An interval noncooperative-cooperative biform game model based on weighted equal contribution division values

Abstract

This paper develops an interval noncooperative-cooperative biform game (referred to as the interval biform game in short hereafter) model that accounts for both strategy choice and coalition formation while also addressing profit allocation with interval coalition characteristic values. This interval biform game consists of four elements: a finite set of players, their strategy choices, coalitions, and interval coalition characteristic functions, and contains both noncooperative and cooperative parts. The payoffs of different strategies are not directly given a priori in the noncooperative part but obtained by solving interval cooperative games in the cooperative part. To solve the interval cooperative game, we extend a real-valued weighted equal contribution division (WECD) approach to an interval-valued version. Subsequently, an interval acceptability degree comparison method is introduced to compare the interval payoff values. We then establish existence and necessary conditions of pure strategy Nash equilibriums and derive a condition for a Nash equilibrium to be efficient in an interval biform game. Finally, numerical examples are furnished to illustrate the validity and applicability of the proposed framework.