Affiliations: Department of Mathematics, Faculty of Science, Ain Shams University, Abbasia, Cairo, Egypt
Correspondence:
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Corresponding author. Shimaa Atef, Department of Mathematics, Faculty of Science, Ain Shams University, Abbasia, Cairo, Egypt. E-mails: [email protected]; [email protected].
Abstract: Decisions in many dilemmas are based on a combination of factors, including as incentive, punishment, reputation, and memory. The impact of memory information on cooperative evolution in multi-round games is a decision-making process in group evolution. The iterated prisoner’s dilemma is an excellent model for the development of cooperation amongst the payoff-maximizing individuals. Since tit-for-tat proved successful in Axelrod’s repeated prisoner’s dilemma tournaments, there has been a great deal of interest in creating new strategies. Every iterative prisoner’s dilemma method bases its decision-making on a specific duration of past contacts with the opponent, which is referred to as the memory’s size. This study examines the impact of strategy memory size on the evolutionary stability of n-person iterated prisoner’s dilemma strategies. In this paper, we address the role that memory plays in decision-making. We interested in the model of the Iterated Prisoner’s Dilemma game for three players with memory two, and we will look at strategies with similar behavior, such as Tit-For-Tat (TFT) strategies as well as Win Stay-Lose Shift (WSLS) strategies. As a result of this paper, we have shown that the effect of memory length is almost non-existent in the competitions of strategies that we studied.
