Common Knowledge and Sequential Team Problems

Abstract

We consider a general sequential team problem based on Witsenhausen's intrinsic model. Our formulation encompasses all teams in which the uncontrolled inputs can be viewed as random variables on a finite probability space, the number of control inputs/decisions is finite and the decisions take values in finite spaces. We define the concept of common knowledge in such teams and use it to construct a sequential decomposition of the problem of optimizing the team strategy profile. If the information structure is classical, our common knowledge based decomposition is identical to classical dynamic program. If the information structure is such that the common knowledge is trivial, our decomposition is similar in spirit to Witsenhausen's standard form based decomposition [17] . In this case, the sequential decomposition is essentially a sequential reformulation of the strategy optimization problem and appears to have limited value. For information structures with nontrivial common knowledge, our sequential decomposition differs from Witsenhausen's standard form based decomposition because of its dependence on common knowledge. Our common knowledge based approach generalizes the common information based methods of [12] – [14] .