Games of capacity allocation in many-to-one matching with an aftermarket

In this paper, we study many-to-one matching (hospital–intern markets) with an aftermarket. We first show that every stable matching system is manipulable via aftermarket. We then analyze the Nash equilibria of capacity allocation games, in which preferences of hospitals and interns are common knowledge and every hospital determines a quota for the regular market given its total capacity for the two matching periods. Under the intern-optimal stable matching system, we show that a pure-strategy Nash equilibrium may not exist. Common preferences for hospitals ensure the existence of equilibrium in weakly dominant strategies whereas unlike in games of capacity manipulation strong monotonicity of population is not a sufficient restriction on preferences to avoid the non-existence problem. Besides, in games of capacity allocation, it is not true either that every hospital weakly prefers a mixed-strategy Nash equilibrium to any larger regular market quota profiles.     

Games with capacity manipulation: incentives and Nash equilibria

Studying the interactions between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and sufficient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal and intern-optimal stable rules. We then introduce generalized games of manipulation in which hospitals move first and state their capacities, and interns are subsequently assigned to hospitals using a sequential mechanism. In this setting, we first consider stable revelation mechanisms and introduce conditions guaranteeing the stability of the outcome. Next, we prove that every stable non-revelation mechanism leads to unstable allocations, unless restrictions on the preferences of the agents are introduced.     

Mixed Strategies in Games of Capacity Manipulation in Hospital–Intern Markets

We investigate games of capacity manipulation in hospital-intern markets as proposed by Konishi and ünver (Soc Choice Welfare, in press). While Konishi and ünver (Soc Choice Welfare, in press) show that there may not exist a pure-strategy Nash equilibrium in general, there exists a mixed-strategy Nash equilibrium in such a game. We show that every hospital weakly prefers a Nash equilibrium to any “larger” capacity profiles, whether the equilibrium is in pure or mixed strategies. In particular, a Nash equilibrium is weakly preferred by hospitals to the outcome that results from truthful reporting.     

Voting rules and efficiency in one-dimensional bargaining games with endogenous protocol

We analyze a rent-seeking contest that determines the bargaining protocol in a one-dimensional bargaining game, where agents preferences over social outcomes are single-peaked. We relate the incentives of agents to make unproductive and costly efforts/investments to the quota rules that are required to implement agreements. When the contest assigns persistent recognition probabilities, we find that simple majority minimizes the total investments and, hence, inefficiency. In case that the contest recurs each period, multiple equilibria exist with the particularity that in each equilibrium only one agent controls the agenda of the bargaining process.     

Electing a parliament

We present a model where a society elects candidates belonging to two parties to a national parliament. The electoral rule determines the seats distribution between the two parties. The policy outcome is a function of the number of seats the two parties win in the election. We analyze two electoral rules, multidistrict majority and single district proportional. We prove that under both systems there is a unique pure strategy perfect equilibrium outcome. We compare the outcomes under the two systems.     

Generalized average rules as stable Nash mechanisms to implement generalized median rules

We consider a problem in which a policy is chosen from a one-dimensional set over which voters have single-peaked preferences. While Moulin (Public Choice 35:437–455, 1980) and others subsequent works have focused on strategy-proof rules, Renault and Trannoy (Mimeo 2011) and Renault and Trannoy (J Pub Econ Theory 7:169–199, 2005) have shown that the average rule implements a generalized median rule in Nash equilibria and provide an interpretation of the parameters in Moulin’s rule. In this article, we first extend their result by showing that a wide range of voting rules which includes the average rule can implement Moulin’s rule in Nash equilibria. Moreover, we show additionally that within this class, generalized average rules are Cournot stable. That is, from any strategy profile, any best response path must converge to a Nash equilibrium.     

An incompatibility between recursive unanimity and strategy-proofness in two-sided matching problems

In this article, we study the incompatibilities for the properties on matching rules in two-sided many-to-one matching problems under responsive preferences. We define a new property called respect for recursive unanimity. This property requires that if every agent matches with its first choice among its really possible choices that are based on a recursive procedure like the well-known top trading cycles algorithm, then we should respect it. More precisely, given a matching problem, we exclude the agents whose first choices are satisfied without any discrepancy among them, and consider the restricted matching problems of the remaining agents. If we reach a state in which all agents are excluded by repeating this procedure, then we should respect the outcome. This property is weaker than stability and is stronger than respect for unanimity (that is also known as weak unanimity). We show that there are no strategy-proof matching rules that respect recursive unanimity.     

Uniform trade rules for uncleared markets

We analyze markets in which the price of a traded commodity is such that the supply and the demand are unequal. Under standard assumptions, the agents then have single peaked preferences on their consumption or production choices. For such markets, we propose a class of Uniform trade rules each of which determines the volume of trade as the median of total demand, total supply, and an exogenous constant. Then these rules allocate this volume “uniformly” on either side of the market. We evaluate these “trade rules” on the basis of some standard axioms in the literature. We show that they uniquely satisfy Pareto optimality, strategy proofness, no-envy, and an informational simplicity axiom that we introduce. We also analyze the implications of anonymity, renegotiation proofness, and voluntary trade on this domain.     

