Abstract
Players’ choices in quantum game schemes are often correlated by a quantum state. This enables players to obtain payoffs that may not be achievable when classical pure or mixed strategies are used. On the other hand, players’ choices can be correlated due to a classical probability distribution, and if no player benefits by a unilateral deviation from the vector of recommended strategies, the probability distribution is a correlated equilibrium. The aim of this paper is to investigate relation between correlated equilibria and Nash equilibria in the MW-type schemes for quantum games.
Highlights
Technological progress that occurred in the last few years made controllable manipulations of single quantum objects possible
I =0 for j, l j ∈ {0, 1, . . . , n − 1}. In this way we have shown that the correlated equilibrium in a bimatrix m × n game is a necessary condition for the existence of the Nash equilibrium (τ ∗, τ ∗ ) in ΓcMW
In quantum game theory it is required that a given quantum scheme coincides with the classical game under specific settings
Summary
Technological progress that occurred in the last few years made controllable manipulations of single quantum objects possible. In the general case of m × n bimatrix games, players’ strategies are identified with permutation matrices which are performed on a mn-level quantum system [4], and measurements are done. This simple model has found applications in many branches of game theory: from evolutionary games [5,6] to games in extensive form [7] and duopoly problems [8,9]. Our goal is to identify elements of a quantum scheme that can be described by classical terms This new approach may provide for further developments of quantum game theory. We formulated a new scheme for bimatrix games
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