Cooperative Games in Stochastic Characteristic Function Form

Additional results are presented in this paper which further extend and modify the theory of cooperative games in characteristic function form so as to encompass situations where the values of the coalitions are random variables with given distribution functions.

We reintroduce the prior nucleolus and provide a new characterization of it in terms of an optimal solution to a finite sequence of consistent and bounded NLP problems. From this new characterization it follows immediately that the prior nucleolus is unique for strictly monotone increasing distribution functions. We also extend the notions of objections and counterobjections to these games and construct and study the prior kernel and prior bargaining set 𝒫ℛ₁⁽ⁱ⁾.

A new notion of solution for the second part of the play of these games is suggested.