Polytope-form games and Index/Degree Theories for Extensive-form games

TL;DR

This paper develops an index theory for extensive-form games with strategy sets as polytopes, extending equilibrium analysis to more general game structures with multiaffine payoffs.

Contribution

It introduces a novel index theory for extensive-form games where strategies form polytopes and payoffs are multiaffine, broadening the scope of equilibrium analysis.

Findings

Established an index theory for polytopal strategy spaces

Extended equilibrium concepts to multiaffine payoff functions

Provided topological insights into mixed strategy equivalences

Abstract

We present an index theory of equilibria for extensive form games. This requires developing an index theory for games where the strategy sets of players are general polytopes and their payoff functions are multiaffine in the product of these polytopes. Such polytopes arise from identifying (topologically) equivalent mixed strategies of a normal form game.