Quantum Information Approach to Normal Representation of Extensive Games

J. Phys. A: Math. Theor.

2014

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 threeparameter 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.

Section: Introductionmentioning

confidence: 99%

Quantum signaling game

J. Phys. A: Math. Theor.

2014

“…Though it was created for research on Nash equilibria in quantum 2 × 2 games, it has also found application in studying some of the refinements of a Nash equilibrium like evolutionarily stable strategies [2]. Moreover, it has been proved that the MW scheme is applicable to finite extensive games [3] and even various problems of duopoly [4,5,6]. These recent papers show uninterrupted interest in research on quantum games played according to the MW idea and they provide sufficient motivation to improve the existing results.…”

Section: Introductionmentioning

confidence: 99%

A Comment on the Generalization of the Marinatto–Weber Quantum Game Scheme

2013

Acta Phys. Pol. B

Iqbal and Toor [Phys. Rev. A 65, 022306 (2002)] and [Commun. Theor. Phys. 42, 335 (2004)] generalized the Marinatto-Weber quantum scheme for 2 × 2 games in order to study bimatrix games of 3 × 3 dimension, in particular the Rock-Paper-Scissors game. In our paper we show that Iqbal and Toor's generalization exhibits certain undesirable property that can considerably influence the game result. To support our argumentation, in the further part of the paper we construct the protocol corresponding to the MW concept for any finite bimatrix game that is free from the fault.

“…Though it was created for research on Nash equilibria in quantum 2 × 2 games, it has also found an application in studying some of the refinements of a Nash equilibrium, such as evolutionarily stable strategies [2,3]. Moreover, the MW scheme turns out to be applicable to finite extensive games [4]. Among other applications, the problem of duopoly is worthy noting.…”

Section: Introductionmentioning

confidence: 99%

A new model for quantum games based on the Marinatto–Weber approach

J. Phys. A: Math. Theor.

2013

The Marinatto-Weber approach to quantum game is a straightforward way to apply the power of quantum mechanics to classical game theory. In the simplest case, the quantum scheme is that players manipulate their own qubits of a two-qubit state either with the identity 1 or the Pauli operator σ x . However, such a simplification of the scheme raises doubt as to whether it could really reflect a quantum game. In this paper we put forward examples which may constitute arguments against the present form of the Marinatto-Weber scheme. Next, we modify the scheme to eliminate the undesirable properties of the protocol by extending the players' strategy sets.