Quantum Strategies

TL;DR

This paper explores how quantum strategies in game theory enable players to reach outcomes beyond classical possibilities, including new equilibria and Pareto improvements, especially in private information games.

Contribution

It demonstrates that quantum strategies can produce equilibria not attainable classically and break classical equivalences like Kuhn's theorem in private information games.

Findings

Quantum strategies lead to correlated equilibria in full information games.

Quantum technology allows outcomes not achievable by classical means in private information games.

Players can attain Pareto superior outcomes using quantum strategies.

Abstract

We investigate the consequences of allowing players to adopt strategies which take advantage of quantum randomization devices. In games of full information, the resulting equilibria are always correlated equilibria, but not all correlated equilibria appear as quantum equilibria. The classical and quantum theories diverge further in games of private information. In the quantum context, we show that Kuhn's equivalence between behavioral and mixed strategies breaks down. As a result, quantum technology allows players to achieve outcomes that would not be achievable with any classical technology short of direct communication; in particular they do not occur as correlated equilibria. In general, in games of private information, quantum technology allows players to achieve outcomes that are Pareto superior to any classical correlated equilibrium, but not necessarily Pareto optimal. A simple economic example illustrates these points.