# Compactification of Extensive Game Structures and Backward Dominance Procedure

## TL;DR

This paper explores how invariant transformations of extensive game structures relate to the backward dominance procedure, providing characterizations for behavioral equivalence and conditions for efficiency improvements.

## Contribution

It characterizes behavioral equivalence via classical transformations and links these to backward dominance and generalized backward induction.

## Key findings

- Behavioral equivalence characterized by classical Coalescing and modified Interchange/Simultanizing.
- Conditions identified for transformations that enhance backward dominance efficiency.
- Discussion of relationships between transformations and Bonanno's generalized backward induction.

## Abstract

We study the relationship between invariant transformations on extensive game structures and backward dominance procedure (BD), a generalization of the classical backward induction introduced in Perea (2014). We show that behavioral equivalence with unambiguous orderings of information sets, a critical property that guarantees BD's applicability, can be characterized by the classical Coalescing and a modified Interchange/Simultanizing in Battigalli et al. (2020). We also give conditions on transformations that improve BD's efficiency. In addition, we discuss the relationship between transformations and Bonanno (2014)'s generalized backward induction.