An Influence Diagram framework for acting under influence by agents with unknown goals

We consider the situation where two agents try to solve each their own task in a commonenvironment. We present a general framework for representing that kind of scenariobased on Influence Diagrams (IDs). The framework is used to model the analysis depthand time horizon of the opponent agent and to determine an optimal policy under variousassumptions on analysis depth of the opponent. Not surprisingly, the framework turnsout to have severe complexity problems even in simple scenarios due to the size of therelevant past. We propose an algorithm based on Limited Memory Influence Diagrams(LIMIDs) in which we convert the ID into a Bayesian network and perform single policyupdate. Empirical results are presented using a simple board game.