The relationship between top trading cycles mechanism and top trading cycles and chains mechanism

In this paper, we show that there is a relationship between two important matching mechanisms: the Top Trading Cycles mechanism (TTC mechanism proposed by Abdulkadiroglu and Sonmez, 1999) and the Top Trading Cycles and Chains mechanism (TTCC mechanism proposed by Roth, Sonmez, and Unver, 2004). Our main result is that when a specific chain selection rule proposed by Roth et al. is used, these two mechanisms are equivalent. While the equivalence is relevant for one specific case of the TTCC mechanism, it is a particularly interesting case since it is the only version identified by Roth et al. to be both Pareto-efficient and strategy-proof.     

School choice: an experimental study

We present an experimental study of three school choice mechanisms. The Boston mechanism is influential in practice, while the Gale-Shapley and Top Trading Cycles mechanisms have superior theoretical properties. Consistent with theory, this study indicates a high preference manipulation rate under Boston. As a result, efficiency under Boston is significantly lower than that of the two competing mechanisms in the designed environment. However, contrary to theory, Gale-Shapley outperforms Top Trading Cycles and generates the highest efficiency. Our results suggest that replacing the Boston mechanism with either Gale-Shapley or Top Trading Cycles mechanism might significantly improve efficiency.     

Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms

There is a wide range of economic problems that involve the exchange of indivisible goods with no monetary transfers, starting from the housing market model of the seminal paper by Shapley and Scarf (1974) to problems such as the kidney exchange or the school choice problem. The classical solution to many of these models is to apply a mechanism called Top Trading Cycles, attributed to David Gale, which satisfies good properties for the case of strict preferences. In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, which generalize the Top Trading Cycles to the general case in which individuals are allowed to report indifferences, while preserving a maximal possible set of its desirable properties.     

Constrained school choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable mechanism or the Top Trading Cycles mechanism to assign children to public schools. There is evidence that for school districts that employ (variants of) the so-called Boston mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures typically impede a student to submit a preference list that contains all his acceptable schools. We study the preference revelation game where students can only declare up to a fixed number of schools to be acceptable. We focus on the stability and efficiency of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guarantee stability or efficiency of either of the two mechanisms. This stands in sharp contrast with the Boston mechanism which has been abandoned in many US school districts but nevertheless yields stable Nash equilibrium outcomes.     

MATCHING MARKETS WITH MIXED OWNERSHIP: THE CASE FOR A REAL‐LIFE ASSIGNMENT MECHANISM*

We consider a common indivisible good allocation problem whose popular applications include on‐campus housing, kidney exchange, and school choice. We show that the so‐called New House 4 (NH4) mechanism, which has been in use at MIT since the 1980s, is equivalent to a natural adaptation of the well‐known Gale–Shapley (GS) mechanism. We run two experiments comparing NH4 with the prominently advocated Top Trading Cycles (TTC) mechanism and NH4 with GS. We find that under NH4, the participation rate is significantly higher than under TTC. Based on a new ordinal test of efficiency, NH4 is more likely to Pareto dominate TTC.     

Incomplete information and singleton cores in matching markets

We study ordinal Bayesian Nash equilibria of stable mechanisms in centralized matching markets under incomplete information. We show that truth-telling is an ordinal Bayesian Nash equilibrium of the revelation game induced by a common belief and a stable mechanism if and only if all the profiles in the support of the common belief have singleton cores. Our result matches the observations of Roth and Peranson [The redesign of the matching market for American physicians: some engineering aspects of economic design, Amer. Econ. Rev. 89 (1999) 748-780] in the National Resident Matching Program (NRMP) in the United States: (i) the cores of the profiles submitted to the clearinghouse are small and (ii) while truth-telling is not a dominant strategy most participants in the NRMP truthfully reveal their preferences.     

A folk theorem for Bayesian games with commitment

The set of all Bayesian–Nash equilibrium payoffs that the players can achieve by making conditional commitments at the interim stage of a Bayesian game coincides with the set of all feasible, incentive compatible and interim individually rational payoffs of the Bayesian game. Furthermore, the various equilibrium payoffs, which are achieved by means of different commitment devices, are also the equilibrium payoffs of a universal, deterministic commitment game.     

