Robust Equilibria in Generic Extensive form Games

TL;DR

This paper establishes an index-theoretic characterization of hyperstable equilibrium components in generic extensive-form games, proving a conjecture and illustrating computation methods with economic examples.

Contribution

It proves the 2-player case of a conjecture linking equilibrium components' essentiality to their index, advancing the understanding of hyperstability in extensive-form games.

Findings

Proves the 2-player case of the conjecture on equilibrium components.

Provides methods to compute hyperstable equilibria in economic examples.

Shows how hyperstability predictions compare with other solution concepts.

Abstract

We prove the 2-player, generic extensive-form case of the conjecture of Govindan and Wilson (1997a,b) and Hauk and Hurkens (2002) stating that an equilibrium component is essential in every equivalent game if and only if the index of the component is nonzero. This provides an index-theoretic characterization of the concept of hyperstable components of equilibria in generic extensive-form games, first formulated by Kohlberg and Mertens (1986). We also illustrate how to compute hyperstable equilibria in multiple economically relevant examples and show how the predictions of hyperstability compare with other solution concepts.