The Limits of Incentives in Economic Matching Procedures

2020 ◽  
Author(s):  
Avinatan Hassidim ◽  
Assaf Romm ◽  
Ran I. Shorrer
Keyword(s):  
Private Information ◽  
Graduate Programs ◽  
Revenue Maximization ◽  
Matching Markets ◽  
Positive Signal ◽  
Best Interest ◽  
High Stakes ◽  
Field Evidence ◽  
Deferred Acceptance ◽  
Strategy Proof

Organizations often require agents’ private information to achieve critical goals such as efficiency or revenue maximization, but frequently it is not in the agents’ best interest to reveal this information. Strategy-proof mechanisms give agents incentives to truthfully report their private information. In the context of matching markets, they eliminate agents’ incentives to misrepresent their preferences. We present direct field evidence of preference misrepresentation under the strategy-proof deferred acceptance in a high-stakes matching environment. We show that applicants to graduate programs in psychology in Israel often report that they prefer to avoid receiving funding, even though the mechanism preserves privacy and funding comes with no strings attached and constitutes a positive signal of ability. Surveys indicate that other kinds of preference misrepresentation are also prevalent. Preference misrepresentation in the field is associated with weaker applicants. Our findings have important implications for practitioners designing matching procedures and for researchers who study them. This paper was accepted by Axel Ockenfels, decision analysis.

Sequential Preference Revelation in Incomplete Information Settings

2021 ◽  
Vol 13 (1) ◽  
pp. 116-147
Author(s):  
James Schummer ◽  
Rodrigo A. Velez
Keyword(s):  
Incomplete Information ◽  
Real World ◽  
Private Information ◽  
Allocation Rules ◽  
Is Strategy ◽  
Strategy Proof ◽  
Simultaneous Move

Strategy-proof allocation rules incentivize truthfulness in simultaneous move games, but real world mechanisms sometimes elicit preferences sequentially. Surprisingly, even when the underlying rule is strategy-proof and nonbossy, sequential elicitation can yield equilibria where agents have a strict incentive to be untruthful. This occurs only under incomplete information, when an agent anticipates that truthful reporting would signal false private information about others’ preferences. We provide conditions ruling out this phenomenon, guaranteeing all equilibrium outcomes to be welfare-equivalent to truthful ones. (JEL C73, D45, D82, D83)

scholarly journals Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions

2019 ◽  
Vol 109 (4) ◽  
pp. 1486-1529 ◽  
Author(s):  
Gabrielle Fack ◽  
Julien Grenet ◽  
Yinghua He
Keyword(s):  
School Choice ◽  
Test Scores ◽  
Real Life ◽  
Truth Telling ◽  
Student Preferences ◽  
Ex Post ◽  
Is Strategy ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Novel Approaches

We propose novel approaches to estimating student preferences with data from matching mechanisms, especially the Gale-Shapley deferred acceptance. Even if the mechanism is strategy-proof, assuming that students truthfully rank schools in applications may be restrictive. We show that when students are ranked strictly by some ex ante known priority index (e.g., test scores), stability is a plausible and weaker assumption, implying that every student is matched with her favorite school/college among those she qualifies for ex post. The methods are illustrated in simulations and applied to school choice in Paris. We discuss when each approach is more appropriate in real-life settings. (JEL D11, D12, D82, I23)

scholarly journals Weighted Matching Markets with Budget Constraints

2019 ◽  
Vol 65 ◽  
pp. 393-421 ◽  
Author(s):  
Anisse Ismaili ◽  
Naoto Hamada ◽  
Yuzhe Zhang ◽  
Takamasa Suzuki ◽  
Makoto Yokoo
Keyword(s):  
Polynomial Time ◽  
Real World ◽  
Stable Matching ◽  
The Other ◽  
Matching Markets ◽  
Pairwise Stability ◽  
Negative Results ◽  
Strategy Proof ◽  
Pareto Efficient ◽  
Coalitional Stability

