  Cooperative Bayesian games (BGs) can model decision-making problems for teams
of agents under imperfect information, but require space and computation time
that is exponential in the number of agents. While agent independence has been
used to mitigate these problems in perfect information settings, we propose a
novel approach for BGs based on the observation that BGs additionally possess a
different types of structure, which we call type independence. We propose a
factor graph representation that captures both forms of independence and
present a theoretical analysis showing that non-serial dynamic programming
cannot effectively exploit type independence, while Max-Sum can. Experimental
results demonstrate that our approach can tackle cooperative Bayesian games of
unprecedented size.
