Local public good equilibrium

We extend ratio equilibrium to local public good economies by defining Local Public Good Equilibrium (LPGE). We employ “share functions” for individual agents that allow easy comparisons of consumption utility, both across consumption bundles and across jurisdiction memberships. Share functions furthermore aggregate for parsimonious calculation of equilibrium public good provision within each potential jurisdiction, allowing us to establish a link with hedonic games and deploy results from that literature. We demonstrate in examples how this enables us to show LPGE existence for a far wider class of economies than prior work seeking to extend ratio equilibrium to local public good economies. In particular, we demonstrate LPGE existence with heterogeneous agents, a finite number of agents and jurisdictions, endogenous jurisdictional revenues and expenditures, and robustness against coalitional deviations. LPGE admits wide-ranging jurisdiction structures, and we demonstrate how it can generate results on sorting that have attracted interest in the extant literature.