Mixed Extensions of decision-form games

In this paper we define the canonical mixed extension of a decision form game. We motivate the necessity to introduce this concept and we show several examples about the new concept. In particular we focus our study upon the mixed equilibria of a finite decision form game. Many developments appear possible for applications to economics, physics, medicine and biology in those cases for which the systems involved do not have natural utility functions but are only capable to react versus the external actions.