scholarly journals A Pseudo-Market Approach to Allocation with Priorities

2018 ◽  
Vol 10 (3) ◽  
pp. 272-314 ◽  
Author(s):  
Yinghua He ◽  
Antonio Miralles ◽  
Marek Pycia ◽  
Jianye Yan
Keyword(s):  
School Choice ◽  
Market Mechanism ◽  
Allocation Problem ◽  
Incentive Compatible ◽  
Indivisible Objects ◽  
Classical Setting ◽  
Monetary Transfer ◽  
Pareto Efficient ◽  
Market Approach ◽  
Special Case

We propose a pseudo-market mechanism for no-monetary-transfer allocation of indivisible objects based on priorities such as those in school choice. Agents are given token money, face priority-specific prices, and buy utility-maximizing random assignments. The mechanism is asymptotically incentive compatible, and the resulting assignments are fair and constrained Pareto efficient. Hylland and Zeckhauser’s (1979) position-allocation problem is a special case of our framework, and our results on incentives and fairness are also new in their classical setting. (JEL D63, D82, H75, I21, I28)

scholarly journals Pareto Efficient Auctions with Interest Rates

2019 ◽  
Vol 33 ◽  
pp. 1989-1995
Author(s):  
Gagan Goel ◽  
Vahab Mirrokni ◽  
Renato Paes Leme
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Utility Functions ◽  
Limited Access ◽  
Incentive Compatible ◽  
Pareto Efficient ◽  
Available Resources

We consider auction settings in which agents have limited access to monetary resources but are able to make payments larger than their available resources by taking loans with a certain interest rate. This setting is a strict generalization of budget constrained utility functions (which corresponds to infinite interest rates). Our main result is an incentive compatible and Pareto-efficient auction for a divisible multi-unit setting with 2 players who are able to borrow money with the same interest rate. The auction is an ascending price clock auction that bears some similarities to the clinching auction but at the same time is a considerable departure from this framework: allocated goods can be de-allocated in future and given to other agents and prices for previously allocated goods can be raised.

scholarly journals Budget Feasible Mechanisms on Matroids

Algorithmica ◽  
2020 ◽  
Author(s):  
Stefano Leonardi ◽  
Gianpiero Monaco ◽  
Piotr Sankowski ◽  
Qiang Zhang
Keyword(s):  
Polynomial Time ◽  
Private Information ◽  
Independent Set ◽  
Deterministic Algorithm ◽  
Matroid Intersection ◽  
Practical Applications ◽  
Incentive Compatible ◽  
The Cost ◽  
Special Case ◽  
Budget Feasible

AbstractMotivated by many practical applications, in this paper we study budget feasible mechanisms with the goal of procuring an independent set of a matroid. More specifically, we are given a matroid $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) . Each element of the ground set E is controlled by a selfish agent and the cost of the element is private information of the agent itself. A budget limited buyer has additive valuations over the elements of E. The goal is to design an incentive compatible budget feasible mechanism which procures an independent set of the matroid of largest possible value. We also consider the more general case of the pair $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) satisfying only the hereditary property. This includes matroids as well as matroid intersection. We show that, given a polynomial time deterministic algorithm that returns an $$\alpha $$ α -approximation to the problem of finding a maximum-value independent set in $${\mathcal {M}}$$ M , there exists an individually rational, truthful and budget feasible mechanism which is $$(3\alpha +1)$$ ( 3 α + 1 ) -approximated and runs in polynomial time, thus yielding also a 4-approximation for the special case of matroids.

scholarly journals Efficient and Incentive‐Compatible Liver Exchange

Econometrica ◽  
2020 ◽  
Vol 88 (3) ◽  
pp. 965-1005
Author(s):  
Haluk Ergin ◽  
Tayfun Sönmez ◽  
M. Utku Ünver
Keyword(s):  
Partial Order ◽  
Design Problem ◽  
Market Design ◽  
Left Lobe ◽  
Elevated Risk ◽  
Blood Type ◽  
Incentive Compatible ◽  
Right Lobe ◽  
Pareto Efficient ◽  
Incentive Compatible Mechanism

Liver exchange has been practiced in small numbers, mainly to overcome blood‐type incompatibility between patients and their living donors. A donor can donate either his smaller left lobe or the larger right lobe, although the former option is safer. Despite its elevated risk, right‐lobe transplantation is often utilized due to size‐compatibility requirement with the patient. We model liver exchange as a market‐design problem, focusing on logistically simpler two‐way exchanges, and introduce an individually rational, Pareto‐efficient, and incentive‐compatible mechanism. Construction of this mechanism requires novel technical tools regarding bilateral exchanges under partial‐order‐induced preferences. Through simulations we show that not only can liver exchange increase the number of transplants by more than 30%, it can also increase the share of the safer left‐lobe transplants.

