Counting Groves-Ledyard equilibria via degree theory

We study the Groves-Ledyard mechanism for determining optimal amounts of public goods in economies whose agents have the most general class of preferences for which a Pareto amount of public goods can be computed independently of income distribution. We use degree theory on affine spaces to show that the number of equilibria in such economies grows exponentially as the number of agents in the economy increases. The large number of equilibria in such simple economic models raises doubts as to whether the Groves-Ledyard mechanism is a workable solution to the Free Rider Problem since individuals may have incentives to falsify their preferences in order to drive the adjustment process to a preferred Nash equilibrium.     

Nash-implementation of competitive equilibria via a bounded mechanism

We deal with the problem of providing incentives for the implementation of competitive outcomes in a pure-exchange economy with finitely many households. We construct a feasible price-quantity mechanism, which fully implements Walras equilibria via Nash equilibria in fairly general environments. Traders’ preferences need neither to be ordered nor continuous. In addition, the mechanism is such that no pure strategy is weakly dominated, hence is bounded (in the sense of Jackson 1992). In particular it makes no use of any integer game.     

Property Rights Assignment: Conflict and the Implementability of Rules

The paper studies the assignment of property rights. By assignment I mean a social mechanism that transfers a valuable resource from an “unowned” state to an “owned” state (for example, a first-possession rule). I argue that any assignment mechanism faces an implementation constraint with one exception, namely the assignment by conflict. I characterize this constraint and show that under some conditions population growth facilitates rule-based assignments because appropriation by conflict becomes more costly. In other cases, however, this effect is reversed. The model may give some insights regarding the emergence and the disappearance of the open-field system in medieval Europe which, paradoxically, both have been attributed to population growth. This paper is dedicated to Horst Hegmann. For helpful and insightful comments in discussions and on the paper I thank Roderick Hay, Horst Hegmann, Christopher Kingston, Guy Kirsch, Krishna Ladha, Marc Law, Anton Miglo, Douglass North, and John Nye. I also thank the editor Amihai Glazer and two anonymous referees for their comments. The usual disclaimer applies.     

Hierarchic competitive equilibria

Without an interiority or strong survival assumption, an equilibrium may not exist in the standard Arrow–Debreu model. We propose a generalized concept of competitive equilibrium, called hierarchic equilibrium. Instead of using standard prices we use hierarchic prices. Existence will be shown without a strong survival assumption and without a non-satiation condition on the preferences. Under standard assumptions this reduces to the Walras equilibrium. Hierarchic equilibria are weakly Pareto optimal and any Pareto optimum can be decentralized without a border condition. We prove the existence of a Pareto optimal hierarchic equilibrium under additional assumptions. Later, we establish a core equivalence result.     

Functional sunspot equilibria

Consider a one step forward looking model where agents believe that the equilibrium values of the state variable are determined by a function whose domain is the current value of the state variable and whose range is the value for the subsequent period. An agent’s forecast for the subsequent period uses the belief, where the function that is chosen is allowed to depend on the current realization of an extrinsic random process, and is made with knowledge of the past values of the state variable but not the current value. The paper provides (and characterizes) the conditions for the existence of sunspot equilibria for the model described.     

Some approximate equilibria

It is by now well-known that there exists a system of prices at which decentralized, utility-maximizing behavior by a finite number of agents, each with convex preferences, leads to outcomes which ‘mesh’ in the aggregate. Technically, a competitive equilibrium is said to exist. The question arises as to what happens with non-convex preferences. Using Non-standard Analysis, we show that, provided the economy is ‘large’ enough, there exist various formulations of approximate competitive equilibria. We also relate our results to other work in this area.     

Learning non-rational expectations equilibria

A hyperinflation model is analyzed under bounded rationality learning. Agents believe in a misspecified model which is correctly specified at theRational Expectations Equilibrium of the model and they adjust their beliefs by means of theLeast Mean Squares algorithm. Convergence of the bounded rationality learning activity to anon-Rational Expectations Equilibrium point is obtained for any set of parameters of the model.

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Sommario In questo lavoro gli autori analizzano il modello di iperinflazioneà la Cagan sotto l'ipotesi di razionalità limitata. Gli agenti non formano le loro aspettative coerentemente con la struttura completa del modello economico, essi si basano su un modello lineare non correttamente specificato che risulta essere corretto soltanto in corrispondenza dell'equilibrio con aspettative razionali. Si ipotizza che i soggetti aggiornino le loro aspettative tramite un algoritmo di apprendimento. Nel caso specifico, l'algoritmo adottato è ilLeast Mean Squares. Il principale risultato del lavoro è che l'apprendimento con razionalità limitata da parte dei soggetti economici può convergere ad un punto che non è un equilibrio con aspettative razionali. Il risultato è particolarmente interessante poiché la maggior parte degli studi noti in questa letteratura, nonostante non assicurino la convergenza ad un equilibrio con aspettative razionali, assicurano la non convergenza ad un equilibrio che non sia di aspecttative razionali. La convergenza ad un equilibrio non di aspettative razionali è dovuta ad una non corretta specificazione del modello secondo cui i soggetti formano le loro aspettative. In particolare, la convergenza ad un equilibrio non di aspettative razionali si verifica allorché i soggetti non tengono conto nel loro apprendimento di una variabile rilevante che essi classificano come rumore bianco.

