Quantum evolutionary stable strategies of 2-player, 2-strategy symmetric games

A. Iqbal, A.H. Toor

Z. W. Sun, Hua Jin

Quantum evolutionary stable strategies (ESSs) are considered as stable solutions to population games on the molecular level. The distributive diagram of the games is brought out in the light of their rescaled games, so that a convenient way to look for quantum ESSs of 2×2 symmetric games can be obtained. It is found that transpositions may take place when a game is quantized. They are related to the parameters in the classical payoff matrix and those of the initial quantum states. One can easily find quantum ESSs by referring to the tables and the figure shown in the main body. This paper draws an overall outline of NEs (Nash equilibria) and ESSs of this kind of game in the classical version as well as in the quantum version.

Jie Zhou, Лей Ма, Yun Li

F. Guinea, Miguel Angel Martin-Delgado

We apply several quantization schemes to simple versions of the Chinos game. Classically, for two players with one coin each, there is a symmetric stable strategy that allows each player to win half of the times on average. A partial quantization of the game (semiclassical) allows us to find a winning strategy for the second player, but it is unstable w.r.t. the classical strategy. However, in a fully quantum version of the game we find a winning strategy for the first player that is optimal: the symmetric classical situation is broken at the quantum level.

Gonzalo Abal, R. Donangelo, Hugo Fort

Ming Lam Leung

This paper unifies the concepts of evolutionary games and quantum strategies. First, we state the formulation and properties of classical evolutionary strategies, with focus on the destinations of evolution in 2-player 2-strategy games. We then introduce a new formalism of quantum evolutionary dynamics, and give an example where an evolving quantum strategy gives reward if played against its classical counterpart.