In this paper, Borm et al. describe how classical, deterministic cooperative games can be extended to cooperative games in which the payoffs are uncertain. This means there is a probability distribution that assigns probabilities to payoffs for all coalitions.
My questions are: what are good examples of cooperative games in which the payoffs are stochastic? Which deterministic cooperative games can be naturally extended to the corresponding stochastic case? To what extent are they relevant to real life?
Essentially every cooperative boardgame has a stochastic payoff. Two popular examples are: Forbidden Desert and Pandemic. You can find more by browsing boardgamegeek.com.