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Many public goods that are provided by coalitions have a group-size effect. Namely, people prefer to consume a public good in a larger coalition. This paper studies local public goods games with anonymous and separable group-size effect. The core is nonempty when coalition feasible sets are monotonic and players' preferences over public goods satisfy a condition called cardinal connectedness. Moreover, a core allocation consists of connected coalitions. [ABSTRACT FROM AUTHOR]

A family of core extensions for cooperative TU-games is introduced. These solution concepts are non-empty when applied to non-balanced games yet coincide with the core whenever the core is non-empty. The extensions suggest how an exogenous regulator can sustain a stable and efficient outcome, financing a subsidy via individual taxes. Economic and geometric properties of the solution concepts are studied. When taxes are proportional, the proportional prenucleolus is proposed as a single-valued selection device. An application of these concepts to the decentralization of a public goods economy is discussed. [ABSTRACT FROM AUTHOR]