Mixed Extensions of decision-form games

TL;DR

This paper introduces the canonical mixed extension of decision form games, focusing on mixed equilibria, with potential applications across various fields where systems react to external actions without natural utility functions.

Contribution

It defines and motivates the concept of mixed extensions in decision form games, providing foundational examples and exploring equilibrium properties.

Findings

Introduction of the canonical mixed extension concept

Analysis of mixed equilibria in finite decision form games

Potential applications in diverse scientific fields

Abstract

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.