We investigate markets with a set of students on one side and a set of colleges on the other. A student and college can be linked by a weighted contract that defines the student's wage, while a college's budget for hiring students is limited. Stability is a crucial requirement for matching mechanisms to be applied in the real world. A standard stability requirement is coalitional stability, i.e., no pair of a college and group of students has any incentive to deviate. We find that a coalitionally stable matching is not guaranteed to exist, verifying the coalitional stability for a given matching is coNP-complete, and the problem of finding whether a coalitionally stable matching exists in a given market, is SigmaP2-complete: NPNP-complete. Other negative results also hold when blocking coalitions contain at most two students and one college. Given these computational hardness results, we pursue a weaker stability requirement called pairwise stability, where no pair of a college and single student has an incentive to deviate. Unfortunately, a pairwise stable matching is not guaranteed to exist either. Thus, we consider a restricted market called a typed weighted market, in which students are partitioned into types that induce their possible wages. We then design a strategy-proof and Pareto efficient mechanism that works in polynomial-time for computing a pairwise stable matching in typed weighted markets.

An Auction Based Task Dispatching and Pricing Mechanism in Bike-sharing

2021 ◽  
Author(s):  
Bing Shi ◽  
Yaping Deng ◽  
Han Yuan
Keyword(s):  
Private Information ◽  
Optimal Algorithm ◽  
Incentive Compatibility ◽  
Unit Cost ◽  
Low Carbon ◽  
Budget Balance ◽  
Coverage Ratio ◽  
Bike Sharing ◽  
Dispatching Algorithm ◽  
Strategy Proof

Abstract As a green and low-carbon transportation way, bike-sharing provides lots of convenience in the daily life. However, the daily usage of sharing bikes results in dispatching problems, i.e. dispatching bikes to the specific destinations. The bike-sharing platform can hire and pay to workers in order to incentivize them to accomplish the dispatching tasks. However, there exist multiple workers competing for the dispatching tasks, and they may strategically report their task accomplishing costs (which are private information only known by themselves) in order to make more profits, which may result in inefficient task dispatching results. In this paper, we first design a dispatching algorithm named GDY-MAX to allocate tasks to workers, which can achieve good performance. However it cannot prevent workers strategically misreporting their task accomplishing costs. Regarding this issue, we further design a strategy proof mechanism under the budget constraint, which consists of a task dispatching algorithm and a worker pricing algorithm. We theoretically prove that our mechanism can satisfy the properties of incentive compatibility, individual rationality and budget balance. Furthermore we run extensive experiments to evaluate our mechanism based on a dataset from Mobike. The results show that the performance of the proposed strategy proof mechanism and GDY-MAX is similar to the optimal algorithm in terms of the coverage ratio of accomplished task regions and the sum of task region values, and our mechanism has better performance than the uniform algorithm in terms of the total payment and the unit cost value.

scholarly journals Heterogeneous Beliefs and School Choice Mechanisms

2020 ◽  
Vol 110 (5) ◽  
pp. 1274-1315 ◽  
Author(s):  
Adam J. Kapor ◽  
Christopher A. Neilson ◽  
Seth D. Zimmerman
Keyword(s):  
School Choice ◽  
Rational Expectations ◽  
Choice Behavior ◽  
Heterogeneous Beliefs ◽  
Welfare Costs ◽  
Subjective Beliefs ◽  
Opposite Conclusion ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof

This paper studies how welfare outcomes in centralized school choice depend on the assignment mechanism when participants are not fully informed. Using a survey of school choice participants in a strategic setting, we show that beliefs about admissions chances differ from rational expectations values and predict choice behavior. To quantify the welfare costs of belief errors, we estimate a model of school choice that incorporates subjective beliefs. We evaluate the equilibrium effects of switching to a strategy-proof deferred acceptance algorithm, and of improving households’ belief accuracy. We find that a switch to truthful reporting in the DA mechanism offers welfare improvements over the baseline given the belief errors we observe in the data, but that an analyst who assumed families had accurate beliefs would have reached the opposite conclusion. (JEL D83, H75, I21, I28)

scholarly journals M-DPOP: Faithful Distributed Implementation of Efficient Social Choice Problems

