ON A MARKET FOR COALITIONS WITH INDIVISIBLE AGENTS AND LOTTERIES

Given a game, the set of joint lotteries over partitions of the agents of any subgame induces a subset of the vectors of balancing weights f or the subgame. Games whose subgames are all balanced with respect to these vectors of balancing weights are called totally L-balanced games . We show that such games are precisely the ones that can be generated from direct lottery markets. Total L-balancedness is equivalent to su peradditivity. Thus, many interesting games that are not totally balan ced, but are superadditive, can be generated from direct lottery marke ts. We also show that the core of a game coincides with the set of lot tery equilibrium utility vectors of its direct lottery. (C) 1997 Acade mic Press.