A characterization of path dependent modes of behavior

In this paper we modify the procedure that explains the coexistence of agents with different modes of behavior studied by Wilson [Wilson R. (1972) Consistent Modes of Behavior. "Technical Report 55, Institute for Mathematical Studies in the Social Sciences, Standford University.] and Roth [Roth, A. (1984) Stable Coalition Formation: Aspects of a Dynamic Theory, Coalitions and Collective Action, 228–233, edited by M. J. Holler. Wuerzberg, Physica-Verlag.]. In particular, we characterize the outcomes of this procedure in structural terms for abstract relational systems by establishing a new solution concept called the admissible hierarchic set. This concept is a refinement of the hierarchic solution [Kosheleva O. M. and V. Kreinovich, (1990) A Hierarchic Analog of von Neumann–Morgenstern Solution Always Exists, Institute of Mathematical Economics, Bielefeld, Germany. Report No. 90-26.] which is a generalization of the von Neumann and Morgenstern solution.