Fuzzy-Inspired Hierarchical Version of the von~Neumann-Morgenstern Solutions as a Natural Way to Resolve Collaboration-Related Conflicts

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Martha Osegueda Escobar, The University of Texas at El PasoFollow

Publication Date

6-2016

Comments

Technical Report: UTEP-CS-16-24a

To appear in Proceedings of International IEEE Conference on Systems, Man, and Cybernetics SMC'2016, Budapest, Hungary, October 9-12, 2016.

Abstract

In situations when several participants collaborate with each other, it is desirable to come up with a fair way to divide the resulting gain between the participants. Such a fair way was proposed by John von Neumann and Oscar Morgenstern, fathers of the modern game theory. However, in some situations, the von Neumann-Morgenstern solution does not exist. To cover such situations, we propose to use a fuzzy-inspired hierarchical version of the von Neumann-Morgenstern (NM) solution. We prove that, in contrast to the original NM solution, the hierarchical version always exists.