Drèze equilibria and welfare maxima

We present an example of a production economy with incomplete markets, von Neumann–Morgenstern utility functions, and a unique Drèze equilibrium in order to illustrate and explain the following phenomenon. There exists a transfer scheme such that every shareholder’s utility after transfers and share adjustments increases the more the firm deviates from the Drèze equilibrium. However, shareholders’ welfare decreases the further the firm departs from the Drèze equilibrium. Shareholders’ welfare is defined as the sum of their utilities where every utility function is normalized such that the marginal utility of today’s consumption equals 1 at the Drèze equilibrium.     

Supply-constrained equilibria in economies with indexed prices

In an exchange economy prices are rigid and the prices are restricted by index functions. The indexes can be of a general type and can be different for each commodity. Indexed prices can appear in other indexes. Also considered are restrictions in terms of a general price index. Existence of a Drèze equilibrium, and particularly a supply-constrained Drèze equilibrium, is proved. The system of indexes must be solvable in terms of unconstrained prices and for the unconstrained commodities a monotonicity condition must hold.     

A bargaining theory of the firm

Suppose that a firm has several owners and that the future is uncertain in the sense that one out of many different states of nature will realize tomorrow. An owner’s time preference and risk attitude will determine the importance he places on payoffs in the different states. It is a well-known problem in the literature that under incomplete asset markets, a conflict about the firm’s objective function tends to arise among its owners. In this paper, we take a new approach to this problem, which is based on non-cooperative bargaining. The owners of the firm play a bargaining game in order to choose the firm’s production plan and a scheme of transfers which are payable before the uncertainty about the future state of nature is resolved. We analyze the resulting firm decision in the limit of subgame-perfect equilibria in stationary strategies. Given the distribution of bargaining power, we obtain a unique prediction for a production plan and a transfer scheme. When markets are complete, the production plan chosen corresponds to the profit-maximizing production plan as in the Arrow–Debreu model. Contrary to that model, owners typically do use transfers to redistribute profits. When markets are incomplete, the production plan chosen is almost always different from the one in a transfer-free Drèze (pseudo-)equilibrium and again owners use transfers to redistribute profits. Nevertheless, our results do support the Drèze criterion as the appropriate objective function of the firm.     

How modern economics learned French: Jacques Drèze and the foundation of CORE

The Center of Operations Research and Econometrics (CORE), founded in 1966, was one of the channels through which economic modelling practices were imported from the USA to Europe. Officially modelled after the Cowles Foundation for Economics Research, it reflected Jacques Drèze's broad experiences in the USA during the 1950s when modelling techniques were not yet anchored in disciplines. CORE gained an international reputation, however, through the rather exclusive community of Neo-Walrasian economists represented by Werner Hildenbrand, Jean Gabszewicz, and Gérard Debreu. After this community modified the disciplinary divisions at CORE, the influence of CORE on continental economics occurred mainly through disequilibrium economics, which still represents a “French accent” in modern macroeconomics. At the same time, operations research and econometrics prospered at CORE while receiving scant attention from economists. This essay tells the story of how CORE changed continental economics through the unique career path of its founder, Jacques Drèze.     

Shadow pricing of labour and capital in an economy with unemployed labour

This paper derives the shadow prices of labour and capital to be used in the public sector in a situation of unemployment. The setting considered is that of a three-good, two-period general equilibrium model. Then shadow prices are compared to their corresponding market prices and shown to closely depend on own and cross-elasticities of supply and demand for labour and investment. In the first part, a rigid wage rate is the sole source of distortion; then, a tax on capital income is introduced so that our formula for the social rate of discount can be contrasted with that of Harberger, Sandmo and Drèze.     

Discount rates and shadow prices for public investment

This paper extends the Harberger–Sandmo–Drèze model for public discount rates to a many-good economy. It derives a formula for discount rates which are specific to each public enterprise or agency and used by them to discount future outputs and inputs evaluated at market prices. Such an approach is shown to be more efficient than that of simply using a single rate for all public projects. It is also more practical than asking each public firm to use second-best shadow prices in their analyses of investment projects.The general results are first provided; then, simple cases are considered and numerical examples presented to help interpret our formula and analyse its main determinants.     

