Many solution methods for Markov Decision Processes (MDPs) exploit structure in the problem and are based on value function factorization. Especially multiagent settings, however, are known to suffer from an exponential increase in value component sizes as interactions become denser, restricting problem sizes and types that can be handled. We present an approach to mitigate this limitation for certain types of multiagent systems, exploiting a property that can be thought of as "anonymous influence" in the factored MDP. We show how representational benefits from anonymity translate into computational efficiencies, both for variable elimination in a factor graph and for the approximate linear programming solution to factored MDPs. Our methods scale to factored MDPs that were previously unsolvable, such as the control of a stochastic disease process over densely connected graphs with 50 nodes and 25 agents.

In multiagent e-marketplaces, buying agents need to select good sellers by querying other buyers (called advisors). Partially Observable Markov Decision Processes (POMDPs) have shown to be an effective framework for optimally selecting sellers by selectively querying advisors. However, current solution methods do not scale to hundreds or even tens of agents operating in the e-market. In this paper, we propose the Mixture of POMDP Experts (MOPE) technique, which exploits the inherent structure of trust-based domains, such as the seller selection problem in e-markets, by aggregating the solutions of smaller sub-POMDPs. We propose a number of variants of the MOPE approach that we analyze theoretically and empirically. Experiments show that MOPE can scale up to a hundred agents thereby leveraging the presence of more advisors to significantly improve buyer satisfaction.