Quantum signaling game

TL;DR

This paper introduces a quantum framework for signaling games, demonstrating that quantum strategies can produce nonclassical outcomes and analyzing equilibrium concepts within this quantum context.

Contribution

It develops a quantum scheme for signaling games, extending classical models with quantum strategies and analyzing equilibrium refinements.

Findings

Quantum signaling games can produce nonclassical results.

The model allows for quantum extensions with unitary operators.

Analysis of Nash and Bayesian equilibria in the quantum setting.

Abstract

We present a quantum approach to a signaling game; a special kind of extensive games of incomplete information. Our model is based on quantum schemes for games in strategic form where players perform unitary operators on their own qubits of some fixed initial state and the payoff function is given by a measurement on the resulting final state. We show that the quantum game induced by our scheme coincides with a signaling game as a special case and outputs nonclassical results in general. As an example, we consider a quantum extension of the signaling game in which the chance move is a three-parameter unitary operator whereas the players' actions are equivalent to classical ones. In this case, we study the game in terms of Nash equilibria and refine the pure Nash equilibria adapting to the quantum game the notion of a weak perfect Bayesian equilibrium.