On the relevance of alternatives in bargaining: generalized average pay-off solutions

We generalize the average pay-off solution proposed by Anbarci (Can J Econ 28:675–682, 1995), which depends on all the alternatives, and show that the Nash and Kalai–Smorodinsky solutions are limits of generalized average pay-off solutions. We formalize the notion of relevant alternatives and compare solutions in terms of the relevance of alternatives. I am much indebted to Roberto Serrano for his guidance and many discussions, and William Thomson for his numerous detailed suggestions for improvements. I thank Youngsub Chun, Michael Maschler, Yeneng Sun, Rajiv Vohra, Oscar Volij, Myrna Wooders, an associate editor, anonymous referees, and seminar participants at Brown University, the National University of Singapore, and the 2003 North American Summer Meetings of the Econometric Society for valuable comments. I gratefully acknowledge research support from Brown University through an Eccleston Fellowship award.