Backhouse and Boianovsky on “disequilibrium theory”. A review article of transforming modern macroeconomics. Exploring disequilibrium microfoundations, 1956–2003

Abstract

This article is an in-depth analysis of Backhouse and Boianovsky's book, Transforming Modern Macroeconomics: Exploring Disequilibrium Microfoundations, 1956–2003. I start with questioning Backhouse and Boianovsky's too broad understanding of the disequilibrium approach. Thereby they bring together theories that should be kept separate, those by Patinkin, Clower and Leijonhuvud on the one hand, and those by Barro and Grossman, Drèze and Benassy, on the other. I also substantiate my disagreement with their claim that an inner link exists between fixed price equilibrium theories and imperfect competition modelling. Finally, I put forward a few conjectures about the reason why fixed price modelling petered out.     

Pricing power supplied on an interruptible basis

This paper deals with Pareto-optimal pricing of an electric utility whose demand is subject to random fluctuations. Its purpose is to extend previous results obtained by Boiteux and Drèze in two directions. First, the maximum power contracted by subscribers is charged instead of the variance of individual consumptions, which makes the model closer to most existing rate structures. Second, subscribers are allowed to choose among several types of supply differentiated by the probability with which their delivery is guaranteed. Most electricity companies are indeed known to supply power on an interruptible basis. In return for a reduction in their electricity bills, some customers give the company the right to cut off part of their supply when demand rises close to generating capacity.     

Repetitive risk aversion

We propose a reasonable condition, which we call repetitive risk aversion (RRA), to be imposed on any utility function to account for the observed data on the relationship between the degree of absolute risk aversion and wealth. We deduce this condition from the concept of the fear of ruin (Aumann and Kurz 1977) and show it to be equivalent to the behaviorally meaningful condition that the risk premium is increasing at a non-increasing rate with the size of the bet. We drive mixed risk aversion, which is known to be stronger than standard and thus proper risk aversion, from RRA. We present several economic applications of RRA to demonstrate that it delivers better comparative static results.I am thankful to Jacques Drèze and Louis Eeckhoudt for their comments. I greatly appreciate the comments of an anonymous reviewer of this journal which have resulted in substantial improvement to both the content and presentation of the paper. An earlier version of this paper was presented at seminars at Brown, CORE, Hopkins, HKUST, Yale, and IMS     

The probability approach to general equilibrium with production

We develop an alternative approach to the general equilibrium analysis of a stochastic production economy when firms’ choices of investment influence the probability distributions of their output. Using a normative approach we derive the criterion that a firm should maximize to obtain a Pareto optimal equilibrium: the criterion expresses the firm’s contribution to the expected social utility of output, and is not the linear criterion of market value. If firms do not know agents utility functions, and are restricted to using the information conveyed by prices then they can construct an approximate criterion which leads to a second-best choice of investment which, in examples, is found to be close to the first best. We are grateful to participants in the 2006 Public Economic Theory Conference, Hanoi, the 2007 CARESS/COWLES workshop on General Equilibrium at Yale University, the 2007 SAET Conference at Kos, Greece, the NSF/NBER 2007 Conference on General Equilibrium at Northwestern University, and seminars at Rice University, the University of Southern California, Indiana University, and U.C. Davis for helpful comments. We particularly thank Jacques Drèze and David Cass for stimulating discussions, and a referee for helpful suggestions for improving the paper.     

A note on monopolistic quantity rationing

It is shown that under incomplete information it may be optimal for a monopolist to ration a single price taker in addition to setting prices, which is in contrast to the case of complete information. As a byproduct it is shown that the star-shaped hull of the offer curve of a price taker exactly consists of the points that can be supported as Drèze-optima.     

Construction of a state space for interrelated securities with an application to temporary equilibrium theory

Summary We construct an endogenous state space in an exchange economy with possibly infinite horizon. Every period agents trade securities whose payoffs depend on future dividends and asset prices. We reject the perfect foresight assumption on the ground that agents have not only limited knowledge of other individuals' endowments and preferences, but also limited capacity to compute equilibria. We choose instead absence of arbitrage as the principle which allows agents to determine if a system of future prices is possible. We give an alogrithm to compute the set of nonarbitrage prices every period, with both finite and infinite horizon. We then apply this endogenous structure of uncertainty to an infinite horizon temporary equilibrium model.I would like to thank Professor Donald Brown for his constant help and guidance. I have also greatly benefited from helpful discussions with Professors Jacques Drèze, Bernard Dumas, Mordecai Kurz, Carsten Nielsen, Jan Werner, and Ho-Mou Wu.     

