The degraded Gaussian multiple access wiretap channel with selfish transmitters: A coalitional game theory perspective

We study the degraded Gaussian multiple access wiretap channel with selfish transmitters, i.e., they are each solely interested in maximizing their individual secrecy rate. The question then arises as to whether selfish transmitters can increase their individual secrecy rate by participating in a collective, i.e, multiple access, protocol instead of operating on their own. If yes, the question arises if there is a protocol that satisfies all the participating transmitters, in the sense that no transmitter has an incentive to deviate from the protocol. We answer these questions in the positive utilizing coalitional game theory. In particular, we show that cooperation is in the best interest of all transmitters and that there exist protocols that incentivize all transmitters to participate. Furthermore, we determine a unique, fair, and stable achievable secrecy rate allocation.