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Guaranteed shares of benefits and costs

We revisit the self-ownership viewpoint to regulate the utilisation of common property resources. Allocating to each agent "the fruit of their own labor" is typically ill-depned, so we look for tight approximations of this decentralised ideal. For each agent i two guarantees limit, from above and below, the impact of other agents on i's allocation. They limit the range of unscripted negotiations, or the choice of a full sharing rule. Our context-free model of the commons is a mapping W from profiles of "types" to a freely transferable amount of benefit or cost. If W is super (resp. sub) modular there is a single tight upper (resp. lower) guarantee, and an infinite menu of tight lower (resp. upper) guarantees, each one conveying a precise normative viewpoint. We describe the menu for essentially all modular two person problems, and familiar examples like the allocation of an indivisible item, cooperative production, and facility location.

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