Cooperative Game with Nondeterministic Returns

Abstract

Abstract We study a non-traditional cooperative game where returns from coalitions are nondeterministic. The long-standing concept of core can be generalized to reflect players’ contentment with their allocations. It is now imperative to formalize the restrictions, such as those pertaining to information, on allocations. The latter are also at times more conducive to fractional representations. With probabilistic structures added, nondeterministic returns become random variables, utility functions attain risk-attitude connotations, and the timing of players’ allocation resolutions gains significance. Under various conditions for utility functions, we show how various core concepts of the general game can be related to its traditionally defined auxiliaries. These developments help pave the way for our illustrations, within two distinct settings, that players’ increased risk aversion would promote the formation of the grand coalition.