  This paper extends the framework of partially observable Markov decision
processes (POMDPs) to multi-agent settings by incorporating the notion of agent
models into the state space. Agents maintain beliefs over physical states of
the environment and over models of other agents, and they use Bayesian updates
to maintain their beliefs over time. The solutions map belief states to
actions. Models of other agents may include their belief states and are related
to agent types considered in games of incomplete information. We express the
agents autonomy by postulating that their models are not directly manipulable
or observable by other agents. We show that important properties of POMDPs,
such as convergence of value iteration, the rate of convergence, and piece-wise
linearity and convexity of the value functions carry over to our framework. Our
approach complements a more traditional approach to interactive settings which
uses Nash equilibria as a solution paradigm. We seek to avoid some of the
drawbacks of equilibria which may be non-unique and do not capture
off-equilibrium behaviors. We do so at the cost of having to represent, process
and continuously revise models of other agents. Since the agents beliefs may be
arbitrarily nested, the optimal solutions to decision making problems are only
asymptotically computable. However, approximate belief updates and
approximately optimal plans are computable. We illustrate our framework using a
simple application domain, and we show examples of belief updates and value
functions.
