Monotonicity of Social Optima With Respect to Participation Constraints

In this paper we consider solutions which select from the core. For games with side payments with at least four players, it is well-known that no core-selection satisfies monotonicity for all coalitions; for the particular class of core-selections found by maximizing a social welfare function over the core, we investigate whether such solutions are monotone for a given coalition. It is shown that if this is the case then the solution actually maximizes aggregate coalition payoff on the core. Furthermore, the social welfare function to be maximized exhibits larger marginal social welfare with respect to the payoff of any member of the coalition. The results may be used to show that there are no monotonic core selection rules of this type in the context of games without side payments.