Core equivalence theorem with production

In production economies, the extent to which non-equilibria are blocked depends on the allocation of control rights among shareholders, because a blocking coalition’s resources are affected by the firms it jointly owns with outsiders. We formulate two notions of blocking. Corporate control is allocated deterministically (majority shares, unanimity, etc.) in one notion and stochastically (partnership dissolution) in the other. Based on each blocking notion, we prove an analog of the Debreu-Scarf theorem for replica production economies, and we prove that the class of economies for core convergence is expanded if the blocking notion is switched from deterministic to stochastic. ∗We are very grateful for comments received from Bob Anderson, Yi-Chun Chen, Eddie Dekel, Peter DeMarzo, Onur Dogan, Marcel K. Richter, Michael Whinston, and especially William Zame, as well as the seminar participants of the 2005 NSF/CEME Mathematical Economics Conference at Berkeley. †Department of Economics, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208, [email protected], http://pubweb.northwestern.edu/ ̃sxi711/ ‡Department of Economics, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208, [email protected], http://faculty-web.at.northwestern.edu/economics/zheng/. Zheng’s work was supported in part by the National Science Foundation grant SES-0214471.