الفهرس 
Analyzing Related Strategic Behavior Through Strictly Alternating Interactions with Memory TwoOnly 14 pages are availabe for public view
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Abstract
This work focuses on game theory, which does not dictate how a player ought to approach a particular game. Rather, it is a set of ideas and resources for breaking down these mathematical operations. It doesn’t teach you how to play the game; instead, it describes characteristics of specific gameplay approaches that you could find intriguing. Even when the analysis suggests a particular course of action to win the game, it does so with the understanding that every player is exerting every effort. The majority of players penalize their opponents for blunders, but this op- tion is never provided.
Game theory has applications in many fields such as computer science, sys- tems, social science domains, philosophy, public health, biology, economics, physics, networks, business, mathematics, traffic engineering, and political science.
This Ph.D. thesis deals with Prisoners’ Dilemma model which the most impor- tant model in Game theory where in the second and third chapters, we interested in two-player iterated Prisoners’ Dilemma Games and in the forth and fifth chap- ters, we interested in three-player iterated Prisoners’ Dilemma Games. Moreover in chapter six, we study two and three player but for zero-determinant strategies.
Our thesis is organized as follows:
1. In Chapter 1, we present the basics needed in the thesis and it contains the most important definitions, examples and theorems, where we explain some basics of Game Theory, Prisoner’s Dilemma, Markov matrix, Payoffs and strategies. Fur- thermore, we state some previous studies in Game Theory that we follows up with our study.
2. In Chapter 2, using r as a relationship coefficient in the alternative iterated prisoner’s dilemma with memory two, we examined how the players’ relationships affected the strategies’ behaviors. The new result is already published in the Jour-nal of Information Sciences Letters, 12, No. 6, 2483-2494, 2023, ISSN 2090-
9551, http://dx.doi.org/10.18576/isl/120625.
under titled: Analyzing Related Strategic Behavior Through Strictly Alternat- ing Interactions with Two-Memory Length.
3. In Chapter 3, we examined M/M/2/∞ through various Game Theory modes, including strictly alternating, random alternating, and simultaneous games. We also derived the expected waiting time for some of these models. The new result is under review in the Journal of Applied Mathematics and Information Sciences.
under titled: Simultaneous and Alternating Models via Queuing System.
4. In Chapter 4, We created the Prisoner’s Dilemma Game extension model, which has three players instead of two. We also analyzed competitions involv- ing certain unique strategy types that share characteristics with the Win Stay-Lose Shift. Therefore, we used various graphs and numerical numbers to indicate which of them was the best and which was the largest in the reward. We also spoke about how players’ relatedness affects how strategies behave. The new result is already published in the Journal of Information Sciences Letters, 12, No. 4, 1875-1889 (2023), ISSN 2090-9551, http://dx.doi.org/10.18576/isl/120412.
under titled: Monitor Reaction of Win Stay-Lose Shift Strategies in Iterated Three-Player Prisoner’s Dilemma Game.
5. In Chapter 5, We talked about the part memory plays in making choices. We examined strategies with comparable behavior, such as Win Stay-Lose Shift (WSLS) and Tit-For-Tat (TFT) strategies, because we were interested in the model of the Iterated Prisoner’s Dilemma Game for three players with memory two. Con- sequently, we have demonstrated that the influence of memory duration is nearly nonexistent in the strategy competitions that we examined. The new result is al- ready published in the Journal of Journal of Intelligent and Fuzzy Systems, vol. 46, no. 4, pp. 8375-8388, (2024)., ISSN 1064-1246,
http://dx.doi.org/10.3233/JIFS-233690.
under titled: Tit-For-Tat and Win Stay-Lose Shift Strategies via Memory-Two.
6. In Chapter 6, We studied Zero Determinant (ZD). First, we demonstrate that even with the relatedness factor, the payoffs for two and three players can be rep- resented by the determinant form as demonstrated by Press and Dyson. To do this, we conducted an analytical examination of the Strategies used in the Iterated Pris- oner’s Dilemma (IPD) game to uphold linear reward connections. The new result is already published in the Journal of Journal of Intelligent and Fuzzy Systems,
(2024)., ISSN 1064-1246, http://dx.doi.org/10.3233/JIFS-239406.
under titled: Relatedness in Zero-determinant Strategies.
7. In Thebibliography: We display all the references used and referred to in the thesis.