  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.
