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Combinatorial allocation involves assigning bundles of items to agents when the use of money is not allowed. Course allocation is one common application of combinatorial allocation, in which the bundles are schedules of courses and the assignees are students. Existing mechanisms used in practice have been shown to have serious flaws, which lead to allocations that are inefficient, unfair, or both. A recently developed mechanism is attractive in theory but has several features that limit its feasibility for practice. This paper reports on the design and implementation of a new course allocation mechanism, Course Match, that is suitable in practice. To find allocations, Course Match performs a massive parallel heuristic search that solves billions of mixed-integer programs to output an approximate competitive equilibrium in a fake-money economy for courses. Quantitative summary statistics for two semesters of full-scale use at a large business school (the Wharton School of Business, which has about 1,700 students and up to 350 courses in each semester) demonstrate that Course Match is both fair and efficient, a finding reinforced by student surveys showing large gains in satisfaction and perceived fairness.

Two basic tenets of the Walrasian model, behavior based on self-interested exogenous preferences and complete and costless contracting have recently come under critical scrutiny. First, social norms and psychological dispositions extending beyond the selfish motives of Homo economicus may have an important bearing on outcomes, even in competitive markets. Second, market outcomes depend on strategic interactions in which power in the political sense is exercised. It follows that economics must become more behavioral and more institutional. We can return to these themes of the classical tradition, now equipped with the more powerful mathematical tools developed over the past century.

We introduce a notion of bargaining set for finite economies and show its convergence to the set of Walrasian allocations.

In this paper, we establish two different characterizations of Walrasian expectations allocations by the veto power of the grand coalition in an asymmetric information economy having finitely many agents and states of nature and whose commodity space is a Banach lattice. The first one deals with Aubin non-dominated allocations, and the other claims that an allocation is a Walrasian expectations allocation if and only if it is not privately dominated by the grand coalition, by considering perturbations of the original initial endowments in precise directions.

This article contends that a new research avenue is open to comparative economics which is the economic comparison between American (closed) and European (open) professional team sports leagues. It starts with sketching the major institutional differences between the two leagues systems. Then it surveys the American modelling of competitive balance in these sports leagues that objects pro-competitive balance regulation as being non Walrasian when (American) teams are profit maximising. A next step is to cover how the Walrasian model has been adapted to European open leagues and their regulation of win maximising clubs

In this paper we study algorithms for computing market equilibrium in markets with linear utility functions. The buyers in the market have an initial endowment given by a portfolio of goods. The market equilibrium problem is to compute a price vector that ensures market clearing, i.e., the demand of a positively priced good equals its supply, and given the prices, each buyer maximizes its utility. The problem is of considerable interest in economics. This paper presents a formulation of the market equilibrium problem as a parameterized linear program. We construct a family of duals corrresponding to these parameterized linear programs and show that finding the market equilibrium is the same as finding a linear program from this family of linear programs. The market-clearing conditions arise naturally from complementary slackness conditions. We then define an auction mechanism that computes prices such that approximate market clearing is achieved. The algorithm we obtain outperforms previously known methods.

1 This article compares how different types of models-Walrasian and heterodox-have integrated unpaid labour and, more specifically, care, as an economic activity. The article will discuss four models that have, each in their own way, incorporated unpaid labour, or care, as a variable, a sector, or parameter. The analysis of these model experiences will both reveal insights into the role of models in general, and appear to shed light on unpaid labour and caring as particular economic activities, with their own behavioural specifications and relationships to other economic variables. 1 The paper has benefited from comments at seminars in the spring of 2004 held at the Institute of Social Studies and Nijmegen University, for which the author would like to express her appreciation. In addition, the author would like to express her gratitude to participants at the 2004 World Congress of Social Economics for helpful comments. Suggestions from two reviewers are gratefully acknowledged and proved helpful in improving earlier versions of the paper.

A notable feature of most markets is that firms are multiproduct, in the sense that they offer for sale more than one single type of good. In this paper, I discuss a recent paper, Kaplan et al. (2016), that explores both empirically and theoretically price dispersion in a multiproduct setting. I discuss, with some detail, their empirical strategy and main empirical findings: a big part of price dispersion for a good in an area comes from stores with the same overall price level pricing individual goods in persistently different ways. I then go over the simple model proposed by the authors that can make sense of the novel empirical finding.

This chapter describes the approaches, models, and concepts of general‐equilibrium (GE) theory. It proceeds with the factual basis of GE problems, then offers a quick tour of the types of GE models available, and examines an equally brief tour of the types of questions GE analysis addresses. The first major fact that can lead us to think in GE terms is the interconnectedness of markets. The structure of the Walrasian model can be viewed from two perspectives: that of a number of individuals buying and selling in different markets, and that of the markets themselves, in which demands and supplies of various goods are equilibrated by movements in prices. The Walrasian tradition in GE modeling has been adapted to examine only some components of allocation problems at a time. The chapter shows some of the basics of the two‐sector model of production and income distribution.