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Authors would like to thank an anonymous referee and all of those who gave comments and suggestions at theSociety of Economic Dynamics and Control Conference (SEDC) '94 (Los Angeles, CA-USA);International Conference on Artificial Neural Networks (ICANN) '94 (Salerno, Italy);World Conference on Neural Networks (WCNN) '94 (San Diego, CA-USA);AMASES '94 Conference (Modena, Italy). The usual disclaimers apply.     

Efficiency of temporary equilibria

A temporary equilibrium model of a production economy with various capital markets in which producers maximize the expected utility of cash flows in various periods is considered. Without restricting the price expectation of producers, it is shown that, if contracts to buy or sell goods at future periods can be trated in a market and if the producer's utility functions are increasing in the cash flow of the first period, then the temporary equilibrium allocations are technically efficient. Also, production is technically efficient even in the presence of some quantity constraints on sales of futures contracts which are sufficient for existence of an equilibrium.     

Existence of spatial cournot equilibria

Since the existence of equilibria in spatial price setting models is highly problematic, this paper suggests spatial Cournot competition to overcome the most severe existence problems. Sufficient conditions for existence are given for a general class of economic environments, and a linear model specification serves to illustrate the properties of a spatial Cournot-Nash equilibrium. Finally, the nature of the free entry equilibrium is discussed.     

Stochastic processes of temporary equilibria

It is the aim of the paper to study within the framework of an ‘overlapping generation model’ the evolution of temporary equilibria. At date t, there are ‘newborn’ agents and ‘old’ agents who were born in previous periods; the old agents hold cash balances (fiat money) that they carried over from the previous period. At the beginning of period t, all agents receive a random endowment of consumption goods. Then the agents exchange these endowments and money on spot markets at date t (trading in future markets is not considered). Once a temporary equilibrium is reached, the economy move to the next date. Agents who were born at date t then become old and meet agents born at period t+1.It is shown that the evolution of temporary equilibria in this model leads to analyse the ergodic properties of a certain class of Markov processes with stationary transition probability.     

Number and definiteness of economic equilibria

The aim of this paper is to show that it is almost equivalent to know with accuracy the equilibria of every economy or simply to know just the number of equilibria of these economies.     

A tractable analysis of contagious equilibria

This paper studies contagious equilibrium in infinitely repeated matching games. The innovation is to identify a key statistic of contagious punishment that, used together with a recursive formulation, generates tractable closed-form expressions for continuation payoffs, off equilibrium. This allows a transparent characterization of the dynamic incentives created by contagious punishment schemes.     

Existence of continuous residential land-use equilibria

This paper presents a general result on the existence of competitive equilibria for residential land markets in continuous space. Following standard residential land-use theory, such markets are postulated to involve finitely many types of household continua bidding for land within a continuous finite-dimensional space. In contrast to the standard approach of defining an excess-demand correspondence on a price space, the problem here is reformulated in terms of a ‘population excess-supply correspondence’ on a utility space. This approach allows the analysis to be carried out entirely in terms of finite-dimensional methods, and in particular, allows standard types of fixed-point arguments to be employed.     

Rent control and complete contract equilibria

This paper develops a theoretical model for analysing the effects of rent control. The model incorporates the roles of optimal long-term contractual arrangements and the responses of individual agents to rent control in determining the economic characteristics of the controlled market equilibrium, and can help to explain the wide variation in empirical results observed across jurisdictions. Necessary and sufficient conditions for a complete contract equilibrium, where the characteristics of the competitive and controlled solutions are identical, are established. It is shown that housing quality, new construction, and the distribution of wealth may not be affected by rent control.     

Regular competitive equilibria in disequilibrium economics

Regular competitive equilibria, in the sense of Guy Laroque, play an important role in disequilibrium economics. In this paper it is shown that the set of economies with only regular competitive equilibria, is open and dense in the set of all economies with respect to the strong Whitney-topology.     

On the uniqueness of local equilibria

The purpose of this paper is to define a new notion of local equilibrium in an exchange economy, where the consumers face lower bounds on net trades. Then, we show that the local equilibrium is unique if the lower bounds are closed enough to 0. By the way, we also provide a convergence result of local equilibrium price toward Walras equilibrium price of a suitable tangent linear economy.     

Real indeterminacy of equilibria and manipulability

In this paper, we analyze the indeterminacy of equilibria in financial markets and propose a selection mechanism. We suggest that there is one equilibrium that prevails over the others, as a result of the market power of the agents that some states of nature become monopolists of certain commodities. Given a financial assets model, we define a price game and show the existence of mixed strategies equilibria. Then we purify these equilibria by considering a price game with incomplete information.     

Ruling out pareto dominated monetary equilibria

It is well known that under nominal money supply rules accomplished through lump sum transfers, non-uniqueness and non-optimality of the resource allocation often obtains in monetary models. We show that uniqueness and optimality of the resource allocation obtains if the monetary authority conducts Friedman's rule through open market operations. Our result necessitates and we provide a clarification of existing irrelevance theorems for open market operations. Our result also provides a partial resolution of the uniqueness-efficiency conflict of nominal money supply rules raised by Woodford (Economic Theory 4 (1994) 345–380).