Three-person games with imperfect coalitions: a sociologically relevant concept in game theory

abstract: in chapter i, two main concepts are proposed for reconciling the diverging interests within a coalition, if side-payments are excluded. the first is to select the joint strategy from a top, defined by notions of dominance between correlated strategies. the second concept is called "ceremonial" and means a normative regulation of the process of consulting a random mechanism. several examples of such "ceremonials" are given. in the following chapter, the possibilities of relaxing the closedness condition for coalitions are discussed on a conceptual level. the resulting notion of imperfect coalitions is applied in the third chapter to three-person games, where it means a chain in the form, that i is connected with j and j with k, but i and k are not connected directly. if player j has in both coalitions (i,j) and (j,k) the role of assigning strategies to signals of the random-device, he can establish a signal-linkage that is optimal for him. given the probability with which thesame random-device is used in the coalition (i,j) as well as in (j,k) given furthermore the influence that j has under certain ceremonials on this probability, we can compute tripels of expected values for the players. these three-element vectors are functions of the pair of ceremonials adopted by the coalitions (i,j) and (j,k). the concluding chapter tries to relate the concepts and results obtained in the earlier chapters to the sociological literature. some suggestions about experimental work on games with imperfect coalitions are made. possible mathematical research on the relation of the vectors of expected values obtained in this paper and the solution theory is sketched.;