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The theory of iterated games provides a systematic framework to explore the players’ relationship and analyzing the behavior of rational players in a long-term. In these games, the behavior of strategies, especially in the cooperative behavior, becomes a dilemma, this dilemma arises when two cooperators receive a higher payoff than two defectors. Since in the Prisoner’s Dilemma game defectors dominate cooperators unless a mechanism for the evolution of cooperation is at work, thus, the purpose of this thesis is to study the cooperative behavior of strategies in the iterated prisoner’s dilemma game (IPD) and study how can this behavior evolve between players.
This thesis consists of four chapters, the first chapter is introductory and defines basic terminology used in the thesis. Many important topics about game theory have been addressed in this chapter, for example, the nature of games, describing strategic games, classifications of games, games in extensive and in normal form, mixed and pure strategies and the concept of a solution and Nash Equilibrium which play important role in the theory of games.
In chapter two, we provide a brief introduction about cooperation in the theory of games, the definition of cooperative dilemma and cooperation in repeated games. Moreover, we present the evolutionary game theory. This includes evolutionary stable strategies (ESS), evolutionary game dynamics, relationship between evolutionary and Nash equilibria and some examples on evolutionary stable strategies (ESS).
In the third chapter, we introduce some mechanisms for evolving the cooperative behavior in PD game. Also, we study the evolution of the cooperative behavior by combining two or three mechanisms together and find the transformed matrices for each situation. We derive the conditions for the evolution of cooperative behavior and study the (ESS) property of the strategies. Moreover, we derive the necessary conditions that make the cooperation risk- dominant and advantageous in a population in the context of the PD game. The results in this chapter have been published in Journal of Game Theory in 2015 entitled “Essam El-Seidy, Ali M. Almuntaser. (2015). On The Evolution of Cooperative Behavior in Prisoner’s Dilemma. Journal of Game Theory, 4(1): 1-5.”.
In the last chapter, we study the IPD game in which there is a relationship (0≤r≤1) between the players . We assume that ,when the players play the IPD game there is some noise , i.e. in each round, a player makes a mistake with probability ε leading to the opposite move. We define the transition rule of each automaton that depends on the initial state of the game and on the payoff of the last move. Then, we describe the method that we shall follow to compute the 16 x16 payoff matrix for IPD game with noise played by finite state automata. After calculating the payoff matrix we study the effect of different values of average relatedness and different values for the payoff values (R ,S ,T ,P) on the behavior of the 16 strategies. The findings in this chapter have been published in International Journal of Scientific & Engineering Research in 2015 under the name “Essam El-Seidy, Salah El Din S.Hussien and Ali M. Almuntaser (2015). On The Behavior of Strategies in Iterated Games Between Relatives , International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-2015.”.