# Math-Bio seminar: "Linear payoff relationships in repeated games"

In 2012, the study of the repeated Prisoner’s Dilemma was revitalized by the discovery of a new class of strategies known as “zero-determinant” (ZD) strategies. Through coercion, for example, ZD strategies allow a player to extort the opponent and obtain an unfair share of the payoffs. More generally, a player can use ZD strategies to unilaterally enforce linear relationships on expected payoffs, capturing classical fair strategies like tit-for-tat as well as extortionate and generous counterparts. I will discuss extensions of ZD strategies to arbitrary repeated games, including those with (i) larger action spaces (beyond just “cooperate” and “defect”), (ii) more than two players, and (iii) asynchronous moves. Beyond the fact that ZD strategies exist for a broad class of biologically-relevant interactions, these strategies can also always be assumed to have a short memory of the past (in fact, a memory of just the most recent round). Therefore, they are robust to changes in the structure of the game and can be implemented relatively easily.