The risk-based core for cooperative games with uncertainty

In coalitional games with uncertain payoffs, a deviating coalition can only form expectations regarding its post-deviation payoff. Classical approaches address the problem from the side of conservatism, expecting the worst, or by explicit assumptions of the emerging state of the world. We borrow the idea of risk from the finance literature and compare the payoff of staying with the original outcome with the risk of deviating. Employing this idea to the core leads to a new concept that we call the risk-based core. We introduce this concept and discuss its properties. We find an inclusion relation between cores of games with increasingly conservative players. The model is also suitable to study cooperative games in partition function form where the value of a coalition depends on the entire partition. For the cores of such games our main result yields many of the familiar inclusion relations as corollaries, while the inclusion of the optimistic core in the optimistic recursive core turns out to be non-robust.