Simple guilt and cooperation

We introduce simple guilt into a generic prisoner’s dilemma (PD) game and solve for the equilibria of the resulting psychological game. It is shown that for all guilt parameters, it is a pure strategy equilibrium that both players defect. But if the guilt parameter surpasses a threshold, a mixed strategy equilibrium and a pure strategy equilibrium in which both players cooperate emerge. We implement three payoff constellations of the PD game in a laboratory experiment and find in line with our equilibrium analysis that first- and second-order beliefs are highly correlated and that the probability of cooperation depends positively on these beliefs. Maximum likelihood estimations of a model of noisy introspection reveal that experimental data is best fitted with positive guilt levels and that omission of guilt results in a substantial increase in the noise parameters.     

THE SOCIAL ROLE OF NOT-FOR-PROFIT ORGANIZATIONS: HOSPITAL PROVISION OF CHARITY CARE

During the 1980s the State of New York shifted from a straight block grant to a matching grant method for reimbursing hospitals, with the matching rate varying from 0 to 75 percent across years. These changes allow estimation of pure "income" and "price" effects for hospitals' supply of uncompensated care (charity and bad debts). The price efrect is positive and significant, but no income effect was found. Hospitals in more concentrated markets provide more charity care, as do teaching hospitals, and the presence of public hospitals in a market reduces private hospitals' provision of charity care.     

Inefficient committees: small elections with three alternatives

We consider small committees which have to elect one of three alternatives using the simple plurality rule. Committee members have common, state-dependent preferences and receive imprecise private signals about the state of nature prior to the election. We are interested in whether the committee decision is efficient, that is whether the probability with which the committee elects the correct alternative is higher than the probability with which one single individual alone—on behalf of the others—would. It has been shown that there exists a unique efficient equilibrium in elections with two alternatives. We show that this result does not extend to elections with more alternatives. Multiple equilibria may exist for the same committee, and there may be both efficient and inefficient ones. Informative voting may or may not be an equilibrium. Also contrary to two-alternative elections, there exist responsive equilibria in which voters vote ‘against’ their signal. As a consequence, only two alternatives receive positive expected vote shares and the outcome is inefficient.     

Migration disequilibrium and specific division rules

We examine the extent to which migration equilibria fail to exist in a global economy in which a specific division rule determines the allocation of a perfectly divisible, nondisposable resource among individuals with single-peaked preferences who reside in local economies. In particular, almost without exception, under the egalitarian, proportional, queuing, and uniform division rules, migration equilibria fail to exist for some sets of preferences. Received: 23 May 1995 / Accepted: 1 October 1996     

PRODUCT DIFFERENTIATION UNDER CONGESTION: HOTELLING WAS RIGHT

We introduce negative network externalities—“congestion costs”—into H. Hotelling's (1929) model of spatial competition with linear transportation costs. For any firm locations on opposite sides of the midpoint, a pure strategy price equilibrium exists and is unique if congestion costs are strong enough relative to transportation costs. We analyze product differentiation and find that Hotelling's Principle of Minimum Differentiation comes closer to holding in the presence of congestion costs. The greater are congestion costs, the less differentiated products can be in (locationally symmetric) equilibrium. In fact, minimum differentiation comes arbitrarily close to holding depending on the magnitude of these costs relative to transportation costs. Intuitively, greater congestion effects stabilize competition at closer quarters, eliminating aggressive pricing equilibria. Thus, negative network externalities can play a significant role in product differentiation. (JEL D21, L15, R12)     

Endogenous Voting Agendas

Existence of a “simple” pure strategy subgame perfect equilibrium is established in a model of endogenous agenda formation and sophisticated voting; upper hemicontinuity of simple equilibrium outcomes is demonstrated; and connections to the set of undominated, or “core,” alternatives are examined. In one dimension with single-peaked preferences, the simple equilibrium outcome is essentially unique and lies in the core, providing a game-theoretic foundation for the median voter theorem in terms of endogenous agenda setting. Existence of equilibrium relies on a general characterization of sophisticated voting outcomes in the presence of “majority-ties,” rather than the standard tie-breaking convention in voting subgames in favor of the alternative proposed later. The model is illustrated in a three-agent distributive politics setting, and it is shown there that the standard tie-breaking convention leads to non-existence of equilibrium.     

