A dynamic game of coalition formation under ambiguity

In a previous paper, we generalized to the mixed strategy case the γ model of coalition formation (introduced by Hart and Kurz in Econometrica 51(4):1047–1064, 1983) for situations in which players have ambiguous expectations about the formation of the coalitions in which they are not involved; then we analyzed the corresponding evolutionary games. In this paper, we embody into the model rationality of the players; it follows that allowing for mixed strategies makes it impossible to construct unequivocally a von Neumann–Morgestein expected utility function coherent (in the sense of de Finetti B in Sul Significato Soggettivo della Probabilità, Fundamenta Mathematicae, T, vol XVIII, pp 298–329, 1931) to every strategy profile. We find out that if the multiplicity of coherent beliefs problem is approached by considering “ambiguity loving” players then existence results for classical static equilibria can be obtained in this model. Moreover, we provide conditions for the game to be dynamically playable and we find how the coalition structure beliefs might evolve coherently (according) to the evolution of the strategies.