zero determinate strategies for Iterated Games

Abstract

Zero Determinant (ZD) strategies is a new class of probabilistic and conditional strategies discovered by Press and Dyson which has been applied on two players. In this thesis, I am interested in applying ZD Strategies in three - player game. Where each player has two pure actions to cooperate or defect, the action in the current state depends only in the previous action in the last state. Also, the transition matrix when one player move from one state to another was determined in case of three players. ZD strategies for multiple players will be explored where the application of ZD has been taken on Iterated three-player Prisoner’s Dilemma game (IPD) with two actions Cooperate(C) or Defect(D). The results in case of the three players correspond to what was obtained in case of two players with different calculation methods. Surprisingly, although the player who adopts ZD strategies can determine the opponents' payoffs in a unilateral way, and with an extortion strategy, he can impose a linear relationship between the expected return for him and the expected payoff of other players, but he cannot determine his own score because his technique is leads to one possible strategy (1,1,1,1,0,0,0,0) which is not valid strategy. Then, a player who uses ZD strategies can't be able to set his expected payoff. We show when three players face each other how the player who uses ZD strategies determines the return of one of his/her opponents greater than the return of the others and also ensures that he receives a greater return from all the opponents. Finally, we will d