Quantum key distribution uses quantum mechanics to guarantee secure communication. BB84 is a widely used quantum key distribution that provides a way for two parties, a sender, Alice, and a receiver, Bob, to share an unconditionally secure key in the presence of an eavesdropper, Eve. In a new approach, we view this protocol as a three player static game in which Alice and Bob are two cooperative players and Eve is a competitive one. In our game model Alice’s and Bob’s objective is to maximize the probability of detecting Eve, while Eve’s objective is to minimize this probability. Using this model we show how game theory can be used to find the strategies for Alice, Bob and Eve.

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