A mechanism implementing the proportional solution

We consider the problem of a commonly owned technology which transforms a single input into a single output. We are interested in implementing a social choice rule called theproportional solution. We introduce a mechanism which implements the proportional solution in Nash, strong (Nash) and undominated Nash equilibria. In the mechanism each agent announces only two numbers which can be interpreted as the total output and her share of the total input-output combination. This paper was originally titled "Doubly implementing the proportional solution." I would like to thank my advisor William Thomson for his detailed comments and suggestions. I would also like to thank Jeffrey Banks and Sung-Whee Shin for their comments. Two anonymous referees and an editor’s comments improved this paper substantially.     

Pareto improving interventions in a general equilibrium model with private provision of public goods

Most of the literature on government intervention in models of voluntary public goods supply focuses on interventions that increase the total level of a public good, which is considered to be typically underprovided. However, an intervention that is successful in increasing the public good level need not benefit everyone. In this paper we take a direct approach to welfare properties of voluntary provision equilibria in a full blown general equilibrium model with public goods and study interventions that have the goal of Pareto improving on the voluntary provision outcome. Towards this end, we study a model with many private goods and non-linear production technology for the public good, and hence allow for relative price effects to serve as a powerful channel of intervention. In this setup we show that Pareto improving interventions generally do exist. In particular, direct government provision financed by “small” , or “local” , lump-sum taxes can be used generically to Pareto improve upon the voluntary provision outcome.     

Stable matchings and the small core in Nash equilibrium in the college admissions problem

Both rematching proof and strong equilibrium outcomes are stable with respect to the true preferences in the marriage problem. We show that not all rematching proof or strong equilibrium outcomes are stable in the college admissions problem. But we show that both rematching proof and strong equilibrium outcomes in truncations at the match point are all stable in the college admissions problem. Further, all true stable matchings can be achieved in both rematching proof and strong equilibrium in truncations at the match point. We show that any Nash equilibrium in truncations admits one and only one matching, stable or not. Therefore, the core at a Nash equilibrium in truncations must be small. But examples exist such that the set of stable matchings with respect to a Nash equilibrium may contain more than one matching. Nevertheless, each Nash equilibrium can only admit at most one true stable matching. If, indeed, there is a true stable matching at a Nash equilibrium, then the only possible equilibrium outcome will be the true stable matching, no matter how different are players' equilibrium strategies from the true preferences and how many other unstable matchings are there at that Nash equilibrium. Thus, we show that a necessary and sufficient condition for the stable matching rule to be implemented in a subset of Nash equilibria by the direct revelation game induced by a stable mechanism is that every Nash equilibrium profile in that subset admits one and only one true stable matching. Received: 30 December 1998 / Accepted: 12 October 2001 This paper is a revision of the paper “Manipulation and Stability in a College Admissions Problem” circulated since 1994. I thank Rich McLean, Abraham Neyman, Mark Satterthwaite, Sang-Chul Suh, and Tetsuji Yamada for helpful discussions. I thank the associate editor and the two anonymous referees for their helpful comments that have greatly improved the paper. I am grateful to the Kellogg G.S.M. at the Northwestern University for the hospitality for my visit. Any errors are mine.     

Bargaining solutions with non-standard objectives

I examine the pure-strategy solutions of the sealed-bid bargaining game with incomplete information, when the buyer's and seller's objectives are other than the standard objective, namely maximization of expected profit. The motivation for this exploration lies in three problems of the standard formulation: the necessity of assuming common priors, the existence of uncountably many Nash equilibria, with no means for the players to coordinate on any one of them, and the uncertain relationship between these equilibria and observed behavior in bargaining experiments. Specifically, I consider two alternative objectives: minimization of maximum regret, and maximization of maximum profit. The solution concept here is not Nash equilibrium, but rather -individually rational strategy bundle. For that reason, I shall, where appropriate, use the word “solution” in place of “equilibrium.” Yet we find that the notion of Nash Equilibrium reappears, in a sense to be explained. In the minimax-regret case I find (in contrast to the case of expected profit) a unique solution; this solution reduces, for priors with coincident support, to the linear equilibrium of Chatterjee-Samuelson. In the maximum-profit case there are many solutions; they turn out to be slight generalizations of the one-step equilibria of Leininger-Linhart-Radner.     

A strategic analysis of network reliability

Abstract. We consider a non-cooperative model of information networks where communication is costly and not fully reliable. We examine the nature of Nash networks and efficient networks. We find that if the society is large, and link formation costs are moderate, Nash networks as well as efficient networks will be ‘super-connected’ i.e. every link is redundant in the sense that the network remains connected even after the link is deleted. This contrasts with the properties of a deterministic model of information decay, where Nash networks typically involve unique paths between agents. We also find that if costs are very low or very high, or if links are highly reliable then there is virtually no conflict between efficiency and stability. However, for intermediate values of costs and link reliability, Nash networks may be underconnected relative to the social optimum.     

