Coupled State Policy Dynamics in Evolutionary Games

International audienceIn this work we want to extend the EGT models by introducing the concept of individual state. We analyze a particular simple case, in which we associate a state to each player, and we suppose that this state determines the set of available actions. We consider deterministic stationary policies and we suppose that the choice of a policy determines the fitness of the player and it impacts the evolution of the state. We define the interdependent dynamics of states and policies and we introduce the State Policy coupled Dynamics (SPcD) in order to study the evolution of the population profile and we prove the relation between the rest points of our system and the equilibria of the game. We then assume that the processes of states and policies move with different velocities: this assumption allows us to solve the system and then to find the equilibria of our game with two different methods: the singular perturbation method and a matrix approach. 9