CvdN Equilibrium and Share Equilibrium in Local Public Good Economies

CvdN equilibrium and share equilibrium are both extensions of the cost-shares-based ratio equilibrium for global public good economies to local public good economies. CvdN equilibrium and share equilibrium differ in terms of the stability requirements for equilibrium jurisdictions. While share equilibrium keeps agents' relative cost shares fixed across jurisdictions and allows each agent to consider unilateral moves to alternative jurisdictions, CvdN equilibrium employs the use of share functions that allow for equilibrium adjustments of relative shares in each jurisdiction and requires the agreement of all agents in alternative jurisdictions. Despite these differences, we demonstrate that CvdN equilibrium extends share equilibrium: every arrangement of an economy that is supported in share equilibrium is also a CvdN equilibrium. However, the reverse is not true and CvdN equilibrium may exist when share equilibrium does not. Thus, CvdN equilibrium provides predictions in more economies and does not contradict share equilibrium when it exists.