A theory of “discrete convex analysis” is developed for integer-valued functions defined on
integer lattice points. The theory parallels the ordinary convex analysis, covering discrete …

This paper describes recent developments in discrete convex analysis. Particular emphasis
is laid on natural introduction of the classes of L-convex and M-convex functions in discrete …

In most of microeconomic theory, consumers are assumed to exhibit decreasing marginal
utilities. This paper considers combinatorial auctions among such buyers. The valuations of …

We introduce a new model of combinatorial contracts in which a principal delegates the
execution of a costly task to an agent. To complete the task, the agent can take any subset of …

An Equivalence Theorem between geometric structures and utility functions allows new
methods for understanding preferences. Our classification of valuations into “Demand …

This paper presents discrete convex analysis as a tool for economics and game theory.
Discrete convex analysis is a new framework of discrete mathematics and optimization …

This paper examines an exchange economy with heterogeneous indivisible objects that can
be substitutable or complementary. We show that a competitive equilibrium exists in such …

Discrete Polymatroids Page 1 Journal of Algebraic Combinatorics 16 (2002), 239–268 c 2003
Kluwer Academic Publishers. Manufactured in The Netherlands. Discrete Polymatroids …

In their 1982 article, Kelso and Crawford proposed a gross substitutes condition for the
existence of core (and equilibrium) in a two-sided matching model. Since then, this condition …

The concept of gross substitute valuations was introduced by Kelso and Crawford as a
sufficient conditions for the existence of Walrasian equilibria in economies with indivisible …