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).     

Nash equilibrium without mutual knowledge of rationality

Summary. In a Nash equilibrium, players' rationality is mutual knowledge. However, both intuition and experimental evidence suggest that players do not know for sure the rationality of opponents. This paper proposes a new equilibrium concept, cautious equilibrium, that generalizes Nash equilibrium in terms of preferences in two person strategic games. In a cautious equilibrium, players do not necessarily know the rationality of opponents, but they view rationality as infinitely more likely than irrationality. For suitable models of preference, cautious equilibrium predicts that a player might take a “cautious” strategy that is not a best response in any Nash equilibrium. Received: January 28, 1998; revised version October 2, 1998     

The structure of the Nash equilibrium sets of standard 2-player games

Summary. In this paper I study a class of two-player games, in which both players action sets are [0,1] and their payoff functions are continuous in joint actions and quasi-concave in own actions. I show that a no-improper-crossing condition is both necessary and sufficient for a finite subset A of to be the set of Nash equilibria of such a game.Received: 21 November 2002, Revised: 9 September 2004, JEL Classification Numbers: C65, C72.I am grateful to an editor of the journal and an anonymous referee for their very helpful comments. I also would like to thank the seminar participants at City University of Hong Kong, Georgia State University, Northwestern University, and Rice University.     

Nash equilibrium when players account for the complexity of their forecasts

Nash equilibrium is often interpreted as a steady state in which each player holds the correct expectations about the other players' behavior and acts rationally. This paper investigates the robustness of this interpretation when there are small costs associated with complicated forecasts. The model consists of a two-person strategic game in which each player chooses a finite machine to implement a strategy in an infinitely repeated 2×2 game with discounting. I analyze the model using a solution concept called Nash Equilibrium with Stable Forecasts (ESF). My main results concern the structure of equilibrium machine pairs. They provide necessary and sufficient conditions on the form of equilibrium strategies and plays. In contrast to the “folk theorem,” these structural properties place severe restrictions on the set of equilibrium paths and payoffs. For example, only sequences of the one-shot Nash equilibrium can be generated by any ESF of the repeated game of chicken.     

Stability of the cooperative equilibrium in N-person prisoners' dilemma with sequential moves

Summary. Nishihara [3] showed that N-person prisoners' dilemma has a cooperative Nash equilibrium, if the players decide their actions sequentially in the order determined by Nature under a certain information structure, and if each player's payoffs satisfy a certain inequality. This paper examines the stability of this cooperative equilibrium against two matters: players' slight mistakes and deviations by coalitions. The main results are as follows: (i) if the inequality on each player's payoffs strictly holds, then the cooperative equilibrium is a strictly proper equilibrium; (ii) if N≤3, and if full cooperation is Pareto efficient in N-person prisoners' dilemma, then the cooperative equilibrium is a strong Nash equilibrium; (iii) the cooperative equilibrium is in general a coalition-proof Nash equilibrium. Received: June 23, 1997; revised version: December 2, 1997     

Uniqueness and comparative statics of Nash equilibrium in a tariff retaliation model

This paper considers uniqueness and comparative statics of Nash equilibrium of a tariff retaliation model. The approach to the problem is geometrical and reminiscent of the analysis for the free trade competitive equilibrium. If the countries have constant elasticity of substitution utility functions, some simple conditions can be used to prove uniqueness of the Nash equilibrium of the tariff retaliation game. The welfare effects of endowment changes are analyzed in terms of the standard terms of trade and volume of trade effects. If the elasticity of substitution of one of the countries is sufficiently high, immiserizing growth will not occur.      

Continuity of the first price auction Nash equilibrium correspondence

Summary. Despite the complexity of the first price auction in the general asymmetric case, analytical results have started to emerge in the literature. Authors have also searched to gain insights by computing numerical estimates of the equilibria for some probability distributions of the valuations. This paper proves that the Nash equilibrium of the first price auction depends continuously, for the weak topology, on the valuation distributions and thus brings robustness to the numerical results as well as some theoretical results. As an example of application, we disprove a conjecture of comparative statics. Received: February 1, 1999; revised version: July 27, 2001     

Housing choices,sorting, and the distribution of educational benefits under deferred acceptance

I study the welfare and distributional consequences of introducing the student‐proposing deferred acceptance in a model where schools have exogenous qualities and the benefit from attending a school is supermodular in school quality and student type. Unlike neighborhood assignment, deferred acceptance induces nonpositive assortative matching where higher type students do not necessarily choose neighborhoods with better schools. Student types are more heterogeneous within neighborhoods under deferred acceptance. Assuming an elastic housing supply, deferred acceptance benefits residents in lower quality neighborhoods with more access to higher quality schools. Moreover, more parents will “vote with their feet” for deferred acceptance, other things equal, than for neighborhood assignment.     

