Details

Autor(en) / Beteiligte

• Grahn, Sofia Camilla Helena

Titel

Topics in cooperative game theory

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2001

Link zum Volltext

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• A class of cooperative games arising from shortest path problems is defined. These shortest path games are shown to be totally balanced and allow a population-monotonic allocation scheme. Possible methods for obtaining core elements are indicated; first, by relating to the allocation rules in taxation and bankruptcy problems, second, by constructing an explicit rule that takes opportunity costs into account by considering the costs of the second best alternative and that rewards players who are crucial to the construction of the shortest path. Finally, noncooperative games arising from shortest path problems are introduced, in which players make bids or claims on paths. The core allocations of the cooperative shortest path game coincide with the payoff vectors in the strong Nash equilibria of the associated noncooperative shortest path game. In this paper it is shown that the core and the bargaining sets of Davis-Maschler and Zhou coincide in a class of shortest path games. No solution concept is population monotonic on the entire set of transferable utility games with a population monotonic allocation scheme. Therefore, two different criteria, maximality and nonextendibility, are introduced to evaluate the performance of solution concepts as population monotonic allocation devices. These two measures are shown to be equivalent and maximal (or nonextendible) solution concepts are characterized. The aspiration based solution is the maximal solution concept that satisfies an additional fairness property, in the sense that gains or sacrifices are evenly distributed over the players. An axiomatization of this solution concept is provided. A set of necessary and sufficient conditions for convexity of a transferable utility game is provided and shown to be minimal: none of the conditions is redundant. The result is used to provide an axiomatization of the Shapley value on the set of convex games.