A preference profile has a one-dimensional Euclidean representation if it can be derived from an arrangement of individuals and alternatives on a line, with each individual preferring the nearer of each pair of alternatives. We provide a polynomial-time algorithm that determines whether a given...

A characterization of a property of binary relations is of type M if it can be stated in terms of ordered M-tuples of alternatives. A characterization of finite type provides an easy test of whether preferences over a large set of alternatives possesses the property characterized. Unfortunately,...

Necessary and sufficient conditions are given for the existence of an Order isomorphism from a given preference relation to Euclidean n-dimensional space ordered by Pareto dominance. This result provides representation for some preference relations not representable by utility functions. It also...

In a two-market Bertrand duopoly,each of two firms chooses one of two markets and a price in that market. All four choices are made simultaneously. In a two-market Cournot duopoly, the firms choose quantities rather than prices.It is well known that in the one-market case the threat of price...

Under what conditions are lexicographically representable preferences continuously representable? This question is actually two questions, since there are two natural definitions of continuity for lexicographic representations. A complete answer is given for one of these questions, and the other...

A characterization of a property of binary relations is of finite type if it is stated in terms of ordered T-tuples of alternatives for some positive integer T. A characterization of finite type can be used to determine in polynomial time whether a binary relation over a finite set has the...

Variations of the Gale-Shapley algorithm have been used and studied extensively in real world markets. Examples include matching medical residents with residency programs, the kidney exchange program and matching college students with on-campus housing. The performance of the Gale-Shapley...