In a decision-theoretic model of a firm, the author represents managers as information processors of limited capacity; efficiency is measured in terms of (1) the number of processors and (2) the delay between the receipt of information by the organization and the implementation of the decision. The author characterizes efficient networks for both one-shot and repeated regimes, as well as the corresponding 'production function' relating the number of items processed to the number of processors and the delay. He sketches some applications to common decision paradigms, and implications for decentralization and organizational returns to scale. Copyright 1993 by The Econometric Society.

In a repeated principal-agent game (supergame) in which each player's criterion is his long-run average expected utility, efficient behavior can be sustained by a Nash equilibrium if it is Pareto-superior to a one-period Nash equilibrium.Furthermore, if the players discount future expected utilities, then for every positive epsilon, and every pair of discount factors sufficiently close to unity (given epsilon), there exists a supergame equilibrium that is within epsilon (in normalized discounted expected utility) of the target efficient behavior.These supergame equilibria are explicitly constructed with simple "review strategies." 1. INTRODUCTION 1.1.Some Background IN A PRINCIPAL-AGENT SITUATION, the agent chooses an action "on behalf of" the principal.The resulting consequence depends on a random state of the environment as well as on the agent's action.After observing the consequence, the principal makes a payment to the agent according to a pre-announced reward function, which depends directly only on the observed consequence.This last restriction expresses the fact that the principal cannot directly observe the agent's action, nor can the principal observe the information on which the agent bases his action.This situation is one of the simplest examples of decentralized decisionmaking in which the interests of the decision-makers do not coincide.2If this action-reward situation occurs only once, I shall call it a short-run principal-agent relationship.The situation can be naturally modeled as a two-move game, in which the principal first announces a reward function to the agent, and then the agent chooses an action (or decision function if he has prior information about the environment).The Nash (or perfect Nash) equilibria of such a game are typically inefficient (unless the agent is neutral towards risk), in the sense that there will typically be another (but nonequilibrium) reward-decision pair that yields higher expected utilities to both players.In order to increase the efficiency of short-run equilibria, the principal could monitor (at least ex post) the information and decision of the agent.However such monitoring would tyically be costly, so that net efficiency need not be increased by monitoring.Another approach to increasing efficiency is suggested by the theory of repeated games.If a game with two or more players is repeated, the resulting situation can be modeled naturally as a game ("supergame") in which the players' actions in any one repetition are allowed to depend on the history of the previous repetitions.In the principal-agent situation, the repetition of the game would l I am grateful to R. A. Aumann, R. W. Rosenthal, and A.

The situation in which a principal-agent relationship is repeated finitely many times (T) is formulated as a sequential game.For any Pareto-optimal cooperative arrangement in the one-period game that dominates a one-period Nash equilibrium, and any positive number epsilon, there exists for every sufficiently large T a (noncooperative) epsilon equilibrium of the T-period game that yields each player an average expected utility that is at least his expected utility in the one-period cooperative arrangement, less epsilon.

When traders come to a market with different information about the items to be traded, the resulting market prices may reveal to some traders information originally available only to others.The possibility for such inferences rests upon traders having "models" or "expectations" of how equilibrium prices are related to initial information.This relationship is endogenous, which motivates the term "rational expectations equilibrium."This paper shows that, in a particular model of asset trading, if the number of alternative states of initial information is finite then, generically, rational expectations equilibria exist that reveal to all traders all of their initial information. INTRODUCTION1WHEN TRADERS COME to a market with different information about the items to be traded, the resulting market prices may reveal to some traders something about the information available to other traders.This phenomenon might be important in the case of assets whose eventual values or utilities are not perfectly known to all traders at the time of purchase, as in the trading of land with uncertain quantities of mineral deposits, or in the trading of common stocks.A thorough theoretical analysis of this situation probably requires a more detailed specification of the trading mechanism than is usual in general equilibrium analysis.Nevertheless, it is tempting to try to obtain results that are as independent as possible of the specifics of the trading mechanism, by using some suitable concept of equilibrium.The possibility for one trader to make inferences from market prices about the information possessed by other traders rests upon his having a "model" or "expectations" of how equilibrium prices are determined, i.e., how equilibrium prices are related to the information initially possessed by the various traders.But this relationship is endogenous to the market system, and if traders have any opportunity to compare the results of the operation of the market with their own models, then a suitable equilibrium concept would require that their models not be obviously controverted by their observations of the market.This motivates the term "rational expectations equilibrium."The particular rational expectations equilibrium that one would obtain depends upon the traders' models or expectations of the relationship between traders' 1 I am grateful to Jerry Green, Leonid Hurwicz, James Jordan, and David Kreps for very helpful discussions of the problems treated in this paper.

[Consider a sequence of markets for goods and securities at successive dates, with no market at any date complete in the Arrow-Debreu sense. A concept of common expectations is proposed that requires traders to associate the same future prices to the same future exogenous events, but does not require them to agree on the (subjective) probabilities associated with those events. An equilibrium is a set of prices at the first date, a set of common price expectations for the future, and a consistent set of individual plans for consumers and producers such that, given the current prices and price expectations, each individual agent's plan is optimal for him, subject to an appropriate sequence of budget constraints. The existence of such an equilibrium is demonstrated under assumptions about technology and consumer preferences similar to those used in the typical Arrow-Debreu theory of complete markets. However, an equilibrium can fail to exist if some provision is not made for the elimination of "unprofitable" enterprises. The usual assumptions of "rationality" imply, in this model, that agents learn from experience and modify their expectations as Bayesians.]

The paper represents an application of the modern theory of competitive equilibrium to the case of uncertainty. Two theorems are presented: the first sets forth sufficient conditions for the existence of a competitive equilibrium for the case in which each economic agent has a given structure of information available and the second sets forth sufficient conditions for the existence of a competitive equilibrium for the case in which any available structure of information may be used. However, if the costs of obtaining information are included in the analysis, the conditions of the theorem may not be met. This is also true if the costs necessary to perform computations are included. In addition if part of the information available to economic agents concerns the behavior of other agents rather than concerning environmental variables, the conditions of the theorem may not be fulfilled. (Author)

We consider optimal capital accumulation in a nonlinear activity analysis model in which production and primary resource supplies are affected by a stationary stochastic process of exogenous shocks; the optimality criterion is the sum of discounted expected future social utilities. Under various neoclassical conditions on technology and preferences, (i) there exists an optimal policy of investment and consumption expressible as a continuous time-invariant function of the capital stocks and the history of stochastic shocks, and (ii) there is a stationary stochastic process of capital stocks that is consistent with the optimal policy.

[This is the second part of a paper concerning an iterative decentralized1 process designed to allocate resources optimally in decomposable environments that are possibly characterized by indivisibilities and other non convexities. Important steps of the process involve randomization. In Part I we presented the basic models and results, together with examples showing that certain assumptions can be satisfied in both classical and non convex cases. Part II goes further with such examples in showing that our process yields optimal allocations in environments in which the competitive mechanism fails, and also shows how abstract conditions used in Part I can be verified in terms of properties of preferences and production functions that are familiar to economists.]