Subject:

Stochastics and operational research 
Abstract:

Game Theory is a mathematical theory to model and analyze socalled conflict situations. In a conflict situation a group of goalseeking individuals (called players), each endowed with his own knowledge, capacities, behavior, likes and dislikes, interact and thereby jointly generate an outcome. Each of the players has a different evaluation of the outcome. The central question in Game Theory is what each player should do, to promote his interest optimally. In the first part of this thesis this question is studied in case of (exchange) economies. Here, the existence and properties of certain solution concepts (e.g., core, bargaining sets and envyfreeness) are studied in economies in which the players can exchange indivisible objects with each other. In the second part of the thesis Coorporative Game Theory is used to allocate the profits/costs of certain resource sharing problems. First, we study a treenetwork problem in which the players can earn some revenue. We propose the nucleolus as a solutionrule and we provide an polynomial time algorithm to compute it. Furthermore, a characterization of the nucleolus as a solutionrule for trees with revenues is provided. In the second resource sharing problem, we study socalled processing situations. Here, certain costs have to be allocated arising from penalties on jobs that have to be completed. The main result provides an allocation of the the total costs which can be considered to be fair in terms of the core. The final chapter of the thesis provides evolutionary foundations for the concept of the Nashequilibrium in Noncooperative Game Theory.