The role and significance of endogenous firing costs in a matching model with endogenous job destruction

Traditional models of the labor market assume fixed firing costs. This paper explores the implications of variable firing costs, building this new assumption into a matching model with endogenous job destruction. The available evidence on the outcomes of cases brought to labor courts suggests that firing costs are negatively related with labor market tightness. In such a case, we may no longer invoke “rigidities” on labor markets as the cause of their poor performance. Our model yields three interesting results. First, labor markets may have multiple equilibria that cannot be Pareto-ordered; each with its own configuration in terms of average duration of unemployment and filled jobs, as well as employment protection. Second, the variability of firing costs produces a positive externality affecting the stability properties of these equilibria. Finally, the two externalities affect the efficiency of the social optimum, modifying the Hosios [Hosios, A.J., 1990. On the efficiency of matching and related models of search and unemployment. Review of Economic Studies 57, 279–298] condition. We use these results to interpret the recent history of European unemployment.     

Rejecter-proposer legislative bargaining with heterogeneous time and risk preferences

This article considers a legislative bargaining model in which the rejecter in the previous round becomes the proposer in the current round. We allow the time and risk preferences to differ across players and the voting quota to be a supermajority or submajority. We show that there exists a stationary subgame perfect equilibrium and that each player’s equilibrium payoff conditional on being a proposer is unique, and we explicitly derive the equilibria and equilibrium payoff. We compare a proposer’s equilibrium payoff when the time interval between two consecutive rounds tends to zero with respect to the protocols of the selection of proposers and the voting quota: we show that a proposer’s equilibrium payoff can be greater in this article’s rejecter-proposer model than in the Baron–Ferejohn random-proposer model; even though the voting quota increases, a proposer’s equilibrium payoff can increase.     

Allocating multiple estates among agents with single-peaked preferences

We consider the problem of allocating multiple social endowments (estates) of a perfectly divisible commodity among a group of agents with single-peaked preferences when each agent’s share can come from at most one estate. We inquire if well-known single-estate rules, such as the Uniform rule, the Proportional rule or the fixed-path rules can be coupled with a matching rule so as to achieve efficiency in the multi-estate level. On the class of problems where all agents have symmetric preferences, any efficient single-estate rule can be extended to an efficient multi-estate rule. If we allow asymmetric preferences however, this is no more the case. For nondictatorial single-estate rules that satisfy efficiency, strategy proofness, consistency, and resource monotonicity, an efficient extension to multiple estates is impossible. A similar impossibility also holds for single-estate rules that satisfy efficiency, peak-only, and a weak fairness property. We would like to express our gratitude to Bhaskar Dutta, Semih Koray, Hervé Moulin, and Yuntong Wang as well as an associate editor and two anonymous referees of this journal for detailed comments and suggestions. We also thank the seminar participants at Bilkent University, Indian Statistical Institute, Bilgi University, University of Warwick, ASSET 2003, and BWED XXVI.     

DO LABOR MARKETS PROVIDE ENOUGH SHORT-HOUR JOBS? AN ANALYSIS OF WORK HOURS AND WORK INCENTIVES

This paper examines the role that work incentives play in the determination of work hours. We use a conventional efficiency wage model to analyze how firms respond to worker preferences regarding wage-hours packages. In contrast to previous work, we study markets in which workers have heterogeneous preferences. In this context we demonstrate that job offers will specify both wages and work hours and many individuals will not be able to work their preferred number of hours. We show that the labor market equilibrium may be characterized by a less than optimal number of short-hour jobs.     

Sincere versus sophisticated voting when legislators vote sequentially

Elsewhere (Groseclose and Milyo 2010), we examine a game where each legislator has preferences over (i) the resulting policy and (ii) how he or she votes. The latter preferences are especially important when the legislator is not pivotal. We show that when the game follows the normal rules of legislatures—most important, that legislators can change their vote after seeing how their fellow legislators have voted—then the only possible equilibrium is one where all legislators ignore their policy preferences. That is, each legislator votes as if he or she is not pivotal. The result, consistent with empirical studies of Congress, suggests that legislators should tend to vote sincerely, rather than sophisticatedly. In this paper we examine how outcomes change if we change the rules for voting. Namely, instead of a simultaneous game, we consider a game where legislators vote sequentially in a pre-determined order. We show that, opposite to the simultaneous game, an alternative wins if and only if a majority of legislators’ policy preferences favor that alternative. Our results suggest that if Congress adopted this change in rules, then sophisticated voting would become frequent instead of rare.     

THE POLITICAL ECONOMY OF BITCOIN

The recent proliferation of bitcoin has been a boon for users but might pose problems for governments. Indeed, some governments have already taken steps to ban or discourage the use of bitcoin. In a model with endogenous matching and random consumption preferences, we find multiple monetary equilibria including one in which bitcoin coexists with official currency. We then identify the conditions under which government transactions policy might deter the use of bitcoin. We show that such a policy becomes more difficult if some users strictly prefer bitcoin because they can avoid other users holding the official currency in the matching process. (JEL C78, E41, E42, E50)