Two Person Decentralized Team Problem With Incomplete Information

Abstract

In this chapter we propose a learning approach to the two person decentralized team problem with incomplete information: Let A and B be the two persons each with two actions at their disposal. At any instant each person picks an action (perhaps randomly) and let i be the action chosen by A and j by B. As a result of their joint actions, both A and B receive the same outcome. The outcome is in general, a random variable whose distribution depends on the action pair (i,j). We assume that the outcome is two valued: +1, (unit gain) and −1 (unit loss) and that neither person has knowledge of the set of actions available to the other person or the actual action chosen by the other person at any instant of time or the distribution of the random outcome as a function of the pair (i,j) of actions. In other words, we consider an interaction between persons wherein there is no transfer of information of any kind at any stage. Just based on the action chosen and the random outcome he receives, each person decides to update the probability distribution over the set of his own actions using a learning algorithm. In this setup our problem is to find conditions on the learning algorithm such that asymptotically each person will maximize his expected outcome or payoff.