Spectrum Sharing For Information Freshness: A Repeated Games Perspective

We consider selfish sources that send updates to a monitor over a shared wireless access. The sources would like to minimize the age of their information at the monitor. Our goal is to devise strategies that incentivize such sources to use the shared spectrum cooperatively. Earlier work has modeled such a setting using a non-cooperative one-shot game, played over a single access slot, and has shown that under certain access settings the dominant strategy of each source is to transmit in any slot, resulting in packet collisions between the sources' transmissions and causing all of them to be decoded in error at the monitor. We capture the interaction of the sources over an infinitely many medium access slots using infinitely repeated games. We investigate strategies that enable cooperation resulting in an efficient use of the wireless access, while disincentivizing any source from unilaterally deviating from the strategy. Formally, we are interested in strategies that are a subgame perfect Nash equilibrium (SPNE). We begin by investigating the properties of the one-stage (slot) optimal and access-fair correlated strategies. We then consider their many-slot variants, the age-fair and access-fair strategies, in the infinitely repeated game model. We prove that the access-fair and age-fair strategies are SPNEs for when collision slots are longer than successful transmission slots. Otherwise, neither is a SPNE. We end with simulations that shed light on a possible SPNE for the latter case.