  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.

Networking and Internet Architecture;Computer Science and Game Theory