Asymmetrical expectations of future interaction and cooperation in the iterated prisoner's dilemma game

Abstract

This paper addresses how players’ asymmetrical expectations of future interaction affect their cooperation in the two-player iterated prisoner's dilemma (IPD) game. A player’ expectation of future interaction reflects his/her willingness to continue the interaction with his/her opponent. With the application of a co-evolutionary learning model with a niching technique that is used to search optimal strategies for players, simulation experiments are conducted to present the cooperative or uncooperative outcomes between the players with distinct expectations. Results indicate that, if one player has higher expectation of future interaction than the other, the former may be exploited by the latter. Such exploitation is mainly due to the former player's higher tendency toward mutual cooperation, which triggers the latter player's unilateral defection. Considering that real-world games always involve uncertainty or external disturbance, the games with uncertain payoffs or noise are also performed. Results indicate that the exploitation also exists in the game with uncertain payoffs. However, it may be absent in the presence of high levels of noise. The reason is that the cooperative tendency of the high-expectation player declines with the increasing level of noise. As a result, the two players are engaged in only low levels of cooperation in the IPD game. Nevertheless, when asymmetrical noise is taken into account, it is the player disturbed with higher levels of noise that is exploited by the other. In other words, the player whose strategy is interfered with higher levels of noise is more afraid of endless mutual defection caused by noise, which makes he/she cooperate more than his/her opponent, even though he/she may have a lower expectation on their future interaction.