Property rights out of anarchy? The Demsetz hypothesis in a game of conflict

The Demsetz hypothesis states that secure claims to property arise when the value of creating those rights is sufficiently high. This paper examines the conditions under which this holds in an anarchy equilibrium in which players may allocate labor to production, to conflict, or to the public good of secure claims to property protection. In a simultaneous choice Nash equilibrium, no secure claims to property are created. However, if players play a sequential choice game in which secure claims to property protection occurs in the first stage, then the strategic benefit of reducing others’ subsequent conflict allocation causes secure claims to property to arise. Secure claims to property in a social contract are imperfect, but for sufficiently high productivity of resources, the social contract welfare dominates autocracy.     

Monotonic extensions on economic domains

The property of “monotonicity” is necessary, and in many contexts, sufficient, for a solution to be Nash implementable (Maskin 1977). In this paper, we follow Sen (1995) and evaluate the extent to which a solution may fail monotonicity by identifying the minimal way in which it has to be enlarged so as to satisfy the property. We establish a general result relating the “minimal monotonic extensions” of the intersection and the union of a family of solutions to the minimal monotonic extensions of the members of the family. We then calculate the minimal monotonic extensions of several solutions in a variety of contexts, such as classical exchange economies, with either individual endowments or a social endowment, economies with public goods, and one-commodity economies in which preferences are single-peaked. For some of the examples, very little is needed to recover monotonicity, but for others, the required enlargement is quite considerable, to the point that the distributional objective embodied in the solution has to be given up altogether. Received: 21 September 1996 / Accepted: 17 August 1998     

Mechanism design for a solution to the tragedy of commons

We consider the problem of the tragedy of commons in cooperative production economies, and propose a mechanism to resolve this tragedy, taking into account that the coordinator cannot perfectly monitor each agent’s labor skill and each agent may have an incentive to overstate as well as understate his own skill. Even in such a situation, the mechanism implements the proportional solution (Roemer in Soc Philos Policy 6:74–92, 1989 and Roemer and Silvestre in J Econ Theory 59:426–444, 1993) in Nash and strong equilibria when it is played as a normal form game. Moreover, the mechanism triply implements the solution in Nash, subgame-perfect, and strong equilibria when it is played as a two-stage extensive form game. We are greatly thankful to Semi Koray, William Thomson, and an anonymous referee of this journal for their concrete and helpful comments on improving the paper. An earlier version of this paper was presented at the annual meeting of the Japanese Economic Association held at Hitotsubashi University in October 2001 and at the Conference on Economic Design held at NYU in July 2002. We are grateful to Takehiko Yamato for his useful comments in the former conference. We are also thankful to Tatsuyoshi Saijo, Kotaro Suzumura, and Yoshikatsu Tatamitani for their kind comments.     

A decentralized and informationally efficient mechanism realizing fair outcomes in economies with public goods

We present a decentralized mechanism (called Lindahl Egalitarian), which yields Pareto efficient and envy free allocations (i.e. fair outcomes). We show that the mechanism is informationally efficient in general production economies with an arbitrary, but finite, number of private and public goods, and a finite number of agents. The mechanism reduces to the Walrasian mechanism starting from equal wealth when no agent cares about public goods. We also prove that the set of Public Competitive equilibrium allocations (from equal endowments and proportional taxation), and the set of the Lindahl Egalitarian equilibrium allocations are the same. We are grateful to Xavier Calsamiglia and Albert Marcet for helpful conversations, and to A. de la Fuente, I. Macho, and an anonimous referee for useful suggestions. A. Manresa’s research has been supported by the grant CICYT PB90-0172. J. Aizpurua acknowledges financial support from the Government of Navarra.     

Double implementation of the Lindahl equilibrium by a continuous mechanism

We consider a class of economies with public goods that have the following properties: (i) The preferences of the agents are convex, interior, and strictly increasing. (ii) The technology for production of public goods is a closed convex cone that satisfies free disposal and an additional mild assumption. No assumptions are made on continuity, completeness or transitivity of preferences. We provide a continuous and feasible mechanism that implements the Lindahl equilibrium by Nash equilibria, and has the following property: For every economy in our class every Nash equilibrium of the game induced by the mechanism is a strong Nash equilibrium.     

