Research On Distributed Game Problems And Algorithms Design

Game theory is a discipline that studies the behavior of decision makers(also known as ”players”),mainly studying their decisions and outcomes when multiple players interact.In game theory,the decision of each player affects the outcome of the entire game,and each player is influenced by the decisions of other players.Many scholars apply game theory to solve practical engineering problems,such as intelligent energy systems,traffic management,etc.Nash Equilibria is a solution concept in game theory that refers to a state in which,in a game,if every player adopts the optimal strategy,then all players’ strategies are mutually coordinated and reach a balance.Generalized Nash Equilibria is an extension of Nash Equilibria and is a solution concept for game models with globally shared coupling constraints.These global constraints couple the feasible action sets of each player together,making it impossible for any player to obtain a higher payoff by changing their strategy.With the rapid development of information technology,the number of players in game models has gradually increased.Traditional centralized generalized Nash Equilibria solving algorithms are no longer able to handle large amounts of computational requirements in a timely manner.Therefore,distributed solving algorithms with better timeliness,scalability,and privacy protection have gradually become a research hotspot.Based on existing research,this paper proposes high availability and high-performance distributed generalized Nash Equilibria solving algorithms for both general non-cooperative games and aggregative games.The research mainly focuses on the following three points:(1)This paper proposes a distributed algorithm based on edge consistency for solving generalized Nash Equilibria under full information.Considering that the existing distributed algorithms based on the primal-dual method for solving generalized Nash Equilibria in non-cooperative game models require a Laplacian matrix whose dimension depends on the number of players to ensure the consistency of dual variables,this means that such algorithms are not suitable for large-scale networks.The algorithm proposed in this paper assumes that each player can communicate with all other players and does not require the construction of an additional Laplacian matrix.Furthermore,considering that most existing studies use global step sizes,where all players use the same step size,this may result in the step sizes being inflexible.The distributed algorithm proposed in this paper uses a locally constant step sizes that depends on the number of neighbors,which improves the flexibility of the algorithm.(2)This paper proposes a distributed algorithm based on edge consistency for solving generalized Nash Equilibria under partial information settings.Taking into account that in many practical applications,some players may not be able to communicate with all other players,this paper introduces a local estimate of the overall actions of all players for each player,so that players in the game only need to communicate with their neighboring players.Through simulation experiments of Cournot games and path planning models,this paper further verifies the consistency of the generalized Nash Equilibria obtained under partial information and full information.(3)This paper studies the average aggregative games with coupling constraints and designs a distributed algorithm for solving the generalized Nash Equilibria in these games based on the proximal operator.To solve this game problem in a distributed manner,this paper introduces local estimates of the aggregate value for each player,ensuring mutual independence among players.Unlike algorithms under partial information setting,the advantage of this algorithm is that local estimates do not depend on the number of players,thus it is efficient and scalable.From an application perspective,this algorithm is more suitable for large-scale networks.At the same time,this paper introduces a consistency subspace for local estimates to ensure their consistency.Finally,through simulation experiments of a charging model,the correctness and practicality of the algorithm are verified.In summary,based on existing research achievements and shortcomings,this paper designs a series of distributed algorithms for solving the generalized Nash Equilibria of game models based on the primal-dual method and proximal operator theory.The research results of this paper will further expand the game model solving method,providing complete theoretical support for distributed game solving practical engineering problems.