A Novel Adaptive Agent-Based Algorithm to Find Mixed Nash Equilibrium in Static Games

The main goal of this paper is to present a novel adaptive agent-based algorithm to calculate players’ mixed Nash equilibrium strategies in a normal form static gamewhich is based on gradual learning occurring through repetitive interaction with the environment. The proposed algorithm not only calculates equilibrium states, but alsomodels dynamic behavior of the participants. Although several algorithms have been suggested over the years to solve theproblem, but many of them consider some imperfect assumptions and neglect some important Principles. The proposed algorithm covers many aspects of real game environments. The unique characteristic of the proposed method is high performance of the algorithm in games ofincomplete information where players utilize limited information about each other as occurring in real games. The algorithm is tested on three classes of games with both pureand mixed Nash equilibrium. The simulation results are robust across the testing games and illustrate the efficiency of thealgorithm.

Keywords:

Game Theory , Nash Equilibrium , Incomplete Information , Imperfect Games , Multi-Agent