Hat Guessing Games and the Use of Coding for Decentralized Control

We study a class of decentralized team decision problems over discrete state spaces with non classical information structures. We present a simple class of problems, where an optimal solution can be obtained via coding. For the example presented, we explicitly construct a coding scheme, called the binary sum coding scheme, and show that it is optimal. This class of problems is motivated by a famous mathematical puzzle called the hats problem.