Title: Θεωρία παιγνίων και εφαρμογές στην οικονομική επιστήμη
Abstract: This thesis deals with the evolutionary game theory and how it applies to economics. First of all, it is necessary to refer the original game theory and to analyze the key elements and then move to the analysis of evolutionary game theory.
In the first part of this study, therefore, we indicate what is on game theory. Specifically, in the first chapter is a brief history of game theory and the second chapter defined game theory as a formal study examining the rationality in a business environment and presents the basics elements of a game. Also, at this chapter i reffer to the description of games, namely, games of cooperation and non-cooperation, and the two ways of representing their strategy, the normal form (matrix) and the extensive form (game tree).
The third chapter sets out the dominant strategy and the corresponding dominant strategy equilibrium and in the fourth chapter we define the Nash Equilimbrium, which is the standard notion of equilibrium in economics. In these two chapters (third and fourth) there are examples of the application for better understanding, and we analyze the prisoner's dilemma, which is the most classic example of game theory. If there is no Nash Equilimbrium (this could happen at narmal strategy games) the game is solved by mixed strategies, which are analyzed in the fifth chapter.
Continuing, at the sixth chapter we can see the extensive games with perfect information and we analyze the method of backward induction. In the seventh chapter, we can see the extensive games with imperfect information and the eighth chapter refers to the zero-sum games and how they can be used together with randomized algorithms for the analysis of problems on-line calculation. Finally, the first part closes with an example application of game theory, the auctions.
The question is “What happens when a game is played more than once?” The answer comes from the second part of this thesis in which we analyse the evolutionary game theory. In the first two chapters of this part we define evolutionary games, we refere where evolutionary games might be applicable and why economic application aren’t common already.
The third and fourth chapter are the most important chapters of the second part. At the third chapter we present the model of the evolutionary game and its elements (expected payoffs, population, states). We describe the stage game which is defined by a fitness function and we emphasize at its two linear specifications. Then we make a full analysis one of the most representative example of evolutionary game theory, the Hawk-Dove game.
This game has two types of players, aggressive (Hawk) and defensive (Dove), which reflects the situation where there is a competitive and an uncompetitive business, and the point is to find which of the two types will eventually prevail. Based on a differential equation, we conclude that the result depends on three parameters: the initial population, the probability with which each strategy is played and the payoff matrix. All this leads in a strategy which is known as evolutionary stable (ESS).
In chapter five, we define the Nash Equilibrium, the Evolutionary Stable Strategy (ESS) and Evolutionary Equilibrium (EE) and in chapter six we analyze the local classification of low dimensions systems. To make clear the applicability of all those we mention at this thesis, we are closing with three examples. More specific we analyze three well-known games which were used by the political and paralleled with situations they had to face with.
Publication Year: 2014
Publication Date: 2014-10-29
Language: en
Type: dissertation
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