On signaling games with quantum chance move

We give formal conditions for a perfect Bayesian-type equilibrium in a quantum signaling game. We show that the conditions imply a classical perfect Bayesian equilibrium if the quantum game coincides with the classical one. Next, we extend the signaling game to include a quantum chance move. We prove that the classical relation between Nash equilibria and perfect Bayesian equilibria is preserved in that case—every perfect Bayesian-type equilibrium implies a Nash equilibrium, but the converse is not true. Lastly, we give a condition for equivalence between Nash equilibria and perfect Bayesian-type equilibria.