Kalai-Smorodinski Bargaining Solution Equilibria

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don’t have an a-priori opinion on the relative importance of all these criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution (Kalai and Smorodinsky, Econometrica 43:513–518, 1975). We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points. Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations; in particular, we consider the extension to multicriteria games of the Selten’s trembling hand perfect equilibrium concept and prove that perfect Kalai-Smorodinsky bargaining solution equilibria exist and properly refine both the perfect equilibria and the Kalai-Smorodinsky bargaining solution equilibria.