الفهرس 
Basic Definitions and NotationOnly 14 pages are availabe for public view
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Abstract
Summary
The thesis topic is related to the Zero Determinant (ZD)strategies, which were concluded in research published in 2012 by researchers Press and Dyson. A player using these strategies can determine the return of the other player between mutual cooperation and mutual defection values regardless of the strategy the opponent uses. Also, a player using ZD strategies can impose a linear relationship in which the return can be greedily distributed.
The aim of this thesis is to apply ZD strategies in the iterated prisoner’s dilemma (IPD) when three players face each other. Show how a player using ZD strategies can dominate the game and control the opponents’ payoff regardless of the strategy used by the other players, even though he cannot determine the payoff for himself. Also, showing the possibility of using the extortion strategy when three players faced each other. Presenting the necessary conditions for choosing a strategy through which it determines the minimum and maximum returns of the opponents, as well as the conditions for choosing an unbeatable strategy from the rest of the opponents. This thesis consists of four chapters as follows:
In chapter one: the basic definitions of game theory and the concepts that were used within the thesis. Presenting game types in their normal and extensive form, and referring to basic concepts such as Nash equilibrium, simple and compound strategy, and the return function. Presenting the most famous examples in game theory, such as the prisoner’s dilemma, the battle of sexes, and Hawk-Dove game. There is a presentation of some conflicts and their division into cooperative or non-cooperative and the study of utility function according to the circumstances faced by the player.
In chapter two: The strategies of the ZD strategies were presented on the iterated prisoner’s dilemma in the stochastic game when two players faced each other. Presenting the transition matrix that shows the player’s transition from one state to another. Show all the advantages that the player who uses the ZD strategies can obtain and enable him to control the game as well as control the returns and clarify the necessary conditions to achieve these strategies.
In chapter three: We presenting ZD strategies when three players face each other in the iterated prisoner’s dilemma. where each player has two pure strategies, cooperation or defection, for one player will not affect in his strategy any of the other two players cooperate and any of them split, where each player expands on vector with 8-tuple dimensions with six independent variables. The transition matrix between three players is shown when the players selection changes from cooperation to defection and vice versa. We consider an iterated prisoner’s dilemma game where players meet multiple times and may all develop their own strategies depending on the opponents’ strategy and history of the game. The results obtained were achieved by assuming the use of one of the players, let it be “X”, ZD strategies. where X can assign the expected results of the opponents between the values of mutual cooperation and mutual defection. If a player using Zero-Determinate strategies tries to develop a strategy to determine his expected return, this leads to one possible strategy (1, 1, 1, 1, 0, 0, 0, 0) making the transition matrix equal to zero then this may not be able to determine its expected return. Finally, a player using ZD strategies can enforce a linear relationship for an extortionate share of payoff with a given range of 𝒳 and the expected payoff is calculated for each player.
In Chapter four: Presenting the necessary conditions for the strategy used by the player who uses ZD strategies on the iterated prisoner’s dilemma game to obtain an indomitable strategy from other players. A player who is familiar with ZD strategies can also control the minimum and maximum returns of his/her opponents by applying some necessary and sufficient conditions in the strategy used by the player.