I count the number of combinatorial choice rules that satisfy certain properties: Kelso-Crawford substitutability, and independence of irrelevant alternatives. The results are important for two-sided matching theory, where agents are modeled by combinatorial choice rules with these properties....

We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agents' preferences. We...

We characterize the core many-to-one matchings as fixed points of a map. Our characterization gives an algorithm for finding core allocations; the algorithm is efficient and simple to implement. Our characterization does not require substitutable preferences, so it is separate from the structure...

In games with strict strategic complementarities, properly mixed Nash equilibria--equilibria that are not in pure strategies--are unstable for a broad class of learning dynamics.

We study the behavioral definition of complementary goods: if the price of one good increases, demand for a complementary good must decrease. We obtain its full implications for observable demand behavior (its testable implications), and for the consumer's underlying preferences. We characterize...