UTA Department of Mathematics

Mathematics and Statistics Colloquium

Date/Time/Room: Friday (11/17/2006) at 2:30pm in 304 Pickard Hall

Speaker: Dr. Javier Arin, Professor
Foundations of Economic Analysis I Department, The University of the Basque Country, Spain

"Coalitional games with veto players: Consistency, Monotonicity and Nash outcomes"

Abstract: In 1997, Dagan, Serrano and Volij presented a simple non-cooperative game for bankruptcy problems. In the game the player with highest claim has a special role. He makes a proposal and the rest of the players in a given order, accept or reject that proposal sequentially. In case of rejection the conflict is solved bilaterally, applying a normative solution concept to a special two-claimant bankruptcy problem. Therefore for any solution defined in the class of two-person bankruptcy problems a non-cooperative game can be formed. They prove that, if the solution satisfies certain properties, the outcome of any Nash equilibrium of the game coincides with the consistent allocation of the solution used to solve the bilateral conflict.

The aim of this paper is to adapt the non cooperative game presented by Dagan, Serrano and Volij for bankruptcy problems to the context of coalitional games with veto players. In our model, a veto player is the proposer and, similarly to Dagan, Serrano and Volij, in case of a negative answer from a responder a bilateral resolution is formulated. Therefore, the game can be seen as a hybrid of cooperative and non-cooperative games. The paper does not try to design a pure non-cooperative game for implementing any particular cooperative solution concept. The paper investigates which are the Nash outcomes of this particular hybrid game and why the Nash outcomes differ from well-known cooperative solution concepts. We investigate the relationship between the Nash outcomes of the game and solution concepts of cooperative games such as the nucleolus, kernel and the egalitarian core.