Certainty Equivalence Principle and Minimax Team Problems

We consider a team problem, with two decision makers for simplicity, where the uncertainties are dealt with in a minimax fashion rather than in a stochastic framework. We do not assume that the players exchange information at any time. Thus new ideas are necessary to investigate that situation. In contrast with the classical literature we do not use necessary conditions, but investigate to what extent ideas comming from the (nonlinear) minimax certainty equivalence theory allow one to conclude here. We are led to the introduction of a “partial team” problem, where one of the decision makers has perfect state information. We then investigate the full team problem, but the main result concerning it is shown to be still rather weak. We nevertheless apply it to the linear quadratic case, where it yields an original result.