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.

翻译：无线秘密共享对于在物联网时代的信息安全至关重要。 一种方法是利用数据链接层无线频道随机性的影响, 产生两个合法用户爱丽丝和鲍勃之间的共同秘密。 本文从游戏理论的角度研究这一秘密共享机制。 特别是, 我们制定合法用户和窃听者夏娃之间不合作的零和零和游戏。 在对称游戏中, 夏娃在传输距离相同时同样有可能从爱丽丝和鲍勃那里成功收到包裹, 我们显示存在纯和混合战略Nash 平衡。 在不对称游戏中, 夏娃有不同的可能性从爱丽丝和鲍勃那里成功接收包裹, 纯粹的战略可能不存在; 在这种情况下, 我们展示如何找到混合战略的纳什平衡。