State policy couple dynamics in evolutionary games

Abstract

Standard Evolutionary Game framework is a useful tool to study large interacting systems and to understand the strategic behavior of individuals in such complex systems. Adding an individual state to model local feature of each player in this context, allows one to study a wider range of problems in various application areas as networking, biology, etc. In this paper, we introduce such an extension of evolutionary game framework and particularly, we focus on the dynamical aspects of this system. Precisely, we study the coupled dynamics of the strategies and the individual states inside a population of interacting individuals. We consider here a two strategies evolutionary game. We first obtain a system of combined dynamics and we show that the rest-points of this system are equilibria of our evolutionary game with individual state. Second, by assuming two different time scales between states and strategy dynamics, we can compute explicitly the equilibria. Then, by transforming our evolutionary game with individual states into a standard evolutionary game, we obtain an equilibrium which is equivalent, in terms of occupation measure, to the previous one. All our results are illustrated with numerical results.

On Nonzero-Sum Game Considered on Solutions of a Hybrid System with Frequent Random Jumps

“…(the validity of the last inclusions follows from the convexity of W i , i = 1, 2). Note that, from the fact that ω i l ∈ W i , it follows that there exists a stationary policy s i ∈ U S i of the player i such that ω i l = ω i l (s i l ) (see (8) and (9)). Let us define a policy of the player i in the hybrid game that consists of: 1.…”

“…Note that problems of optimal control and zero-sum games considered on the solutions of the hybrid system similar to one we are dealing with have been studied in [2], [3], [4], [13], [16] (see also related results in [1], [5], [8] and [15]). The present paper continues this line of research by developing a technique allowing one to deal with non-zero sum games.…”

Non-Markov Stateful Evolutionary Games

“…This pioneering effort has centered around the works of Eitan Altman, and his colleagues Ilaria Brunetti and Yezekael Hayel [15][16][17][18][19][20], who introduce the Markov-Decision-Evolutionary-Game (MDEG) and variants thereof.…”

Non-Markov Stateful Evolutionary Games

“…Another approach of integrating state into game theory extends from the pioneering work of Eitan Altman, and his colleagues Ilaria Brunetti and Yezekael Hayel [21][22][23][24][25][26] who introduce the Markov-Decision-Evolutionary-Game (MDEG) and variants thereof.…”