Research On Distributed Algorithm For Nash Equilibrium Search Problem Of Two-network Zero-sum Games

In recent years,two-network zero-sum game has been widely used in military,science,engineering and other fields,and its Nash equilibrium search algorithm has also become the main research hotspot in related fields.However,when solving the actual game problems,the existing Nash equilibrium search algorithms have the disadvantages of heavy communication burden,slow convergence speed and high computational cost.Therefore,this paper optimizes the traditional twonetwork zero-sum game Nash equilibrium search algorithm from the above three aspects,and designs three new distributed algorithms to better realize Nash equilibrium search.The specific research contents are as follows:In order to reduce the communication burden within the cluster in the two-network zero-sum games,a distributed event triggered projection subgradient algorithm is proposed based on the event triggering mechanism under the fixed undirected communication topology.By setting communication trigger condition for each agent,the agent can interact with its neighbors only when the trigger condition is met,which reduces the communication frequency among agents.In addition,through convergence analysis,it is proved that the proposed algorithm can reduce the communication burden and make the states of all agents converge to Nash equilibrium.Finally,numerical simulation verifies the effectiveness of the algorithm.In order to improve the convergence performance of two-network zero-sum game Nash equilibrium search algorithm,a distributed multi-step projection subgradient algorithm based on multi-step method is proposed under the time-varying directed communication topology.In the new algorithm,the state update of the agent depends on the weighted combination of the subgradients of itself and its neighbors,in which the subgradients of the neighbors are used as the inertial acceleration term to improve the convergence performance of the algorithm.In addition,the convergence analysis shows that the proposed algorithm can drive the states of all agents to converge to Nash equilibrium.Finally,the effectiveness of the algorithm is verified by simulation.In order to reduce the computational cost of agents in two-network zero-sum games,a distributed random sleep projection subgradient algorithm is proposed based on random sleep strategy under time-varying directed communication topology.The agent performs projection subgradient iteration with a given probability according to the independent and identically distributed Bernoulli random variables,which reduces the query of subgradient information.In addition,the new algorithm uses random decreasing step size to relax the requirement of step size.Through convergence analysis,it is proved that the new algorithm not only reduces the computational cost of all agents,but also makes the states of all agents converge to Nash equilibrium with probability 1.Finally,the effectiveness of the algorithm is verified by simulation.