A secure communication game with a relay helping the eavesdropper

In this work a four terminal Gaussian network composed of a source, a destination, an eavesdropper and a jammer relay is studied. The jammer relay does not hear the source transmission. It assists the eavesdropper and aims to decrease the achievable secrecy rates. The source, on the other hand, aims to increase the achievable secrecy rates. Assuming Gaussian strategies at the source and the jammer relay, this problem is formulated as a two-player zero-sum continuous game, where the payoff is the achieved secrecy rate. For this game the Nash equilibrium is generally achieved with mixed strategies. The optimal cumulative distribution functions for the source and the jammer relay that achieve the value of the game, which is the equilibrium secrecy rate, are found.