  In this paper, we study contention resolution protocols from a game-theoretic
perspective. In a recent work, we considered acknowledgment-based protocols,
where a user gets feedback from the channel only when she attempts
transmission. In this case she will learn whether her transmission was
successful or not. One of the main results of ESA2016 was that no
acknowledgment-based protocol can be in equilibrium. In fact, it seems that
many natural acknowledgment-based protocols fail to prevent users from
unilaterally switching to persistent protocols that always transmit with
probability 1. It is therefore natural to ask how powerful a protocol must be
so that it can beat persistent deviators.
  In this paper we consider age-based protocols, which can be described by a
sequence of probabilities of transmitting in each time step. Those
probabilities are given beforehand and do not change based on the transmission
history. We present a 3-player age-based protocol that can prevent users from
unilaterally deviating to a persistent protocol in order to decrease their
expected transmission time. It is worth noting that the answer to this question
does not follow from the results and proof ideas of ESA2016. Our protocol is
non-trivial, in the sense that, when all players use it, finite expected
transmission time is guaranteed. In fact, we show that this protocol is
preferable to any deadline protocol in which, after some fixed time, attempt
transmission with probability 1 in every subsequent step. An advantage of our
protocol is that it is very simple to describe, and users only need a counter
to keep track of time. Whether there exist $n$-player age-based protocols that
do not use counters and can prevent persistence is left as an open problem for
future research.
