Roy Radner

Competitive Equilibrium Under Uncertainty

This paper extends the general equilibrium analysis of the previous reading by examining the states of nature that particular individuals are capable of distinguishing. Equilibrium is examined under the condition that individuals engage in no trades that would involve delivery or receipt of goods based on distinctions that the individual is unable to make. The alternative extreme would permit two persons to trade provided one of them is able to distinguish states of nature. This would entail a great degree of trust and would ignore the communication costs when one party has to inform the other that his actions are now expected. In practice some institutions do rely on trust (together with some policing of honesty). One thinks of public accountants scrutinizing the records of corporations as a check that the managers do provide to owners the correct portion of profits. Many circumstances involve agency relations where an individual hires another to make decisions for him. These too rely on trust, which is not included in the model. Thus the model represents one extreme of possible extensions of the model from Chapter 11.

Equilibrium under uncertainty

Publisher Summary This chapter reviews several concepts of equilibrium that have appeared in the recent literature on markets and uncertainty and focuses on various theories of equilibrium under uncertainty in a sequence of markets, in the absence of complete forward markets for contingent delivery. A stationary state is in full equilibrium, not merely when demands equal supplies at the currently established prices but also when the same prices continue to rule at all dates—when prices are constant over time. The test of equilibrium over time is considered to be more important than mere arithmetical sameness or difference, noting that it implies constant prices in a stationary economy but does not necessarily implies constant prices in an economy subject to change. The Arrow–Debreu model provides a solid foundation of equilibrium analysis upon which to build. Modern decision theory and probability theory enable dealing more effectively with the issues raised by uncertainty and with the conceptual problems of describing an economy that is both stationary and subject to change.

Risk vs. profit potential: A model for corporate strategy

Abstract A firm whose net earnings are uncertain, and that is subject to the risk of bankruptcy, must choose between paying dividends and retaining earnings in a liquid reserve. Also, different operating strategies imply different combinations of expected return and variance. We model the firms cash reserve as the difference between the cumulative net earnings and the cumulative dividends. The first is a diffusion (additive), whose drift/volatility pair is chosen dynamically from a finite set, A . The second is an arbitrary nondecreasing process, chosen by the firm. The firms strategy must be nonclairvoyant . The firm is bankrupt at the first time, T , at which the cash reserve falls to zero ( T may be infinite), and the firms objective is to maximize the expected total discounted dividends from 0 to T , given an initial reserve, x ; denote this maximum by V ( x ). We calculate V explicitly, as a function of the set A and the discount rate. The optimal policy has the form: 1. (1) pay no dividends if the reserve is less than some critical level, a , and pay out all of the excess above a ; 2. (2) choose the drift/volatility pairs from the upper extreme points of the convex hull of A , between the pair that minimizes the ratio of volatility to drift and the pair that maximizes the drift; furthermore, the firm switches to successively higher volatility/drift ratios as the reserve increases to a . Finally, for the optimal policy, the firm is bankrupt in finite time, with probability one.

The Joint Exploitation of a Productive Asset: A Game-Theoretic Approach

SummaryIn the present paper we explore the set of equilibria in a game-theoretic model in which players can jointly exploit a productive asset. As in repeated games, we find that under certain circumstances there may be efficient as well as inefficient equilibria. In the model we study, efficient trigger-strategy equilibria may exist from some starting states (stocks of assets) but not others. More precisely, there is a stock level, sayy′, such that an efficient trigger-strategy equilibrium exists from starting stocks greater than or equal toy′, but not from those strictly less thany′. (This statement is meant to include the cases in whichy′ is zero or infinite.) Under some circumstances, there may exist a new kind of equilibrium, which we call aswitching equilibrium. We show that, in our model, whenever y′ is positive (and finite), there is an open intervalI with upper endpoint y′ such that, from any starting stock inI there is an equilibrium of the dynamic game with the following structure: the players follow an inefficient but growing path until the stock reaches the levely′, and then follow an (efficient) trigger strategy after that. The use of a continuous-time model enables us to conveniently decouple the delay of information from the time interval between decisions.

Optimal replacement policy

Optimal Replacement Policy. By D. W. Jorgenson, J. J. McCall and D. Radner. Amsterdam, North‐Holland, 1967. xii, 225 pp. 83/4“. 60s.

The sealed-bid mechanism: An experimental study

This paper presents the results of a set of experiments performed to test the properties of a bargaining mechanism (called the sealed-bid mechanism) used to structure bargaining under incomplete information. Our results indicate that the mechanism performs quite well. When using it, experimental subjects are able to capture a large portion of the potential gains from trade. In addition, the behavior of the subjects is qualitatively consistent with one particular equilibrium of the mechanism, namely, the one with linear bidding strategies. Finally, an experiment performed allowing experienced subjects to repeat the experiment for relatively large numbers of rounds, suggests that, with enough experience, other equilibria may appear, in which the subjects use “step function” strategies. Journal of Economic Literature Classification Numbers: 022. 026.

Equilibria of the Sealed- Bid Mechanism for Bargaining with Incomplete Information*, '

We study the Nash equilibria of the sealed-bid bargaining mechanism with incomplete information, a nonzero-sum game. For the case of uniform priors, we describe two uncountably numerous families of equilibria: the first has differentiable strategies; in the second the strategies are step-functions. The efficiencies of these equilibria range from “second best” to zero. For independent nonuniform priors, we show that a similar situation obtains. These results seem discouraging with regard to using the sealed-bid mechanism in practice. The mechanism might be salvaged, however, if bargainers turn out to confine themselves to linear-strategy equilibria.

A note on unanimity of stockholders' preferences among alternative production plans: a reformulation of the Ekern-Wilson model

This note, which was stimulated by Ekern and Wilsons study of the theory of the firm in an economy with incomplete markets, gives conditions for ex ante and ex post stockholders to be unanimous in their respective preferences among alternative production plans. This modest extension of Ekern and Wilsons analysis is facilitated by reinterpreting their model in standard Arrow-Debreu terms.

Rational expectations in microeconomic models: An overview

Abstract This paper is an expository introduction to several topics of current research in the general equilibrium theory of rational expectations. More specifically, we discuss the existence of exact and approximate rational expectations equilibria, the implementation of equilibria, the behavior of learning and smoothing processes by which traders construct expectations from repeated observations of the market, and the lagged use of the information revealed by prices in an intertemporal sequence of markets. The purpose of this discussion is to introduce papers on these topics appearing in the Journal of Economic Theory Symposium on Rational Expectations in Microeconomic Models .

Information Processing in Firms and Returns to Scale

The study of returns to scale in firms has traditionally focused on technological returns to scale in the production process. However, as the scale of a firm’s production grows, so does its administrative apparatus. The process of managing a firm, although not as well understood nor as extensively studied as the production process itself, uses significant resources and is important to the profitability of the other operations in the firm. Therefore, this process may also have a significant impact on returns to scale. The purpose of this paper is to explore this impact.