Markov Decision Evolutionary Games

We present a class of evolutionary games involving large populations that have many pairwise interactions between randomly selected players. The fitness of a player depends not only on the actions chosen in the interaction but also on the individual state of the players. Players have a finite life time during which they participate in several local interactions and take actions. The actions taken by a player determine not only the immediate fitness but also the transition probabilities to its next individual state. We define and characterize the Evolutionary Stable Strategies for these games and propose a method to compute them. We illustrate the model and results through a networking problem.