Homotopy methods to compute equilibria in game theory

This paper presents a survey of the use of homotopy methods in game theory. Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by various selection theories. We present the relevant techniques underlying homotopy algorithms. We give detailed expositions of the Lemke–Howson algorithm and the van den Elzen–Talman algorithm to compute Nash equilibria in 2-person games, and the Herings–van den Elzen, Herings–Peeters, and McKelvey–Palfrey algorithms to compute Nash equilibria in general n-person games. We explain how the main ideas can be extended to compute equilibria in extensive form and dynamic games, and how homotopies can be used to compute all Nash equilibria.     

Extensive-form games and strategic complementarities

I prove the subgame-perfect equivalent of the basic result for Nash equilibria in normal-form games of strategic complements: the set of subgame-perfect equilibria is a nonempty, complete lattice—in particular, subgame-perfect Nash equilibria exist. For this purpose I introduce a device that allows the study of the set of subgame-perfect equilibria as the set of fixed points of a correspondence. My results are limited because extensive-form games of strategic complementarities turn out—surprisingly—to be a very restrictive class of games.     

Evolutionary Stability of Pure-Strategy Equilibria in Finite Games

Sufficient conditions for pure-strategy Nash equilibria of finite games to be (Lyapunov) stable under a large class of evolutionary dynamics, the regular monotonic selection dynamics, are discussed. In particular, it is shown that in almost all finite extensive-form games, all the pure-strategy equilibria are stable. In such games, all mixed-strategy equilibria close to pure-strategy equilibria are also stable.Journal of Economic LiteratureClassification Numbers: C70, C72.     

Secure implementation experiments: Do strategy-proof mechanisms really work?

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept used in social choice theory. Saijo, Sjöström and Yamato [Saijo, T., Sjöström, T., Yamato, T., 2003. Secure implementation: Strategy-proof mechanisms reconsidered. Working paper 4-03-1. Department of Economics, Pennsylvania State University] argue that this concept has serious drawbacks. In particular, many strategy-proof mechanisms have a continuum of Nash equilibria, including equilibria other than dominant strategy equilibria. For only a subset of strategy-proof mechanisms do the set of Nash equilibria and the set of dominant strategy equilibria coincide. For example, this double coincidence occurs in the Groves mechanism when preferences are single-peaked. We report experiments using two strategy-proof mechanisms. One of them has a large number of Nash equilibria, but the other has a unique Nash equilibrium. We found clear differences in the rate of dominant strategy play between the two.     

On ‘Informationally Robust Equilibria’ for Bimatrix Games

Informationally robust equilibria (IRE) are introduced in Robson (Games Econ Behav 7: 233–245, 1994) as a refinement of Nash equilibria for strategic games. Such equilibria are limits of a sequence of (subgame perfect) Nash equilibria in perturbed games where with small probability information about the strategic behavior is revealed to other players (information leakage). Focusing on bimatrix games, we consider a type of informationally robust equilibria and derive a number of properties they form a non-empty and closed subset of the Nash equilibria. Moreover, IRE is a strict concept in the sense that the IRE are independent of the exact sequence of probabilities with which information is leaked. The set of IRE, like the set of Nash equilibria, is the finite union of polytopes. In potential games, there is an IRE in pure strategies. In zero-sum games, the set of IRE has a product structure and its elements can be computed efficiently by using linear programming. We also discuss extensions to games with infinite strategy spaces and more than two players. The authors would like to thank Marieke Quant for her helpful comments.     

Egalitarianism and Efficiency in Repeated Symmetric Games

We analyze the symmetric equilibria of repeated symmetric games where there is a conflict of interests over equilibria—the battle-of-the-sexes or the hawk–dove game are key examples. If one restricts attention to symmetric equilibria, efficient equilibria must be egalitarian. For finitely repeated games, and generic discount factors, there is a unique outcome path which ensures efficiency within the class of symmetric equilibria. This is also true for the infinitely repeated games if the players are sufficiently impatient. Journal of Economic Literature Classification Numbers: C72, C73.