Language：English   Publishing type：Research paper (scientific journal)  

We prove that a mixture continuous preference relation 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 our condition on the continuity of a preference relation is strictly weaker than the usual continuity assumed by them.

DOI： 10.1016/j.jmateco.2009.09.002

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Language：English   Publishing type：Research paper (scientific journal)  

We consider a sufficient condition for the nonemptiness of the weak core in a finite exchange economy where every commodity is available only in integer quantities. We show that if the aggregate upper contour set is discretely convex, then the weak core is nonempty. In addition, we give two sufficient conditions for the aggregate upper contour set to be discretely convex. One is that every upper contour set of every agent is M-natural-convex. The other is that the number of commodities is two and every agent's preference relation is weakly monotone and discretely convex.

DOI： 10.1016/j.jmateco.2006.07.009

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Language：English   Publishing type：Research paper (scientific journal)  

We consider a pure exchange economy with a continuum of agents and finitely many indivisible commodities. Every commodity can be consumed only in integer amounts. Thus, agents' preferences are locally satiated and no commodity bundle has necessarily local cheaper points. We introduce a core which is an intermediate concept between the strong core and the weak core. In our economy, this core is the most natural concept in the sense that it coincides with the set of all exactly feasible Walras allocations.

DOI： 10.1016/j.jmateco.2004.09.004

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Language：English   Presentation type：Oral presentation (general)  

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Language：Japanese   Presentation type：Oral presentation (general)  

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Language：Japanese   Presentation type：Oral presentation (general)  

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Language：English   Presentation type：Oral presentation (general)  

We prove the convergence of core allocations for a sequence of economies with bads. We assume that consumers' preference relations are similar in three aspects. First, consumers' preference relations are equi-convex. Second, every upper contour set of every consumer has the same asymptotic cone. Third, the rate of convergence to the common asymptotic cone is uniform among consumers. Under these assumptions, we prove that, for every sequence of core allocations, a measure of noncompetitiveness converges to zero and consumers' consumption vectors at core allocations converge in measure to their demand vectors. We exemplify that the third assumption cannot be dispensed with in our core convergence theorems.

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Language：English   Presentation type：Oral presentation (general)  

We give a sufficient condition for the core convergence in economies with bads. We assume that consumers' preference relations are similar mainly in two aspects. First, consumers' preference relations are equi-convex. Second, the rate of convergence of the upper contour sets at endowment vector to its asymptotic cones is similar among consumers. The second point played a key role even in proving the existence of a Walrasian equilibrium for an economy with a continuum of consumers and with bads.

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Language：English   Presentation type：Oral presentation (general)  

Venue：Waseda University  

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Language：Japanese   Presentation type：Oral presentation (general)  

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Language：English   Presentation type：Oral presentation (general)  

Venue：Doshisha University  

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Language：Japanese   Presentation type：Oral presentation (general)  

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Language：English   Presentation type：Oral presentation (general)  

Venue：University of Glasgow Adam Smith Business School  

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Language：Japanese   Presentation type：Oral presentation (general)  

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Language：English   Presentation type：Oral presentation (general)  

Venue：University of Naples Federico II  

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Language：English   Presentation type：Oral presentation (general)  

Venue：University of Vienna & Institute of Advanced Studies  

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