Game theory is a formal, mathematical discipline which studies situations of competition and cooperation between several parties. This course aims at providing an introduction to this research field. After following this course, the student is able to:
- model a given decision situation of conflict or cooperation in game theoretical terms.
- compute solutions for non-cooperative, cooperative and stochastic games.
- explain and derive structural properties of non-cooperative, cooperative and stochastic games.
- design and analyse algorithms for non-cooperative, cooperative, and stochastic games and interpret solution concepts of games in context and in applications.
Game theory is a formal, mathematical discipline which studies situations of competition and cooperation between several parties. As a mathematical discipline it has been of eminent importance for developments in the economic and political sciences since the beginning of the last century, but since the beginning of this millennium, it plays an increasing role also in Operations Research and the Engineering sciences. No less than eight game theorists have received Nobel prizes, with prominent examples such as Nash, Aumann, Shapley, Hurwicz and Myerson. The course Game Theory aims at giving a first introduction to noncooperative, cooperative and stochastic game theory. In noncooperative games the players are selfish and they only care about their personal wellbeing. Each of them will choose a strategy, unaware of the strategy of the other players, and tries to maximize his own payoff. The Nash equilibrium concept is of importance here. In cooperative games the players do have interest in possible cooperation. They are allowed to make binding agreements. An important question is how the joint payoff should be reallocated among the participating players in a fair way. Stochastic games may roughly be described as a dynamic series of noncooperative games in which the current game and the actions of the players determine which game will be played in the next period. In these games important concepts are optimal strategies for the players and the value of the game. In all three parts, attention is paid to the design of algorithms for efficient computation of solutions. The theory will be illustrated, where possible, with examples and applications.