  Multiple autonomous agents interact over a random communication network to
maximize their individual utility functions which depend on the actions of
other agents. We consider decentralized best-response with inertia type
algorithms in which agents form beliefs about the future actions of other
players based on local information, and take an action that maximizes their
expected utility computed with respect to these beliefs or continue to take
their previous action. We show convergence of these types of algorithms to a
Nash equilibrium in weakly acyclic games under the condition that the belief
update and information exchange protocols successfully learn the actions of
other players with positive probability in finite time given a static
environment, i.e., when other agents' actions do not change. We design a
decentralized fictitious play algorithm with voluntary and limited
communication (DFP-VL) protocols that satisfy this condition. In the voluntary
communication protocol, each agent decides whom to exchange information with by
assessing the novelty of its information and the potential effect of its
information on others' assessments of their utility functions. The limited
communication protocol entails agents sending only their most frequent action
to agents that they decide to communicate with. Numerical experiments on a
target assignment game demonstrate that the voluntary and limited communication
protocol can more than halve the number of communication attempts while
retaining the same convergence rate as DFP in which agents constantly attempt
to communicate.
