Private Information Compression in Dynamic Games among Teams

We investigate finite-horizon stochastic dynamic games among teams. Each team has its own dynamic system, whose evolution is affected by the actions of all players in all teams. Within each team, members share their local states with each other with a delay of d > 0. Actions are observed by all agents along with noisy observations of the systems. Such games feature the difficulties of the increasing domain of strategies and interdependence of actions and information over time. In these games, we identify a subclass of Nash Equilibria where the agents use Sufficient Private Information Based (SPIB) strategies, i.e. agents make decisions based on compressed versions of their private information along with the common information. We establish the existence of such equilibria; the proof of existence is not based on standard techniques since SPIB strategies do not feature perfect recall. Finally, we investigate a special case of our model where each agent has their own dynamic system. We show that agents can compress their private information further in this case. Our results provide a foundational step in addressing the difficulties of dynamic games among teams.