Enjoy the silence: an experiment on truth-telling

We analyze experimentally two sender–receiver games with conflictive preferences. In the first game, the sender can choose to tell the truth, to lie, or to remain silent. The latter strategy is costly. In the second game, the receiver must decide additionally whether or not to costly punish the sender after having observed the history of the game. We investigate the existence of two kinds of social preferences: lying aversion and preference for truth-telling. In the first game, senders tell the truth more often than predicted by the sequential equilibrium analysis, they remain silent frequently, and there exists a positive correlation between the probability of being truthful and the probability of remaining silent. Our main experimental result for the extended game shows that those subjects who punish the sender with a high probability after being deceived are precisely those who send fewer but more truthful messages. Finally, we solve for the Perfect Bayesian Nash Equilibria of a reduced form of the baseline game with two types of senders. The equilibrium predictions obtained suggest that the observed excessive truth-telling in the baseline game can be explained by lying aversion but not by a preference for truth-telling.

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Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users. Financial support through the Ramón y Cajal program of the Spanish Ministry of Education and Science is gratefully acknowledged. This work was initiated while the author was working at Maastricht University.     

Optimal truncation in matching markets

Although no stable matching mechanism can induce truth-telling as a dominant strategy for all participants (Roth, 1982), recent studies have presented conditions under which truthful reporting by all agents is close to optimal (Immorlica and Mahdian, 2005, Kojima and Pathak, 2009, Lee, 2011). Our results demonstrate that in large, uniform markets using the Men-Proposing Deferred Acceptance Algorithm, each woman's best response to truthful behavior by all other agents is to truncate her list substantially. In fact, the optimal degree of truncation for such a woman goes to 100% of her list as the market size grows large. In general one-to-one markets we provide comparative statics for optimal truncation strategies: reduction in risk aversion and reduced correlation across preferences each lead agents to truncate more. So while several recent papers focused on the limits of strategic manipulation, our results serve as a reminder that without pre-conditions ensuring truthful reporting, there exists a potential for significant manipulation even in settings where agents have little information.     

For the Student: Matching and Economic Design

This article presents a brief survey of two‐sided matching. We introduce the reader to the problem of two‐sided matching in the context of the college admission model and explain two central requirements for a matching mechanism: stability and non‐manipulability. We show how the frequently used ‘Boston Mechanism’ fails these key requirements and describe how an alternative, the Deferred Acceptance Algorithm, leads to stable matchings but fails to be non‐manipulable in general. A third mechanism, the Top Trading Cycle, is efficient and non‐manipulable when only one side of the match acts strategically. We also discuss some applications of matching theory.     

企业制度变革中的博弈与均衡——一个关于国有企业民营化的实证研究

企业制度运行以利益相关者之间的共有理念为心理依托；这种共有理念体现在人们博弈均衡之中，是人们行为选择的默认前提，其形成和发展具有不以个人意志为转移的客观规律；企业制度变革的任务，是通过企业利益相关者之间的博弈和信任，在适应和调整共有理念的基础上，塑造合理的企业控制权主体。     

Not quite the best response: truth-telling,strategy-proof matching,and the manipulation of others

Following the advice of economists, school choice programs around the world have lately been adopting strategy-proof mechanisms. However, experimental evidence presents a high variation of truth-telling rates for strategy-proof mechanisms. We crash test the connection between the strategy-proofness of the mechanism and truth-telling. We employ a within-subjects design by making subjects take two simultaneous decisions: one with no strategic uncertainty and one with some uncertainty and partial information about the strategies of other players. We find that providing information about the out-of-equilibrium strategies played by others has a negative and significant effect on truth-telling rates. That is, most participants in our within-subjects design try and fail to best-respond to changes in the environment. We also find that more sophisticated subjects are more likely to play the dominant strategy (truth-telling) across all the treatments. These results have potentially important implications for the design of markets based on strategy-proof matching mechanisms.     

Equilibria under deferred acceptance: Dropping strategies,filled positions,and welfare

We study many-to-one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.Roth and Sotomayor (1990) showed that equilibrium outcomes can be unstable. We prove that any stable matching is obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the ‘rural hospital theorem’ cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the equilibrium that is reached and (b) welfare levels are not bounded by the optimal stable matchings (with respect to the true preferences).     

