Behavioral Equivalence of Extensive Game Structures

TL;DR

This paper characterizes when two extensive game structures with imperfect information are behaviorally equivalent, showing they can be transformed into each other through specific elementary transformations.

Contribution

It provides a necessary and sufficient condition for behavioral equivalence of extensive game structures using elementary transformations.

Findings

Behavioral equivalence characterized by elementary transformations

Transformation criteria involve interchanging moves and coalescing moves

Provides a formal method to identify equivalent game structures

Abstract

Two extensive game structures with imperfect information are said to be behaviorally equivalent if they share the same map (up to relabelings) from profiles of structurally reduced strategies to induced terminal paths. We show that this is the case if and only if one can be transformed into the other through a composition of two elementary transformations, commonly known as \textquotedblleft Interchanging of Simultaneous Moves\textquotedblright\ and \textquotedblleft Coalescing Moves/Sequential Agent Splitting.\textquotedblright