Mechanism Design without Money via Stable Matching

Mechanism design without money has a rich history in social choice literature. Due to the strong impossibility theorem by Gibbard and Satterthwaite, exploring domains in which there exist dominant strategy mechanisms is one of the central questions in the field. We propose a general framework, called the generalized packing problem (\gpp), to study the mechanism design questions without payment. The \gpp\ possesses a rich structure and comprises a number of well-studied models as special cases, including, e.g., matroid, matching, knapsack, independent set, and the generalized assignment problem. We adopt the agenda of approximate mechanism design where the objective is to design a truthful (or strategyproof) mechanism without money that can be implemented in polynomial time and yields a good approximation to the socially optimal solution. We study several special cases of \gpp, and give constant approximation mechanisms for matroid, matching, knapsack, and the generalized assignment problem. Our result for generalized assignment problem solves an open problem proposed in \cite{DG10}. Our main technical contribution is in exploitation of the approaches from stable matching, which is a fundamental solution concept in the context of matching marketplaces, in application to mechanism design. Stable matching, while conceptually simple, provides a set of powerful tools to manage and analyze self-interested behaviors of participating agents. Our mechanism uses a stable matching algorithm as a critical component and adopts other approaches like random sampling and online mechanisms. Our work also enriches the stable matching theory with a new knapsack constrained matching model

Approximately Stable, School Optimal, and Student-Truthful Many-to-One Matchings (via Differential Privacy)

We present a mechanism for computing asymptotically stable school optimal matchings, while guaranteeing that it is an asymptotic dominant strategy for every student to report their true preferences to the mechanism. Our main tool in this endeavor is differential privacy: we give an algorithm that coordinates a stable matching using differentially private signals, which lead to our truthfulness guarantee. This is the first setting in which it is known how to achieve nontrivial truthfulness guarantees for students when computing school optimal matchings, assuming worst- case preferences (for schools and students) in large markets

A data-driven game theoretic strategy for developers in software crowdsourcing: a case study

Crowdsourcing has the advantages of being cost-effective and saving time, which is a typical embodiment of collective wisdom and community workers’ collaborative development. However, this development paradigm of software crowdsourcing has not been used widely. A very important reason is that requesters have limited knowledge about crowd workers’ professional skills and qualities. Another reason is that the crowd workers in the competition cannot get the appropriate reward, which affects their motivation. To solve this problem, this paper proposes a method of maximizing reward based on the crowdsourcing ability of workers, they can choose tasks according to their own abilities to obtain appropriate bonuses. Our method includes two steps: Firstly, it puts forward a method to evaluate the crowd workers’ ability, then it analyzes the intensity of competition for tasks at Topcoder.com—an open community crowdsourcing platform—on the basis of the workers’ crowdsourcing ability; secondly, it follows dynamic programming ideas and builds game models under complete information in different cases, offering a strategy of reward maximization for workers by solving a mixed-strategy Nash equilibrium. This paper employs crowdsourcing data from Topcoder.com to carry out experiments. The experimental results show that the distribution of workers’ crowdsourcing ability is uneven, and to some extent it can show the activity degree of crowdsourcing tasks. Meanwhile, according to the strategy of reward maximization, a crowd worker can get the theoretically maximum reward

The Principal-Agent Matching Market

We propose a model based on competitive markets in order to analyse an economy with several principals and agents. We model the principal-agent economy as a two-sided matching game and characterise the set of stable outcomes of this principal-agent matching market. A simple mechanism to implement the set of stable outcomes is proposed. Finally, we put forward examples of principal-agent economies where the results fit.principal-agent, moral hazard, matching, implementation

Matching under Preferences

Matching theory studies how agents and/or objects from different sets can be matched with each other while taking agents\u2019 preferences into account. The theory originated in 1962 with a celebrated paper by David Gale and Lloyd Shapley (1962), in which they proposed the Stable Marriage Algorithm as a solution to the problem of two-sided matching. Since then, this theory has been successfully applied to many real-world problems such as matching students to universities, doctors to hospitals, kidney transplant patients to donors, and tenants to houses. This chapter will focus on algorithmic as well as strategic issues of matching theory. Many large-scale centralized allocation processes can be modelled by matching problems where agents have preferences over one another. For example, in China, over 10 million students apply for admission to higher education annually through a centralized process. The inputs to the matching scheme include the students\u2019 preferences over universities, and vice versa, and the capacities of each university. The task is to construct a matching that is in some sense optimal with respect to these inputs. Economists have long understood the problems with decentralized matching markets, which can suffer from such undesirable properties as unravelling, congestion and exploding offers (see Roth and Xing, 1994, for details). For centralized markets, constructing allocations by hand for large problem instances is clearly infeasible. Thus centralized mechanisms are required for automating the allocation process. Given the large number of agents typically involved, the computational efficiency of a mechanism's underlying algorithm is of paramount importance. Thus we seek polynomial-time algorithms for the underlying matching problems. Equally important are considerations of strategy: an agent (or a coalition of agents) may manipulate their input to the matching scheme (e.g., by misrepresenting their true preferences or underreporting their capacity) in order to try to improve their outcome. A desirable property of a mechanism is strategyproofness, which ensures that it is in the best interests of an agent to behave truthfully

The collapse of a medical clearinghouse (and why such failures are rare)

The collapse of the clearinghouse for the entry-level gastroenterology labor market offers a unique opportunity to study how stable clearinghouses succeed and fail. To explore the reasons for the failure of the clearinghouse (and why failures of this kind of clearinghouse have been so rare), we conduct an experimental investigation of demand shocks of the kind that occurred in the gastroenterology market. We find that a reduction in demand for positions leads to the collapse of the match only when it is detectable by firms before being detected by workers (as in the unexpected shock that took place in 1996, which could be seen by firms in their reduced applicant pools). Simple demand and supply imbalances do not seem to interfere with the operation of the centralized match. Our results suggest an affirmative answer to the question posed by market participants about whether the clearinghouse could be successfully restarted, and that this would relieve some of the distress now reported in that market, by allowing it to operate later, at a more uniform time, and with more national scope.