Coexistence of Age and Throughput Optimizing Networks: A Spectrum Sharing Game

We investigate the coexistence of an age optimizing network (AON) and a throughput optimizing network (TON) that share a common spectrum band. We consider two modes of long run coexistence: (a) networks compete with each other for spectrum access, causing them to interfere and (b) networks cooperate to achieve non-interfering access. To model competition, we define a non-cooperative stage game parameterized by the average age of the AON at the beginning of the stage, derive its mixed strategy Nash equilibrium (MSNE), and analyze the evolution of age and throughput over an infinitely repeated game in which each network plays the MSNE at every stage. Cooperation uses a coordination device that performs a coin toss during each stage to select the network that must access the medium. Networks use the grim trigger punishment strategy, reverting to playing the MSNE every stage forever if the other disobeys the device. We determine if there exists a subgame perfect equilibrium, i.e., the networks obey the device forever as they find cooperation beneficial. We show that networks choose to cooperate only when they consist of a sufficiently small number of nodes, otherwise they prefer to disobey the device and compete.