Abstract
Over the last twenty years, quantum game theory has given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing bimatrix games introduced by J. Eisert, M. Wilkens and M. Lewenstein. The scheme assumes that players’ strategies are unitary operations and the players act on the maximally entangled two-qubit state. The quantum nature of the scheme has been under discussion since the article by Eisert et al. came out. The aim of our paper was to identify some of non-classical features of the quantum scheme.
Highlights
We review relevant material connected with the notion of strategic-form games and payoff regions in those games
We find that the strategy profiles (32) are no longer Nash equilibria in (25)
It is not obvious that playing the quantum game really changes the rules of the game if we look at a unitary operator as an extension of a mixed strategy
Summary
Are just a very smart part of the huge literature devoted to the EWL scheme It was shown in [1] that a quantum way of playing the Prisoner’s Dilemma game can lead to a reasonable and Pareto efficient outcome. Does the quantum solution provided by the EWL scheme really solve the input classical game? (to what extent the quantum solution solves the underlying classical game). Can the quantum solution be obtained in a classical game? There have been discussions about van Enk and Pike’s arguments It is claimed in [20] that the EWL approach to the Hawk–Dove game enables the players to obtain a game result that is not achievable in the classical game. The purpose of this article is, on the one hand, to show that the form of the scheme considered in [19,20,21] does not fully describe the EWL scheme, on the other hand, to draw attention to other non-classical properties of the scheme
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