New characterizations of M-convex functions and their applications to economic equilibrium models with indivisibilities
✍ Scribed by Kazuo Murota; Akihisa Tamura
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 221 KB
- Volume
- 131
- Category
- Article
- ISSN
- 0166-218X
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✦ Synopsis
The concept of M-convex functions plays a central role in "discrete convex analysis", a uniÿed framework of discrete optimization recently developed by Murota and others. This paper gives two new characterizations of M-and M " -convex functions generalizing Gul and Stacchetti's results on the equivalence among the single improvement condition, the gross substitutes condition and the no complementarities condition for set functions (utility functions on {0; 1} vectors) as well as Fujishige and Yang's observation on the connection to M-convexity. We also discuss implications of our results in an exchange economy with indivisible goods.