Replica core equivalence theorem: An extension of the Debreu–Scarf limit theorem to double infinity monetary economies

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

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 (partne...

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Indivisible Commodities and an Equivalence Theorem on the Strong Core

We consider a pure exchange economy with finitely many indivisible commodities that are available only in integer quantities. We prove that in such an economy with a sufficiently large number of agents, but finitely many agents, the strong core coincides with the set of cost-minimized Walras allocations. Because of the indivisibility, the preference maximization does not imply the cost minimiza...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials