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.     

Subgame perfect implementation of stable matchings in marriage problems

We study a sequential matching mechanism, an extensive form game of perfect information, to implement stable matchings in marriage problems. It is shown that the SPE (subgame perfect equilibrium) of this mechanism leads to the unique stable matching when the Eeckhout (Econ Lett 69:1–8, 2000) condition for the existence of a unique stable matching holds. This result does not extend to preferences that violate the Eeckhout condition, even if the matching problem has a unique stable matching. We then introduce a weaker condition, called the α ^M condition, under which the SPE outcome of the men-move-first mechanism is the men-optimal stable matching. The α ^M condition is necessary and sufficient for the men-optimal stable matching to be Pareto optimal for men.     

Games of Capacity Manipulation in Hospital-intern Markets

In this paper, we analyze capacity manipulation games in hospital-intern markets inspired by the real-life entry-level labor markets for young physicians who seek residencies at hospitals. In a hospital-intern market, the matching is determined by a centralized clearinghouse using the preferences revealed by interns and hospitals and the number of vacant positions revealed by hospitals. We consider a model in which preferences of hospitals and interns are common knowledge. Hospitals play a capacity-reporting game. We analyze the equilibria of the game-form under the two most widely used matching rules: hospital-optimal and intern-optimal stable rules. We show that (i) there may not be a pure strategy equilibrium in general; and (ii) when a pure strategy equilibrium exists, every hospital weakly prefers this equilibrium outcome to the outcome of any larger capacity profile. Finally, we present conditions on preferences to guarantee the existence of pure strategy equilibria.     

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.     

Stable coalition governments: the case of three political parties

We explore to what extent we can propose fixed negotiation rules and simple mechanisms (or protocols) that guarantee that political parties can form stable coalition governments. We analyze the case in which three parties can hold office in the form of two-party coalitions. We define a family of weighted rules that select political agreements as a function of the bliss points of the parties and electoral results (Gamson’s law and equal share among others are included). We show that every weighted rule yields a stable coalition. We use implementation theory to design a protocol (in the form of a mechanism) that guarantees that a stable coalition will govern. We find that no dominant solvable mechanism can be used for this purpose, but there is a simultaneous unanimity mechanism that implements it in Nash and strong Nash equilibrium. Finally, we analyze the case of a larger number of political parties.     

An Efficient and Egalitarian Negotiation Procedure for Economies with Externalities

We construct a simple mechanism that can be used in situations when a group of well informed agents try to cooperate in the production and allocation of a good with external effects. We start by auctioning the right to have the initiative in the negotiation, then the winner proposes an allocation that is implemented if the rest of the players unanimously accept it. In case of a rejection, the process is started again. We show that the outcome of any stationary subgame perfect Nash equilibrium leads to an efficient allocation of the good with externalities, together with an equal split of the surplus that cooperation generates.     

Games implementing the stable rule of marriage problems in strong Nash equilibria

In a marriage problem, we introduce a condition called “exclusive matchability (EM)”: the condition mainly says that each pair of a man and a woman can choose to be a matching pair regardless of others' actions. This condition is essential to strong Nash implementation of the stable rule. We show that any mechanism which satisfies exclusive matchability implements the stable rule in strong Nash equilibria. Received: 17 May 1999/Accepted: 30 August 2001 I would like to thank anonymous referees for their helpful comments. Financial support from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged.     

NASH EQUILIBRIUM AND BUYER RATIONING RULES: EXPERIMENTAL EVIDENCE

Laboratory experiments compare the results of two different buyer rationing rules on Bertrand-Edgeworth duopoly markets. The two rationing rules, a value queue and a random queue, specify the ordering of buyers and generate different predictions under otherwise identical conditions. These experiments show market outcome can chane significantly with a change in the ordering of buyers. The direction of these changes agrees with the predictions of the stage-game Nash equilibrium. Thus, the single-shot Nash equilibrium is show to have predictive power even in repeated games.     

NETWORK STRUCTURE IN A LINK FORMATION GAME: AN EXPERIMENTAL STUDY

In this article, we use an experiment to evaluate the performance of alternative refinements in a Myersonian link formation game with a supermodular payoff function. Our results show that a non‐cooperative refinement, the global games (GG) approach, outperforms alternative cooperative refinements (strong Nash equilibrium, coalition‐proof Nash equilibrium, and pairwise stable Nash equilibrium) in explaining the observed experimental behavior in the static game of complete information with three players. The results are robust to some comparative statics and the GG approach shows a high predictive power under incomplete information. However, under repeated interaction or with a greater number of players, the GG approach loses predictive power, but so do the cooperative refinements. The results illustrate the importance of coordination failure in practice and the need to design mechanisms to reduce this effect in practical decision‐making problems. (JEL C70, C92, D20, D44, D82)     

Political equilibria with electoral uncertainty

After an election, when party positions and strengths are known, there may be a centrally located large party at the core position. Theory suggests that such a core party is able to form a minority government and control policy. In the absence of a core party, theory suggests that the outcome be a lottery associated with coalition risk. Stochastic models of elections typically indicate that all parties, in equilibrium, will adopt positions at the electoral center. This paper first presents an existence theorem for local Nash equilibrium (LNE) under vote maximization, and then constructs a more general model using the notion of coalition risk. The model allows for the balancing of office and policy motivations. Empirical analyses of elections in the Netherlands and Israel are used as illustrations of the model and of the concept of a structurally stable LNE. The figures and tables are reproduced from Schofield and Sened (2006) with permission from Cambridge University Press.     

