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We consider the problem of designing distribution rules to share “welfare” (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., the Shapley value and its weighted variants; however, a characterization of the space of distribution rules that guarantees the existence of a Nash equilibrium is unknown. Our work provides an exact characterization of this space for a specific class of scalable and separable games that includes a variety of applications such as facility location, routing, network formation, and coverage games. Given arbitrary local welfare functions , we prove that a distribution rule guarantees equilibrium existence for all games (i.e., all possible sets of resources, agent action sets, etc.) if and only if it is equivalent to a generalized weighted Shapley value on some “ground” welfare functions ′, which can be distinct from . However, if budget-balance is required in ...

Potential Games Are Necessary to Ensure Pure Nash Equilibria in Cost Sharing Games