On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.     

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.     

On a general equilibrium model of the incidence of the corporation tax under uncertainty

This paper addresses two issues. First, we demonstrate that when there is uncertainty in a general equilibrium model of a large country the usual rule for the auctioneer, that of searching for a set of relative prices at which excess demand in each market is zero, is no longer appropriate. It is suggested that the setting of expected demand to expected supply in each market would be a convenient generalization. Secondly, results on the incidence of the corporation income tax when there is uncertainty in the corporate sector, and alternatively when there is uncertainty in the noncorporate sector, are presented.     

A note on the existence of a monetary equilibrium over an infinite horizon

Summary. This note considers an economy with ‘inside money’ that extends over an infinite horizon in the case of certainty. It shows the existence of an equilibrium and the indeterminacy of the overall price level when the supply of balances is set exogenously.Received: 6 November 2003, Revised: 2 September 2004 JEL Classification Numbers: D50, E40, E50.G. Bloise: I am indebted to Jacques Dréze, Leo Ferraris, Cuong Le Van, Luca Panaccione, Herakles Polemarchakis and Pietro Reichlin for the long discussions and their valuable suggestions. I also thank an anonymous referee for her/his advices.     

Walrasian versus quasi-competitive equilibrium and the core of a production economy

Summary. This paper presents very general conditions guaranteeing that a quasi-competitive equilibrium is a Walrasian equilibrium. We also develop a generalization (and a simplified proof) of Nikaidos and McKenzies extensions of the classic Debreu-Scarf theorem on core convergence, and apply the first result to obtain an equivalence between the set of Edgeworth equilibria and the set of Walrasian equilibria in a production economy.Received: 6 September 2002, Revised: 14 November 2003, JEL Classification Numbers: C71, D50, D51.     

Assessing the impact of environmental charges a partial general equilibrium model of the forest sector

This paper provides a theoretical and empirical analysis of how environmental charges affect a particular sector of the economy. Our approach allows a simple comparison of how partial and general equilibrium results may differ.A research grant from the Nordic Council is gratefully acknowledged.     

On the impact of a tax shock in Portugal

In 1999, Cavaco Silva, the Portuguese Prime Minister from 1985 to 1995, proposed a comprehensive tax reform package, which is to this day the basic reference in the tax policy debate in Portugal. A tax shock would consist of 4pp cuts in the corporate income tax and in the firms social security contribution rates, and a 5pp reduction in the highest personal income tax rate. These cuts would be financed by combating tax evasion, curbing wasteful public expenditure and, if necessary, by increasing the VAT rate by up to 2pp. Using a dynamic general equilibrium model to evaluate the effects of this tax shock, we find that the long-term GDP gains would be between 0.72% and 2.91% while the effects on lifetime private welfare would range between -0.99% and 0.9%. The efficiency of this tax reform package depends critically on the way the tax cuts are financed to ensure deficit neutrality. Because investment is subject to adjustment costs, to alleviate the long-run trade-off between GDP and welfare, tax policy changes must induce a significant increase in net labor income.Received: July 2001, Accepted: March 2002, JEL Classification: C68, D58, E62, H21, H30Correspondence to: Alfredo M. PereiraA previous version of this paper was presented at the Society of Computational Economics and SPiE conferences. Thanks are due to Fernando Chau, Emanuel Santos, and two anonymous referees for very insightful comments and suggestions. The views in this article are of the authors alone and do not reflect the position of the Portuguese Ministry of Finance.     

On the nature of equilibria in a Downsian model with candidate valence

We analyze mechanisms that are used to allocate dormitory rooms to students at college campuses. Students consist of newcoming freshmen, who do not currently occupy any rooms, and more senior students each of whom occupies a room from the previous year. In addition to the rooms already occupied by the existing tenants, there are vacated rooms by the graduating class. Students have strict preferences over dormitory rooms. Each student shall be assigned a dormitory room in an environment where monetary transfers are not allowed. An existing tenant can move to another room as a result of the assignment. We show that you request my house–I get your turn mechanisms are the only mechanisms that are Pareto-efficient, individually rational, strategy-proof, weakly neutral, and consistent.     

传统价格理论的局限--以软件产品价格形成机理解释为例

软件产品在产权、信息及交易上所表现出的特别性使传统的以物质产品为研究对象的价格理论及即使在其具有最强解释力的成本价值与使用价值均衡领域均陷入困境.本文分析了传统价格理论解释无力的局限性原因.