Win Stay--Lose Shift: An Elementary Learning Rule for Normal Form Games

In this paper we study a simple learning paradigm for iterated normal form games in an evolutionary context. Following the decision-theoretic concept of satisficing, we design players with a certain asperation level. If their payoff is below this level, they change their current action; otherwise, they repeat it. We consider stochastic generalizations of this win stay--lose shift principle that average the received payoff over several rounds of the game before comparing it to their asperation level and allow the strategies to adapt their asperation level in the course of the play. Our analysis is twofold. On the one hand, we study the evolution of such strategies for the Prisoner’s Dilemma; on the other hand, we consider contexts where a randomly selected game is assigned to the players. In the presence of such high uncertaintly, win stay--lose shift strategies turn out to be very successful. Using computer simulations we address questions such as: What is a favorable asperation level? How many rounds should one observe before updating the current action? What is the impact of noise?