Strategic Interaction Over Age of Information on a Quantum Wiretap Channel

We investigate a scenario where a transmitter (Alice) sends information to a legitimate receiver (Bob) through a quantum channel in the presence of an eavesdropper (Eve). The information leaked to Eve is made unavailable to Bob, which causes the system to behave like a partially degraded wiretap channel. We consider Alice and Eve to be strategic players interested in minimizing the resulting age of information at Bob's and Eve's, respectively. We frame the resulting system as two M/M/1 queues, fed by the remaining information and the eavesdropped data, respectively, for which we can exploit well-known results. The strategic interaction among the players is captured by a game-theoretic formulation, where Alice chooses her data generation rate and Eve controls the interception probability, both subject to a cost for their action. We obtain a characterization of the resulting Nash equilibria, exploring the conditions for their existence depending on the cost parameters. The most important finding of our analysis lies in the evaluation of the price of anarchy, which is found to be extremely high in the presence of multiple Nash equilibria. Thus, the application of distributed management ought to be carefully controlled to avoid inefficient outcomes.