Characterizing Paretian Preferences

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, there is no characterization of finite type for Pareto representability in R..2. A partial result along the same lines is obtained for Pareto representability in R..k, k .. 2.

Marriage Matching with Correlated Preferences

Authors of experimental, empirical, theoretical and computational studies of two-sided matching markets have recognized the importance of correlated preferences. We develop a general method for the study of the effect of correlation of preferences on the outcomes generated by two-sided matching mechanisms. We then illustrate our method by using it to quantify the effect of correlation of preferences on satisfaction with the men-propose Gale-Shapley matching for a simple one-to-one matching problem.

A Comparison of Two-Market Bertrand Duopoly and Two-Market Cournot Duopoly

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 undercutting means that Bertrand equilibrium prices and profits will be lower and quantities higher than Cournot equilibrium prices, profits and quantities.We find a quite different consequence of price undercutting in two-market duopoly. In the two-market case the threat of price undercutting means that Bertrand equilibria are in continuous mixed strategies, while every Cournot duopoly has an equilibrium in pure strategies, or in strategies that are pure in each market.

Is Altruism Feasible? Interdependent Preferences Provide the Answer

Is it possible to be altruistic in the face of altruism? With a naive definition of altruism, the answer is no. If an altruistic consumer is defined to be one whose preferences over allocations satisfy an appropriate interdependence condition, then the answer is yes. However, altruism in the face of malice is impossible. One of our findings is that if two consumers are mutually altruistic, exactly one of them should adopt selfish preferences over allocations.

Recognizing a Single-Issue Spatial Election

A single-issue spatial election is a voter preference profile derived from an arrangement of candidates and voters on a line, with each voter preferring the nearer of each pair of candidates. We provide a polynomial-time algorithm that determines whether a given preference profile is a single-issue spatial election and, if so, constructs such an election. This result also has preference representation and mechanism design applications.

Marriage Matching and Intercorrelation of Preferences

Men's and women's preferences are intercorrelated to the extent that men rank highly those women who rank them highly. Intercorrelation plays an important but overlooked role in determining outcomes of matching mechanisms. We study via simulation the effect of intercorrelated preferences on men's and women's aggregate satisfaction with the outcome of the Gale-Shapley matching mechanism. We conclude with an application of our results to the student admission matching problem.

Three-agent Peer Evaluation

I show that every rule for dividing a dollar among three agents impartially (so that each agent's share depends only on her evaluation by her associates) underpays some agent by at least one-third of a dollar for some consistent profile of evaluations. I then produce an impartial division rule that never underpays or overpays any agent by more than one-third of a dollar, and for most consistent evaluation profiles does much better.

A Universal Formula for Continuous Utility

A single formula assigns a continuous utility function to every representable preference relation.

Can a Newly Proposed Mechanism for Allocating Contracts in U.S. Electricity Wholesale Markets Lead to Lower Prices? A Game Theoretic Analysis

This study of the wholesale electricity market compares the cost-minimizing performance of the auction mechanism currently in place in U.S. markets with the performance of a proposed replacement. The current mechanism chooses an allocation of contracts that minimizes a fictional cost calculated using pay-as-offer pricing. Then suppliers are paid the market clearing price. The proposed mechanism uses the market clearing price in the allocation phase as well as in the payment phase. In concentrated markets, the proposed mechanism outperforms the current mechanism even when strategic behavior by suppliers is taken into account. The advantage of the proposed mechanism increases with increased price competition.

Finite Characterizations and Paretian Preferences

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 property characterized. Unfortunately, Pareto representability in R2 has no characterization of finite type (Knoblauch, 2002). This result is generalized below Rl, l larger than 2. The method of proof is applied to other properties of binary relations.

Continuous Paretian Preferences

Two forms of continuity are defined for Pareto representations of preferences. They are designated continuity and coordinate continuity. Characterizations are given of those Pareto representable preferences that are continuously representable and, in dimension two, of those that are coordinate-continuously representable.