  The problem of controlling multi-agent systems under different models of
information sharing among agents has received significant attention in the
recent literature. In this paper, we consider a setup where rather than
committing to a fixed information sharing protocol (e.g. periodic sharing or no
sharing etc), agents can dynamically decide at each time step whether to share
information with each other and incur the resulting communication cost. This
setup requires a joint design of agents' communication and control strategies
in order to optimize the trade-off between communication costs and control
objective. We first show that agents can ignore a big part of their private
information without compromising the system performance. We then provide a
common information approach based solution for the strategy optimization
problem. This approach relies on constructing a fictitious POMDP whose solution
(obtained via a dynamic program) characterizes the optimal strategies for the
agents. We also show that our solution can be easily modified to incorporate
constraints on when and how frequently agents can communicate.
