Agent interaction in distributed POMDPs and its implications on complexity

The ability to coordinate effectively is critical for agents to accomplish their goals in a multi-agent system. A number of researchers have modeled the coordination problem for multi-agent systems using decision theory. The most general models have proven to be extremely complex to solve optimally (NEXP-complete). Some of the more restricted models have been much more tractable, though still difficult (NP-complete). What is missing is an understanding about why some models are much easier than others. This work fills this gap by providing a condition that distinguishes between problems in NP and those strictly harder than NP. This condition relates to the quantity of information each agent has about the others, and whether this information can be represented in a succinct way. We show that the class of problems that satisfy this condition is NP-complete. We illustrate this idea with two interaction protocols that satisfy the condition. For those problems that do not satisfy this condition we demonstrate how our theoretical results can be used to generate an NP approximation of the original problem.