Evolutionary Stable Strategies (ESS)

Game theory developed to study the strategic interaction among rational self regarding players (players seeking to maximize their own payoffs). However, by the early 1970’s the theory underwent a transformation and part of it morphed into evolutionary game theory, which allows to increase our understanding of dynamical systems, especially in biology and, more recently, in psychology and the social sciences, with significant ramifications for philosophy. The players are not required to be rational at all, but only to have (perhaps hardwired) strategies that are passed on to their progeny. In short, the notion of player is displaced by that of strategy, and consequently the notion of a player’s knowledge, complete or incomplete, is dispensed with. What drives systems is not the rationality of the players but the differential success of the strategies. As before, we consider only two-player games. A game with strategies s1,.....sn for both players is strategy symmetric (symmetric, in brief) if: 1. when i=j the payoffs for the two identical strategies are the same, which means that along the main diagonal (top left to bottom right) the payoffs in each box are the same 2. the payoffs in the remaining boxes on one side of the main diagonal are mirror images of their counterparts on the other side. For example, The Prisoners’ Dilemma is a symmetric game. Along the main diagonal, the payoffs are the same in each box that is, (1,1) and (6,-6); moreover, we have (-10, 10) in the top right box and (10, -10) in the bottom left, which are mirror images of each other.