A Finite Characterization of Perfect Equilibria

TL;DR

This paper derives an explicit finite bound for the levels in Lexicographic Probability Systems used to characterize perfect equilibria, advancing theoretical understanding in game theory.

Contribution

It provides a formula for the finite bound on LPS levels in the characterization of perfect equilibria, building on recent developments in Real Algebraic Geometry.

Findings

Explicit formula for the bound on LPS levels

Advances theoretical understanding of perfect equilibria

Utilizes recent results in Real Algebraic Geometry

Abstract

Govindan and Klumpp [7] provided a characterization of perfect equilibria using Lexicographic Probability Systems (LPSs). Their characterization was essentially finite in that they showed that there exists a finite bound on the number of levels in the LPS, but they did not compute it explicitly. In this note, we draw on two recent developments in Real Algebraic Geometry to obtain a formula for this bound.