Quantum horse racing game

In this research, we investigate the horse racing game, a two-player game with six strategies. Our objective is to develop a theoretical framework for the game by employing the process of quantization. The Nash equilibrium (NE) of the quantum horse racing game is analyzed through an examination of the payoff matrix, and the results are compared to those of the classical horse racing game. Our findings demonstrate that the quantum horse racing game features both pure and mixed strategy NE, whereas the classical horse racing game possesses only mixed strategy NE. Additionally, our results indicate that the quantum horse racing game can mitigate the risks associated with the zero-sum game while outperforming the classical game.