Equilibrium in abstract political economies: with an application to a public good economy with voting

Consider an abstract political economy which has a collective choice rule together with strategic interactions among players. We prove that there exists an equilibrium in such an economy by synthesizing an equilibrium existence theorem in generalized games by Shafer and Sonnenschein (1975) and a voting core existence theorem in simple games by Schofield (1984, 1989). The theorem can be applied to a public good economy where public good provisions are determined by a class of voting rule.Thanks are due to David Austen-Smith, Jeffrey Banks, Marcus Berliant, Steve Ching, Ryo-Ichi Nagahisa, Mary Beth Savio, Norman Schofield, and Tomoichi Shinotsuka. Detailed comments from an anonymous referee of the journal are gratefully acknowledged. Errors are, of course, my own.