We prove that a preference relation which is continuous on every straight line has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but...

We consider an exchange economy where every commodity can be consumed only in integer amounts. Inoue [Inoue, T., 2005. Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only. Journal of Mathematical Economics...

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...

We consider an atomless exchange economy with indivisible commodities. Every commodity can be consumed only in integer amounts. In such an economy, because of the indivisibility, the preference maximization does not imply the cost minimization. We prove that the strong core coincides with the...

We prove that every transferable utility (TU) game can be generated by a coalition production economy. Given a TU game, the set of Walrasian payoff vectors of the induced coalition production economy coincides with the core of the balanced cover of the given game. Therefore, a Walrasian...