ZERO-DETERMINANT STRATEGIES OF THREE-PLAYER REPEATED GAMES UNDER NOISY OBSERVATION

Abstract

The emergence of zero-determinant (ZD) strategies has generated considerableinterest, particularly in the context of the Iterated Prisoner's Dilemma (IPD). In this game,players sustain cooperation to avoid retaliation in subsequent rounds. This study investigatesthe application of ZD strategies within a three-player repeated game framework, with aparticular focus on the inuence of observation errors. We analyze how ZD strategies interactwith the inherent incompleteness of observations, demonstrating that even under imperfectmonitoring, certain strategies can still enforce linear payoff relationships. Both the discountfactor and observation errors are considered in the analysis, and a numerical example isprovided to illustrate the robustness and limitations of ZD strategies in a non-3X3 Prisoner'sDilemma game. These results contribute to a deeper understanding of strategic decision-making in repeated games and highlight the potential of ZD strategies to control long-termoutcomes even amidst observational uncertainty.