Zero - Determinant strategies for multiplayer prisoner's dilemma game

This study introduces the concept of Zero-Determinant (ZD) strategies, encompassing both altruistic and exploitative tactics within the framework of game theory. In the Iterated Prisoner's Dilemma, it is widely acknowledged that, under specific circumstances, employing benevolent and coercive strategies leads to an expected linear correlation between the long-term rewards of participants. The research not only validates the presence of these conditions in the Multiplayer Iterated Prisoner's Dilemma but also reveals that a participant using a less potent coercive strategy can influence their counterpart by establishing a linear link between their opponent's payoff and their own, provided specific conditions are met. Additionally, the study investigates the dynamics of coordinating actions based on Zero-Determinant strategies within the context of game-play alliances.