Multi-Agent Filtering with Infinitely Nested Beliefs

In partially observable worlds with many agents, nested beliefs are formed when agents simultaneously reason about the unknown state of the world and the beliefs of the other agents. The multi-agent filtering problem is to efficiently represent and update these beliefs through time as the agents act in the world. In this paper, we formally define an infinite sequence of nested beliefs about the state of the world at the current time $t$ and present a filtering algorithm that maintains a finite representation which can be used to generate these beliefs. In some cases, this representation can be updated exactly in constant time; we also present a simple approximation scheme to compact beliefs if they become too complex. In experiments, we demonstrate efficient filtering in a range of multi-agent domains.