Wireless Secret Sharing Game between Two Legitimate Users and an Eavesdropper

Wireless secret sharing is crucial to information security in the era of Internet of Things. One method is to utilize the effect of the randomness of the wireless channel in the data link layer to generate the common secret between two legitimate users Alice and Bob. This paper studies this secret sharing mechanism from the perspective of game theory. In particular, we formulate a non-cooperative zero-sum game between the legitimate users and an eavesdropper Eve. In a symmetrical game where Eve has the same probability of successfully receiving a packet from Alice and Bob when the transmission distance is the same, we show that both pure and mixed strategy Nash equilibria exist. In an asymmetric game where Eve has different probabilities of successfully receiving a packet from Alice and Bob, a pure strategy may not exist; in this case, we show how a mixed strategy Nash equilibrium can be found.