Fuzzy Bargaining Games: Conditions of Agreement, Satisfaction, and Equilibrium

Game theory in its several variants is widely recognized as a contribution to social and economic modeling. One relevant development of classical game theory, Generalized Game Theory (GGT), entails its extension and generalization through the formulation of the mathematical theory of rules and rule complexes. Social theory concepts such as norm, value, belief, role, social relationship, and institution as well as game can be defined in a uniform way in terms of rules and rule complexes. Among the applications, one major initiative has been the conceptualization of fuzzy games and equilibria. In this paper a GGT model of 2-person fuzzy bargaining games is outlined. Two key concepts are applied: (1) players’ value (or “utility”) structures consisting of ideal points or expectation levels, on the one hand, and limits of acceptance, on the other; (2) fuzzy judgment functions in which players deal with imprecise information and use approximate reasoning in making decisions and negotiating agreements. Such fuzzy judgment functions can take into account economic, socio-psychological, and cultural and institutional aspects of the bargaining context, which affect the bargaining process in specifiable ways. Several significant results are obtained from the application of this model: the opportunities (or not) for agreement, the participants’ satisfaction levels with an agreement, and the question whether or not the agreed “price” is an equilibrium price.