A Note on Kuhn's Theorem with Ambiguity Averse Players

TL;DR

This paper examines the limitations of Kuhn's Theorem in extensive games when players are ambiguity averse and employ maxmin decision rules, challenging the theorem's applicability beyond expected utility maximizers.

Contribution

It constructs an example demonstrating that Kuhn's Theorem does not hold in environments with ambiguity averse players using maxmin decision rules.

Findings

Kuhn's Theorem fails with ambiguity averse players.

Ambiguity aversion affects strategy equivalence in extensive games.

The example highlights the limits of traditional game-theoretic assumptions.

Abstract

Kuhn's Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrate the limits of Kuhn's Theorem in an environment with ambiguity averse players who use maxmin decision rule and full Bayesian updating.