  In this paper we study the problem of information sharing among rational
self-interested agents as a dynamic game of asymmetric information. We assume
that the agents imperfectly observe a Markov chain and they are called to
decide whether they will share their noisy observations or not at each time
instant. We utilize the notion of conditional mutual information to evaluate
the information being shared among the agents. The challenges that arise due to
the inter-dependence of agents' information structure and decision-making are
exhibited. For the finite horizon game we prove that agents do not have
incentive to share information. In contrast, we show that cooperation can be
sustained in the infinite horizon case by devising appropriate punishment
strategies which are defined over the agents' beliefs on the system state. We
show that these strategies are closed under the best-response mapping and that
cooperation can be the optimal choice in some subsets of the state belief
simplex. We characterize these equilibrium regions, prove uniqueness of a
maximal equilibrium region and devise an algorithm for its approximate
computation.