scholarly journals Efficiency, Welfare, and Political Competition *

2015 ◽  
Vol 131 (1) ◽  
pp. 461-518 ◽  
Author(s):  
Felix J. Bierbrauer ◽  
Pierre C. Boyer
Keyword(s):  
Private Information ◽  
Political Competition ◽  
Income Taxation ◽  
Symmetric Equilibrium ◽  
Public Goods Provision ◽  
Trade Off ◽  
Private Goods ◽  
Incentive Compatible ◽  
Equity And Efficiency ◽  
Pareto Efficient

Abstract We study political competition in an environment in which voters have private information about their preferences. Our framework covers models of income taxation, public-goods provision, or publicly provided private goods. Politicians are vote-share maximizers. They can propose any policy that is resource-feasible and incentive-compatible. They can also offer special favors to subsets of the electorate. We prove two main results. First, the unique symmetric equilibrium is such that policies are surplus-maximizing and hence first-best Pareto-efficient. Second, there is a surplus-maximizing policy that wins a majority against any welfare-maximizing policy. Thus, in our model, policies that trade off equity and efficiency considerations are politically infeasible.

The Day Care Assignment: A Dynamic Matching Problem

2014 ◽  
Vol 6 (4) ◽  
pp. 362-406 ◽  
Author(s):  
John Kennes ◽  
Daniel Monte ◽  
Norovsambuu Tumennasan
Keyword(s):  
School Choice ◽  
Day Care ◽  
Student Mobility ◽  
Entry And Exit ◽  
Choice Problem ◽  
Matching Problem ◽  
Day Care Centers ◽  
Dynamic Matching ◽  
Strategy Proof ◽  
Pareto Efficient

We study the problem of centralized allocation of children to public day care centers, illustrated by the case of Denmark. Our framework applies to problems of dynamic matching in which there is entry and exit of agents over time; for example, the school choice problem once student mobility is taken into account. We show that there does not exist any mechanism that is both stable and strategy-proof. We also show that the well-known Top Trading Cycles mechanism is neither Pareto efficient nor strategy-proof. Finally, a mechanism in which parents sequentially choose menus of schools is both strategy-proof and Pareto efficient. (JEL C73, D82, I21)

Dictatorial Mechanisms in Constrained Combinatorial Auctions

2013 ◽  
Vol 13 (1) ◽  
pp. 363-380 ◽  
Author(s):  
Anat Lerner ◽  
Rica Gonen
Keyword(s):  
Dominant Strategy ◽  
Combinatorial Auctions ◽  
Budget Constraints ◽  
Basic Properties ◽  
Incentive Compatible ◽  
Private Values ◽  
Multidimensional Types ◽  
Possibility Space ◽  
Pareto Efficient ◽  
Strategy Incentive

AbstractWe study the possibility space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto efficient combinatorial auctions in a model with two players and two nonidentical items (four outcomes). Our model has multidimensional types, private values, nonnegative prices, and quasilinear preferences for the players with one relaxation – the players are subject to publicly known budget constraints. We show that the space we study essentially includes one type of mechanisms: autocratic mechanisms (a form of dictatorship). Furthermore, we prove that there are families of autocratic mechanisms that uniquely fulfill the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto efficient. The mechanisms in the autocratic families are identical except for two to three price parameters that differentiate them.

A stable and Pareto efficient update of matching in school choice

2016 ◽  
Vol 143 ◽  
pp. 111-113 ◽  
Author(s):  
Yasunori Okumura
Keyword(s):  
School Choice ◽  
Pareto Efficient

Optimizing for Distributional Goals in School Choice Problems

2020 ◽  
Vol 66 (8) ◽  
pp. 3657-3676
Author(s):  
Aaron L. Bodoh-Creed
Keyword(s):  
Public Schools ◽  
School Choice ◽  
Optimization Problems ◽  
Incentive Compatibility ◽  
Neighborhood Schools ◽  
Boston Public Schools ◽  
Incentive Compatible ◽  
The Status ◽  
Student Welfare

I investigate three goals of school choice: welfare, encouraging neighborhood schools, and diversity. I use optimization problems to find the best stable and incentive compatible match for any combination of these objectives. These problems assume there is a continuum of students and school seats, which allows me to describe the incentive compatibility conditions in a tractable form. I prove that the set of stable matchings is generically continuous in the distribution of students and the school capacities, which implies that the characterization of the possible stable matches in the continuum model approximates the set of stable matches in a matching market with a large, but finite, number of students. I then apply my framework to data from Boston Public Schools. If the mechanism conditions on demographics, the improvement (relative to the status quo) in student welfare is equivalent to moving 291 students (out of 3,479) to schools one rank higher in their preference lists. In contrast, if the mechanism does not condition on demographics, the welfare improvement is equivalent to moving only 25.1 students to schools one rank higher. Improvements in the distributional goals can be made (e.g., increasing enrollment in neighborhood schools by 50%) without reducing welfare or diversity. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

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