The aim of the paper is to examine the notion of simple Kantian equilibrium in 2×2 symmetric games and their quantum counterparts. We focus on finding the Kantian equilibrium strategies in the general form of the games. As a result, we derive a formula that determines the reasonable strategies for any payoffs in the bimatrix game. This allowed us to compare the payoff results for classical and quantum way of playing the game. We showed that a very large part of 2×2 symmetric games, in which the arithmetic mean of the off-diagonal payoffs is greater than the other payoffs, have more beneficial Kantian equilibria when they are played with the use of quantum strategies. In that case, both players always obtain higher payoffs than when they use the classical strategies.The aim of the paper is to examine the notion of simple Kantian equilibrium in 2×2 symmetric games and their quantum counterparts. We focus on finding the Kantian equilibrium strategies in the general form of the games. As a result, we derive a formula that determines the reasonable strategies for any payoffs in the bimatrix game. This allowed us to compare the payoff results for classical and quantum way of playing the game. We showed that a very large part of 2×2 symmetric games, in which the arithmetic mean of the off-diagonal payoffs is greater than the other payoffs, have more beneficial Kantian equilibria when they are played with the use of quantum strategies. In that case, both players always obtain higher payoffs than when they use the classical strategies.

arXiv:2104.04698SymmetryMar 8, 20221 citation

Negating van Enk-Pike's assertion on quantum games OR Is the essence of a quantum game captured completely in the original classical game?

Nilesh Vyas, Colin Benjamin

S. J. van Enk and R. Pike in PRA 66, 024306 (2002), argue that the equilibrium solution to a quantum game isn't unique but is already present in the classical game itself. In this work, we debunk this assertion by showing that a random strategy in a particular quantum (Hawk-Dove) game is unique to the quantum game. In other words the equilibrium solution of the quantum Hawk-Dove game can not be obtained in the classical Hawk-Dove game. Moreover, we provide an analytical solution to the quantum $2\times2$ strategic form Hawk-Dove game using random mixed strategies. The random strategies which we describe are evolutionary stable implying both Pareto optimality and Nash equilibrium with their payoff's classically unobtainable.S. J. van Enk and R. Pike in PRA 66, 024306 (2002), argue that the equilibrium solution to a quantum game isn't unique but is already present in the classical game itself. In this work, we debunk this assertion by showing that a random strategy in a particular quantum (Hawk-Dove) game is unique to the quantum game. In other words the equilibrium solution of the quantum Hawk-Dove game can not be obtained in the classical Hawk-Dove game. Moreover, we provide an analytical solution to the quantum $2\times2$ strategic form Hawk-Dove game using random mixed strategies. The random strategies which we describe are evolutionary stable implying both Pareto optimality and Nash equilibrium with their payoff's classically unobtainable.

Jan 30, 20171 citation

On quantum game approach to correlated equilibrium

Piotr Frąckiewicz

Global Virtual ConferenceMay 16, 20163 citations

2\times2

strategic form Hawk-Dove game using random mixed strategies. The random strategies which we describe are evolutionary stable implying both Pareto optimality and Nash equilibrium with their payoff's classically unobtainable.