Implementation of stable solutions in a restricted matching market

I analyze the admission mechanism used in Spanish universities. The system is open to strategic manipulation. This is because students are not allowed to express the whole list of available options. However, the mechanism implements the set of stable matchings in Nash equilibrium and the student's optimum in strong equilibrium. The mechanism also implements the students' optimum, in Nash equilibrium, under the class of “non-reverse” preferences. All these properties come from the fact that colleges do not have the opportunity to misrepresent their preferences. Received: 30 June 1995 / Accepted: 31 January 1997     

Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model

Fershtman and Nitzan (Eur. Econ. Rev. 35:1057–1067, 1991) presented a continuous dynamic public good game and solved the model for feedback Nash equilibria. Wirl (Eur. J. Polit. Econ. 12:555–560, 1996) extended the model and considered nonlinear strategies. Both models do not include uncertainty and hence neglect an important factor in the theory of public goods. We extend the framework of Nitzan and Fershtman and include a diffusion term. We consider two cases. In the first case, the volatility of the diffusion term is dependent on the current level of the public good. This set-up will in principle lead to the same type of feedback strategies computed under certainty. In the second case, the volatility is dependent on the current rate of public good provision by the agents. The results are qualitatively different. We provide a detailed discussion as well as numerical examples. In particular, we show that in both cases uncertainty signifies the free rider effect.     

A study of proportionality and robustness in economies with a commonly owned technology

Abstract. Studying one-input one-output economies, we say that an allocation is proportional if the input-output ratio is identical among agents and if each agent maximizes her welfare given this ratio. We propose three equity axioms based on this definition, and we use them to compare the main solutions to this simple equity problem. We also combine efficiency, robustness axioms and our proportionality axioms to characterize two solutions. Received: 11 June 1997 / Accepted: 26 May 2000     

Repeated two-person zero-sum games with unequal discounting and private monitoring

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.     

Rational expectations equilibrium and the strategic choice of costly information

This paper studies costly information acquisition in one-good production economies when agents acquire private information and prices transmit information. Before asset markets open, agents choose the quality of their private information. After this information stage, agents trade assets in sequentially complete markets taking into account their private information and the information revealed by equilibrium prices (rational expectations equilibrium, (Radner, R., 1979. Rational expectations equilibrium: generic existence and the information revealed by prices, Econometrica 47, 655–678.)). An overall equilibrium in asset and information market is defined as a Nash equilibrium of the information game in which agents’ actions are information choices and their utility payoffs are the ex-ante expected utilities of the corresponding rationale expectations equilibrium. This paper shows that for a generic set of economies parameterized by endowments and productivity shocks, an overall equilibrium in information and asset market (a Nash equilibrium of the induced information game) with costly information acquisition and fully-revealing prices exists. In other words, informational efficiency is in general consistent with costly information acquisition.     

An Essay on Distributive Justice and the Equal Ownership of Natural Resources

The article argues that, in seeking to establish criteria for distributive justice, consideration should be given to the manner in which Earth's natural resources are owned. The views of seven notable authorities on this issue are presented, ranging from an unrestricted right of private ownership to some form of public or collective ownership. The possibility of a system of ownership that is private but equal is discussed.     

Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem

This study considers a situation in which agents choose the location of a public facility from a street according to a given mechanism. Agents have single-dipped preferences over a set of feasible locations. We analyze coalitional behavior for any given mechanism for this situation. We identify a necessary and sufficient condition for a mechanism to possess a strong Nash equilibrium by applying the minimax theorem of von Neumann and Morgenstern (1944). We introduce a class of core solutions and show that these solutions are characterized by strong Nash implementability. As a byproduct of these results, we propose a simple mechanism that implements any core solution in strong Nash equilibria.     

论我国现行土地制度对物业税的影响

本文基于土地所有权与土地使用权可以相对分离,土地使用权具有物权特性,土地使用权人享有相应期限内的土地收益权,对土地使用权课征不动产税可以弥补土地出让制度的缺陷,可以规范中央与地方的财政分配关系等方面的分析认为,虽然中外土地制度存在差异,但是中国土地公有制并不能成为开征不动产税的障碍。     

试论城市经营的本质

文章论述了城市公共物品所有权、经营权和管理权的相互关系 ,指出城市经营就是对城市公共物品产权的再认识 ,认为公共物品所有权应实现多元化 ,所有权、经营权与管理权可以分离 ;并就城市经营过程中政府职能转变的原因和目标定位进行探讨 ,认为政府应由全能型向专职型过渡 ,指出在市场经济条件下城市政府应履行好经济制导管理、城市公共物品经营配套、城市整体形象策划三大职责     

Gradient dynamics in population games: Some basic results

When each player in a population game continuously adjusts her action to move up the payoff gradient, then the state variable (the action distribution) obeys a nonlinear partial differential equation. We find conditions that render gradient adjustment myopically optimal and analyze two broad classes of population games. For one class, we use known results to establish the existence and uniqueness of solutions to the PDE. In some cases, these solutions exhibit shock waves or rarefaction waves. For a second class, we use a local form of Nash equilibrium to characterize the steady state solutions of the PDE and find sufficient conditions for asymptotic convergence.