2008 ◽  
Vol 32 ◽  
pp. 705-755 ◽  
Author(s):  
A. Petcu ◽  
B. Faltings ◽  
D. C. Parkes
Keyword(s):  
Social Choice ◽  
Private Information ◽  
Choice Problem ◽  
Best Interest ◽  
Distributed Constraint Optimization ◽  
The Social ◽  
Structured Problems ◽  
Distributed Implementation ◽  
Distributed Constraint Optimization Problem ◽  
Sparse Problems

In the efficient social choice problem, the goal is to assign values, subject to side constraints, to a set of variables to maximize the total utility across a population of agents, where each agent has private information about its utility function. In this paper we model the social choice problem as a distributed constraint optimization problem (DCOP), in which each agent can communicate with other agents that share an interest in one or more variables. Whereas existing DCOP algorithms can be easily manipulated by an agent, either by misreporting private information or deviating from the algorithm, we introduce M-DPOP, the first DCOP algorithm that provides a faithful distributed implementation for efficient social choice. This provides a concrete example of how the methods of mechanism design can be unified with those of distributed optimization. Faithfulness ensures that no agent can benefit by unilaterally deviating from any aspect of the protocol, neither information-revelation, computation, nor communication, and whatever the private information of other agents. We allow for payments by agents to a central bank, which is the only central authoritythat we require. To achieve faithfulness, we carefully integrate the Vickrey-Clarke-Groves (VCG) mechanism with the DPOP algorithm, such that each agent is only asked to perform computation, report information, and send messages that is in its own best interest. Determining agent i's payment requires solving the social choice problem without agent i. Here, we present a method to reuse computation performed in solving the main problem in a way that is robust against manipulation by the excluded agent. Experimental results on structured problems show that as much as 87% of the computation required for solving the marginal problems can be avoided by re-use, providing very good scalability in the number of agents. On unstructured problems, we observe a sensitivity of M-DPOP to the density of the problem, and we show that reusability decreases from almost 100% for very sparse problems to around 20% for highly connected problems. We close with a discussion of the features of DCOP that enable faithful implementations in this problem, the challenge of reusing computation from the main problem to marginal problems in other algorithms such as ADOPT and OptAPO, and the prospect of methods to avoid the welfare loss that can occur because of the transfer of payments to the bank.

scholarly journals Controlled School Choice with Soft Bounds and Overlapping Types

2017 ◽  
Vol 58 ◽  
pp. 153-184 ◽  
Author(s):  
Ryoji Kurata ◽  
Naoto Hamada ◽  
Atsushi Iwasaki ◽  
Makoto Yokoo
Keyword(s):  
School Choice ◽  
Stable Matching ◽  
Extended Model ◽  
The Public ◽  
Distributional Constraints ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Stability Definition ◽  
Model Computer ◽  
Straightforward Extension

School choice programs are implemented to give students/parents an opportunity to choose the public school the students attend. Controlled school choice programs need to provide choices for students/parents while maintaining distributional constraints on the composition of students, typically in terms of socioeconomic status. Previous works show that setting soft-bounds, which flexibly change the priorities of students based on their types, is more appropriate than setting hard-bounds, which strictly limit the number of accepted students for each type. We consider a case where soft-bounds are imposed and one student can belong to multiple types, e.g., “financially-distressed” and “minority” types. We first show that when we apply a model that is a straightforward extension of an existing model for disjoint types, there is a chance that no stable matching exists. Thus we propose an alternative model and an alternative stability definition, where a school has reserved seats for each type. We show that a stable matching is guaranteed to exist in this model and develop a mechanism called Deferred Acceptance for Overlapping Types (DA-OT). The DA-OT mechanism is strategy-proof and obtains the student-optimal matching within all stable matchings. Furthermore, we introduce an extended model that can handle both type-specific ceilings and floors and propose a extended mechanism DA-OT* to handle the extended model. Computer simulation results illustrate that DA-OT outperforms an artificial cap mechanism where we set a hard-bound for each type in each school. DA-OT* can achieve stability in the extended model without sacrificing students’ welfare.

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