Coalitional ZP-Equilibrium in Games and its Existence

We introduce a solution concept for games in normal form with undetermined parameters, coalitional ZP-equilibrium, based on the notions of Z-equilibrium of [Zhukovskii and Chikrii [1994] Linear quadratic differential games, Kiev, Naoukova Doumka] and ZS-equilibrium of [Larbani and Lebbah [1999] A concept of equilibrium for a game under uncertainity. Europ. J. Oper. Res. 117, 145-156]. For each coalition structure, ZP-equilibrium ensures both the stability of the partition and equilibrium of coalitional strategies (in Pareto sense). We show that under some quasiconcavity conditions on payoff functions, the coalitional ZP-equilibrium exists in compact, convex and continuous normal form games involving undetermined parameters.