses on the performance of equalizer zero-determinant(ZD)strategies in discounted repeated Stackelberg asymmetric games.In the leader-follower adversarial scenario,the strong Stackelberg equilibrium(SSE)deriving from the opponents’best response(BR),is technically the optimal strategy for the leader.However,computing an SSE strategy may be difficult since it needs to solve a mixed-integer program and has exponential complexity in the number of states.To this end,the authors propose an equalizer ZD strategy,which can unilaterally restrict the opponent’s expected utility.The authors first study the existence of an equalizer ZD strategy with one-to-one situations,and analyze an upper bound of its performance with the baseline SSE strategy.Then the authors turn to multi-player models,where there exists one player adopting an equalizer ZD strategy.The authors give bounds of the weighted sum of opponents’s utilities,and compare it with the SSE strategy.Finally,the authors give simulations on unmanned aerial vehicles(UAVs)and the moving target defense(MTD)to verify the effectiveness of the proposed approach.展开更多
This paper designs a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints.Due to the uncertainty of parameters in set constraints,the authors aim to find a gene...This paper designs a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints.Due to the uncertainty of parameters in set constraints,the authors aim to find a generalized Nash equilibrium in the worst case.However,it is challenging to obtain the exact equilibria directly because the parameters are from general convex sets,which may not have analytic expressions or are endowed with high-dimensional nonlinearities.To solve this problem,the authors first approximate parameter sets with inscribed polyhedrons,and transform the approximate problem in the worst case into an extended certain game with resource allocation constraints by robust optimization.Then the authors propose a distributed algorithm for this certain game and prove that an equilibrium obtained from the algorithm induces anε-generalized Nash equilibrium of the original game,followed by convergence analysis.Moreover,resorting to the metric spaces and the analysis on nonlinear perturbed systems,the authors estimate the approximation accuracy related toεand point out the factors influencing the accuracy ofε.展开更多
基金supported by the National Key Research and Development Program of China under Grant No.2022YFA1004700the National Natural Science Foundation of China under Grant No.62173250Shanghai Municipal Science and Technology Major Project under Grant No.2021SHZDZX0100.
文摘This paper focuses on the performance of equalizer zero-determinant(ZD)strategies in discounted repeated Stackelberg asymmetric games.In the leader-follower adversarial scenario,the strong Stackelberg equilibrium(SSE)deriving from the opponents’best response(BR),is technically the optimal strategy for the leader.However,computing an SSE strategy may be difficult since it needs to solve a mixed-integer program and has exponential complexity in the number of states.To this end,the authors propose an equalizer ZD strategy,which can unilaterally restrict the opponent’s expected utility.The authors first study the existence of an equalizer ZD strategy with one-to-one situations,and analyze an upper bound of its performance with the baseline SSE strategy.Then the authors turn to multi-player models,where there exists one player adopting an equalizer ZD strategy.The authors give bounds of the weighted sum of opponents’s utilities,and compare it with the SSE strategy.Finally,the authors give simulations on unmanned aerial vehicles(UAVs)and the moving target defense(MTD)to verify the effectiveness of the proposed approach.
基金supported partly by the National Key R&D Program of China under Grant No.2018YFA0703800the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No.XDA27000000the National Natural Science Foundation of China under Grant Nos.61873262 and 61733018。
文摘This paper designs a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints.Due to the uncertainty of parameters in set constraints,the authors aim to find a generalized Nash equilibrium in the worst case.However,it is challenging to obtain the exact equilibria directly because the parameters are from general convex sets,which may not have analytic expressions or are endowed with high-dimensional nonlinearities.To solve this problem,the authors first approximate parameter sets with inscribed polyhedrons,and transform the approximate problem in the worst case into an extended certain game with resource allocation constraints by robust optimization.Then the authors propose a distributed algorithm for this certain game and prove that an equilibrium obtained from the algorithm induces anε-generalized Nash equilibrium of the original game,followed by convergence analysis.Moreover,resorting to the metric spaces and the analysis on nonlinear perturbed systems,the authors estimate the approximation accuracy related toεand point out the factors influencing the accuracy ofε.