CREDIT RATING AND DEBT CRISES

We develop an equilibrium theory of credit rating in the presence of rollover risk. By influencing rational creditors, ratings affect sovereigns' probability of default, which in turn affects ratings. Our analysis reveals a pro‐cyclical impact of credit rating: In equilibrium the presence of a rating agency increases default risk when it is high and decreases default risk when it is low.     

论住房抵押贷款终止偿付型理性违约

住房抵押贷款债务人不仅会进行提前偿付型理性违约 ,在相关机制不健全时也会进行终止偿付型理性违约。终止偿付型理性违约是指在住房抵押贷款存续期内 ,债务人在自身财务状况正常的情况下 ,因经济理性而从某一时刻起终止继续履行对尚欠贷款本息的偿还责任的违约行为。它发生的客观性在于住房抵押贷款债务人对所购住房损失最小化或收益最大化的财务预期能否顺利实现。建立终止偿付型理性违约发生的条件模型 ,可找出抵押率、贷期、已还款量和已履约时间等变量与条件模型的内在关系 ,进而设计出我国金融机构主动防范终止偿付型理性违约风险的思路。     

A General Approach to Rational Learning in Games

This paper provides a general framework for analysing rational learning in strategic situations in which the players have private priors and private information. The author analyses the behaviour of Bayesian rational players both in a repeated game and in a recurrent game when they are uncertain about opponents' behaviour and the game they are playing. The aim of the paper is to explain how Bayesian rational agents learn by playing and to characterize the outcome of this learning process. By studying the concept of 'conjectural equilibrium' and analysing the process of convergence of players' behaviour, the roles played by the notions of merging and of consistency are demonstrated.     

Coordination with communication under oath

We focus on the design of an institutional device aimed to foster coordination through communication. We explore whether the social psychology theory of commitment, implemented via a truth-telling oath, can reduce coordination failure. Using a classic coordination game, we ask all players to sign voluntarily a truth-telling oath before playing the game with cheap talk communication. Three results emerge with commitment under oath: (1) coordination increased by nearly 50%; (2) senders’ messages were significantly more truthful and actions more efficient, and (3) receivers’ trust of messages increased.     

Information at equilibrium

Summary. In a game with rational expectations, individuals simultaneously refine their information with the information revealed by the strategies of other individuals. At a Nash equilibrium of a game with rational expectations, the information of individuals is essentially symmetric: the same profile of strategies is also an equilibrium of a game with symmetric information; and strategies are common knowledge. If each player has a veto act, which yields a minimum payoff that no other profile of strategies attains, then the veto profile is the only Nash equilibrium, and it is is an equilibrium with rational expectations and essentially symmetric information; which accounts for the impossibility of speculation. Received: June 20, 2001; revised version: January 9, 2002 RID="*" ID="*" We wish to thank Pierpaolo Battigalli, Fran?oise Forges, Franco Donzelli, Leonidas Koutsougeras, Aldo Rustichini, Rajiv Vohra and Nicholas Yannelis for their comments. Correspondence to: H. Polemarchakis     

Voluntary Participation and Provision of Public Goods in Large Finite Economies

We consider a public good provision game with voluntary participation. Agents participating in the game provide a public good and pay the fees according to a mechanism (allocation rule), while nonparticipants can free‐ride on the participants. We examine how the equilibrium public good provision level is affected by enlarging the population of an economy. We introduce a condition for an allocation rule, the asymptotic uniform continuity in replication (AUCR), which requires that small changes in the population must yield only small changes in the public good provision and which is satisfied by many mechanisms. We show that under AUCR, the equilibrium level of the public good converges to zero as the economy is replicated in the sense of Milleron.     

Coordination need not be a problem

In a game of common interest there is one action vector that all players prefer to every other. Yet there may be multiple Pareto-ranked Nash equilibria in the game and the “coordination problem” refers to the fact that rational equilibrium play cannot rule out Pareto-dominated equilibria. In this paper, I prove that two elements — asynchronicity and a finite horizon — are sufficient to uniquely select the Pareto-dominant action vector (in subgame perfect equilibrium play). Asynchronicity may be exogenously specified by the rules of the game. Alternatively, in a game where players choose when to move, asynchronicity may emerge as an equilibrium move outcome.