  We study two-sided matching markets in which one side of the market (the
players) does not have a priori knowledge about its preferences for the other
side (the arms) and is required to learn its preferences from experience. Also,
we assume the players have no direct means of communication. This model extends
the standard stochastic multi-armed bandit framework to a decentralized
multiple player setting with competition. We introduce a new algorithm for this
setting that, over a time horizon $T$, attains $\mathcal{O}(\log(T))$ stable
regret when preferences of the arms over players are shared, and
$\mathcal{O}(\log(T)^2)$ regret when there are no assumptions on the
preferences on either side. Moreover, in the setting where a single player may
deviate, we show that the algorithm is incentive compatible whenever the arms'
preferences are shared, but not necessarily so when preferences are fully
general.
