Subbalanced games and bargaining sets (Q818541)

In this paper, the authors define \(\text{MB}_{1}\), a modified version of \textit{R. Vohra}'s bargaining set [J. Math. Econ. 20, 19--34 (1991; Zbl 0719.90101)]. An example is provided to show that \(\text{MB}_{1}\) need not exist in a non-superadditive weakly balanced game. To study the existence of \(\text{MB}_{1}\), a new version of the KKM theorem is proposed and the concept of a subbalanced game is introduced. The authors also provide conditions for the non-emptiness of \(\text{MB}_{2},\) a bargaining set introduced by \textit{L. Zhou} [Games Econ. Behav. 6, 512--526 (1994; Zbl 0807.90143)] which imposes the additional restriction that the objective coalition not be a subset of the counterobjecting coalition.