Cooperative Game Theory with Nontransferable Utility

Abstract

AbstractThe central assumption of the cooperative game theory, that agents can impose binding agreements among themselves, is a huge step from the settings of the noncooperative game for acknowledging cooperative nature and capacity of economic agents. Yet, it is also a source of criticism for being “naive” to underestimate the complex dynamics among agents. When the cooperative game theory is utilized on top of the convenience of the transferable utility (TU) assumption, such criticism for being oversimplified and unrealistic is amplified. On the other hand, when detailed information on individual payoff scheme for various coalition structures is available, nontransferable utility (NTU) assumption can be accommodated.This is an introductory article that surveys a few central advances in game theory on NTU cooperative game situation. First, common criticisms of TU assumptions are presented, providing a motivation for the development of the NTU theory. Next, the role of the Nash bargaining solution in the development of the NTU theory is presented. Then, a few attempts to provide effectivity criteria for NTU settings in specifying the coalitional function is presented, which allows one to specify a coalitional‐form NTU game. Subsequently, the definition of the NTU coalitional form game is presented. Then, the NTU version of the definition and the theory of the core are described. Next, a few value concepts of NTU games, primarily the Shapley NTU value, are described, utilizing a few numerical examples. Finally, the axiomatization approach that has been fruitful in characterizing and comparing various NTU solution concepts is briefly surveyed.