  In this paper, we consider distributed decision-making over stochastic
communication links in multi-agent systems. We show how to extend the current
literature on potential games with binary log-linear learning (which mainly
focuses on ideal communication links) to consider the impact of stochastic
communication channels. More specifically, we derive conditions on the
probability of link connectivity to achieve a target probability for the set of
potential maximizers (in the stationary distribution). Furthermore, our toy
example demonstrates a transition phenomenon for achieving any target
probability for the set of potential maximizers.
