Nash Equilibrium-Based Asymptotic Stability Analysis of Multi-Group Asymmetric Evolutionary Games in Typical Scenario of Electricity Market

Abstract

This paper introduces new theoretical insights into Nash equilibrium-based asymptotic stability (NEAS) of two-group and three-group asymmetric evolutionary games in typical scenarios of electricity market (EM). EM competition has become a complex dynamic evolution process accomplished by more complex characteristics of market economy behavior. Replicator dynamics in evolutionary game theory, as well as Lyapunov stability theory, are employed to solve incomplete-information and bounded-rationality game issues in EM, so as to overcome theoretical demerits of classical game theory in solving multi-group games in EM. First, the NEAS of a unilateral two-group asymmetric evolutionary game (AEG) is investigated. Then, this is expanded to a complicated $2\times 2\times 2$ trilateral multi-group AEG, and the NEAS of it under different game situations in EM is thoroughly discussed. Finally, a practical case study is conducted for verification. The case illustrates how the factors affect the payoff matrix which will change ultimate evolutionary stable state of the multi-group AEG in EM. One main finding demonstrates the complete dynamics behavior and multi-group evolutionary stable strategy (MESS) of the AEG system in 3-D mixed strategy space. The other one reveals that EM policies formulated by government and other factors can gradually influence the MESS via changing the payoff distribution matrix.