Two-Player Asymmetric Contests with Ratio-Form Contest Success Functions

I examine players' equilibrium effort levels in two-player asymmetric contests with ratio-form contest success functions. I first characterize the Nash equilibrium of the simultaneous-move game. I show that the equilibrium effort ratio is equal to the valuation ratio, and that the prize dissipation ratios for the players are the same. I also show that the prize dissipation ratio for each player is less than or equal to the minimum of the players' probabilities of winning at the Nash equilibrium and thus never exceeds a half. Then I examine how the equilibrium effort ratio, the prize dissipation ratios, and the players' equilibrium effort levels respond when the players' valuations for the prize or their abilities change.     

NOMINAL WAGE CONTRACTS AND THE MONETARY TRANSMISSION MECHANISM

We introduce staggered and synchronized nominal wage contracts into a one‐sector monetary dynamic general equilibrium model to analyze the importance of the monetary transmission mechanism. We find a stronger monetary propagation mechanism under a synchronized setting as compared to a staggered setting. This causes the economy under staggering to be less volatile, better matching the data, as well as bringing about lower welfare costs (measured in terms of consumption). However, our results are mixed when it comses to evaluating the contemporaneous correlations and cross‐correlations. We conclude that overall staggered contracts do better in matching the U.S. economy. (JEL E32, E51, J41)     

A necessary and sufficient condition for stable matching rules to be strategy-proof

We study one-to-one matching problems and analyze conditions on preference domains that admit the existence of stable and strategy-proof rules. In this context, when a preference domain is unrestricted, it is known that no stable rule is strategy-proof. We introduce the notion of the no-detour condition, and show that under this condition, there is a stable and group strategy-proof rule. In addition, we show that when the men’s preference domain is unrestricted, the no-detour condition is also a necessary condition for the existence of stable and strategy-proof rules. As a result, under the assumption that the men’s preference domain is unrestricted, the following three statements are equivalent: (i) a preference domain satisfies the no-detour condition, (ii) there is a stable and group strategy-proof rule, (iii) there is a stable and strategy-proof rule.     

Existence and Nash implementation of efficient sharing rules for a commonly owned technology

Suppose that a group of individuals owns collectively a technology which produces a consumption good by means of a (possibly heterogeneous) input. A sharing rule associates input contributions with a vector of consumptions that are technologically feasible. We show that the set of allocations obtained by any continuous sharing rule contains Pareto efficient allocations. We also present a mechanism that implements in Nash equilibrium the Pareto efficient allocations contained in an arbitrary sharing rule. Received: 29 June 1998/Accepted: 15 November 2000     

ENDOGENOUS DESTRUCTION IN CONFLICT: THEORY AND EXTENSIONS

This article develops a general equilibrium model of conflict to characterize the implications of endogenous destruction for bargaining and fighting. Specifically, we consider the scenario where two contending parties engage in bargaining to avoid fighting when there are direct costs (e.g., arms buildups) and indirect costs (e.g., destruction to consumable resources) of conflict. Without imposing specific functional form restrictions on conflict, production, and destruction technologies, we show their interactions in determining an optimal decision between fighting and bargaining. We find that, under the shadow of conflict, bargaining is costly as the contending parties always allocate more resources to arming for guarding settlement through bargaining than in the event of fighting. In contrast to conventional thinking that bargaining is Pareto superior over fighting, we show conditions under which fighting dominates bargaining as the Nash equilibrium choice. The positive analysis may help explain the general causes of fighting, without resorting to the assumption of incomplete information or misperceptions. (JEL D74, H56, C7)     

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.     

Nash Implementation with Lottery Mechanisms

Consider the problem of exact Nash Implementation of social choice correspondences. Define a lottery mechanism as a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. When preferences over alternatives are strict, we show that Maskin monotonicity (Maskin in Rev Econ stud 66: 23–38, 1999) is both necessary and sufficient for a social choice correspondence to be Nash implementable. We discuss how to relax the assumption of strict preferences. Next, we examine social choice correspondences with private components. Finally, we apply our method to the issue of voluntary implementation (Jackon and Palfrey in J Econ Theory 98: 1–25, 2001).I thank Toyo Sakai for his comments on a previous draft. I also thank two anonymous referees and an editor of this journal for helpful comments that improved this paper. A previous version circulated as “A note on Maskin monotonicity”. After the results presented here were obtained, I became aware of a new unpublished paper by Benoit and Ok (2004). The result of Theorem 2 and the discussion that follows is partially similar to their Theorem 1.     

COLLUSION IN PROCUREMENT AUCTIONS: AN EXPERIMENTAL EXAMINATION

Experimental methods are used to examine the existence and detectability of collusion in environments that exhibit critical parallels to procurement auctions. We find that given the opportunity sellers often raise prices considerably. Moreover, noncollusive Nash equilibrium predictions are insufficient to dismiss "suspicious" behavior as innocuous: in an environment where identical prices are predicted in a noncollusive Nash equilibrium, common prices are observed only when sellers communicate. In a second environment designed to parallel construction procurement contracting, market rotations are observed both with and without collusion, but collusion can often be detected from the pattern of losing bids.     

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two-sided many-to-many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation/dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation/dropping strategies. We prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 1), i.e., independently of the quotas. Then, we show that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 2). Finally, we show that this result cannot be extended neither to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1—Example 1), nor to group manipulations (even when all quotas equal 1—Example 2).