We consider the situation where two agents try to solve each their own task in a common

environment. We present a general framework for representing that kind of scenario

based on Influence Diagrams (IDs). The framework is used to model the analysis depth

and time horizon of the opponent agent and to determine an optimal policy under various

assumptions on analysis depth of the opponent. Not surprisingly, the framework turns

out to have severe complexity problems even in simple scenarios due to the size of the

relevant 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 policy

update. Empirical results are presented using a simple board game.