On the values of Bayesian cooperative games with sidepayments

In this paper, we study the solution concept of value in transferable utility (TU) games with asymmetric information. In our model contingent contracts are required to be incentive compatible, and thus utility might not be not fully transferable. Our approach differs from the standard methodology of TU games with complete information, which summarizes the cooperative possibilities through the characteristic function. Instead, we consider a model in which monetary transfers are modeled as additional sidepayments in a non-transferable utility (NTU) game. Our main result states that [18] generalization of the Shapley NTU value and Salamanca (2020) extension of the Harsanyi NTU value are interim utility equivalent in our model with sidepayments. As a consequence of this result, we obtain a generalization of the Shapley TU value to games with incomplete information. Its formula, however, cannot be described by a simple closed form expression as in the case of complete information