Properties and applications of dual reduction

TL;DR

This paper explores the dual reduction process in finite games, demonstrating its ability to simplify game analysis while preserving equilibria, and discusses various applications and properties of this method.

Contribution

It introduces applications of dual reduction and investigates its properties, highlighting its usefulness in studying Nash and correlated equilibria.

Findings

Dual reduction preserves all equilibria of the original game.

It simplifies the analysis of complex finite games.

The paper demonstrates practical applications of dual reduction.

Abstract

The dual reduction process, introduced by Myerson, allows to reduce a finite game into a smaller dimensional game such that any equilibrium of the reduced game is an equilibrium of the original game. This holds both for Nash equilibrium and correlated equilibrium. We present examples of applications of dual reduction and argue that this is a useful tool to study Nash equilibria and correlated equilibria. We then investigate its properties.