A central issue in school choice is the design of a student assignment mechanism. Education literature provides guidance for the design of such mechanisms but does not offer specific mechanisms. The flaws in the existing school choice plans result in appeals by unsatisfied parents. We formulate the school choice problem as a mechanism design problem and analyze some of the existing school choice plans including those in Boston, Columbus, Minneapolis, and Seattle. We show that these existing plans have serious shortcomings, and offer two alternative mechanisms each of which may provide a practical solution to some critical school choice issues.

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School Choice: A Mechanism Design Approach

We develop a model of matching with contracts which incorporates, as special cases, the college admissions problem, the Kelso-Crawford labor market matching model, and ascending package auctions. We introduce a new "law of aggregate demand" for the case of discrete heterogeneous workers and show that, when workers are substitutes, this law is satisfied by profit-maximizing firms. When workers are substitutes and the law is satisfied, truthful reporting is a dominant strategy for workers in a worker-offering auction/matching algorithm. We also parameterize a large class of preferences satisfying the two conditions.,

/pdf/matching-with-contracts-3c5aa6cbwt.pdf

Matching with Contracts

The concept of fair division is as old as civil society itself Aristotle's "equal treatment of equals" was the first step toward a formal definition of distributive fairness The concept of collective welfare, more than two centuries old, is a pillar of modern economic analysis Reflecting fifty years of research, this book examines the contribution of modern microeconomic thinking to distributive justice Taking the modern axiomatic approach, it compares normative arguments of distributive justice and their relation to efficiency and collective welfare The book begins with the epistemological status of the axiomatic approach and the four classic principles of distributive justice: compensation, reward, exogenous rights, and fitness It then presents the simple ideas of equal gains, equal losses, and proportional gains and losses The book discusses three cardinal interpretations of collective welfare: Bentham's "utilitarian" proposal to maximize the sum of individual utilities, the Nash product, and the egalitarian leximin ordering It also discusses the two main ordinal definitions of collective welfare: the majority relation and the Borda scoring method The Shapley value is the single most important contribution of game theory to distributive justice A formula to divide jointly produced costs or benefits fairly, it is especially useful when the pattern of externalities renders useless the simple ideas of equality and proportionality The book ends with two versatile methods for dividing commodities efficiently and fairly when only ordinal preferences matter: competitive equilibrium with equal incomes and egalitarian equivalence The book contains a wealth of empirical examples and exercises

Fair Division and Collective Welfare

Two-person Cooperative Games

Game theory and water resources

https://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/117.pdf

Stable matchings and preferences of couples

We consider the problem of allocating indivisible objects when agents may desire to consume more than one object and monetary transfers are not possible. Each agent receives a set of objects and free disposal is allowed. We are interested in allocation rules that satisfy “appealing” properties from an economic and social point of view. Our main result shows that sequential dictatorships are the only efficient and coalitional strategy-proof solutions to the multiple assignment problem. Adding resource-monotonicity narrows this class down to serial dictatorships.

Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems

https://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/156.pdf

Paths to stability for matching markets with couples

https://core.ac.uk/download/pdf/6527106.pdf

Strategy-proofness and population-monotonicity for house allocation problems

https://cris.maastrichtuniversity.nl/ws/files/4504917/guid-9ab575ba-d47c-45bd-89f8-840e9edd862c-ASSET1.0

Bettina Klaus

Papers

Stable matchings and preferences of couples

Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems

Paths to stability for matching markets with couples

Strategy-proofness and population-monotonicity for house allocation problems

Stable many-to-many matchings with contracts