Supersymmetry and quantum games

In this paper we show the connection between the supersymmetry and quantum games. 1 Quantum games Game theory is the study of rational decision making of competing agents in some conflict situation. It was developed in the 1930’s in the context of economic theory and was first formalized by von Neumann and Morgenstern in The Theory of Games and Economic Behavior [1]. Subsequently much work was done on game theory and it is now a mature discipline used in areas such as the social sciences, biology and engineering. In recent time it is believed that quantum mechanics has the potential to bring about a spectacular revolution in quantum game. The combination of quantum mechanics and game theory promises to improve the odds of winning and may provide new insight into novel many areas as military warfare, anthropology, social psychology, economics, politics, business, philosophy, biology, physics and cryptology. With the recent interest in quantum computing and quantum information theory, there has been an effort to recast classical game theory using quantum probability amplitudes, and hence study the effect of quantum superposition, interference and entanglement on the agents’ optimal strategies. A natural question arise: can supersymmetric quantum mechanics play a role in quantum game theory. We know that a quantum game may be regarded as a family of games provided by quantum correlations which are absent in classical settings, and our geometric