The Value Function with Regret Minimization Algorithm for Solving the Nash Equilibrium of Multi-Agent Stochastic Game

Abstract

In this paper, we study the value function with regret minimization algorithm for solving the Nash equilibrium of multi-agent stochastic game (MASG). To begin with, the idea of regret minimization is introduced to the value function, and the value function with regret minimization algorithm is designed. Furthermore, we analyze the effect of discount factor to the expected payoff. Finally, the single-agent stochastic game and spatial prisoner's dilemma (SDP) are investigated in order to support the theoretical results. The simulation results show that when the temptation parameter is small, the cooperation strategy is dominant; when the temptation parameter is large, the defection strategy is dominant. Therefore, we improve the level of cooperation between agents by setting appropriate temptation parameters.

Stability of Generalized Minimax Regret Equilibria with Scalar Set Payoff

“…Recently, Zhang and Chen et al [3] studied existence of general n person noncooperative game problems and minimax regret equilibria with set payoff by using Kakutani-Fan-Glicksberg fixed point theorem and a nonlinear scalarization function. For more information, refer to [4] [5] [6] [7].…”