Existence of Berge equilibrium in conflicts under uncertainty

Abstract

The main tool for conflict resolution (equilibration) is the equilibrium strategy. Among the torrent of publications in this field, including the seven Nobel prize winners of 1994–2012, the Nash equilibrium is the fundamental one. Such equilibrium. however, does not necessarily exist. In this case, it is only natural to introduce a new notion of equilibrium, that of Berge. It was discussed in the paper which established existence of the Berge equilibrium in the mixed strategies and proposed sufficient conditions reducible to determination of the saddle point of a special Germeier convolution of the gain functions.