Existence of share equilibrium in symmetric local public good economies

Share equilibrium was introduced in van den Nouweland and Wooders (2011) as an extension of Lindahl's original equilibrium concept (Lindahl, 1919) to local public good economies. The current paper contains a comprehensive study of the possible share equilibrium outcomes of symmetric individuals, exposing the forces that shape equilibrium and explaining the circumstances under which symmetric individuals can potentially have different equilibrium share indices. We provide an existence result for symmetric economies and a characterization of symmetric economies that admit share equilibria. We also establish equivalence between share equilibrium configurations in symmetric economies and core configurations in which the players all have the same utility.