Affiliations:
Department of Mathematics, Faculty of Science, Ain Shams University, Abbasia, Cairo, Egypt
Correspondence:
[*]
Corresponding author. Shimaa Atef, Department of Mathematics, Faculty of Science, Ain Shams University, Abbasia, Cairo, Egypt. E-mails: [email protected]; [email protected].
Abstract: Relatedness is necessary and causal in the development of social life. Interlayer relatedness is a measure of how one player’s decisions affect the decisions of other players in the game. The relatedness can be positive or negative. We had to determine how effective each strategy was under specific conditions, and how the correlation between players affected their payoffs. In this paper, we analytically study the strategies that enforce linear payoff relationships in the Iterated Prisoner’s Dilemma (IPD) game considering both a relatedness factor. As a result, we first reveal that the payoffs of two players and three players can be represented by the form of determinants as shown by Press and Dyson even with the factor.
