Buyer's preferences over auctions depend on their measure of absolute risk aversion. If it is constant and they have independent private values, they are indifferent between a first-price auction (FPA), a second-price auction (SPA), and a first-price auction in which the number of bidders is revealed before bids are taken (FPA- R). If they have decreasing absolute risk aversion, they prefer the SPA to the FPA-R to the FPA. Their preference for the SPA is diminished to the extent that their values are affiliated. Affiliation also causes them to prefer the number of bidders to be revealed, whereas the seller then prefers to keep it secret. Copyright 1987 by The Econometric Society.
When a decision rule is implemented using a Bayesian incentive compatible mechanism in which the messages are publically obser vable, the players' information is augmented by their observation of each others' strategies. In this paper the authors study the set of Bayesian implementable decision rules which have the further property that the information c onveyed in the process of thier implementation does not invalidate the optimality of the players' strategies. Such rules are called posterior implementable. The authors concentrate on a two-person problem with two possible decisions and, for this problem, they obtain a complete characterization of the set of posterior implementable decision rules. Copyright 1987 by The Econometric Society.
This paper offers an interpretive comparison of the Arrow-Pratt and Ross characterizations of comparative risk aversion for expected utility maximizers. The tools used in this comparison are then applied to obtain a strengthening of the Ross cha racterization. This strengthened result is in turn extended to the ca se of general, smooth, nonexpected utility preferences over probabili ty distributions. Copyright 1987 by The Econometric Society.
Empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions. Lau and Gallant and Golub have worked out methods for imposing the appropriate curvature conditions locally, but those local techniques frequently fail to yield satisfactory results. We develop two methods for imposing curvature conditions globally in the context of cost function estimation. The first method adopts Lau's technique to a generalization of a functional form first proposed by McFadden. Using this Generalized McFadden functional form, it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally. The second method adopts a technique used by McFadden and Barnett, which is based on the fact that a non-negative sum of concave functions will be concave. Our various suggested techniques are illustrated using the U.S. Manufacturing data utilized by Berndt and Khaled
THIS PAPER DISCUSSES the problem of aggregating probability judgements and shows that Arrow-type paradoxes arise in this context, just as in the context of aggregating preferences. The need to aggregate probability judgements may arise in several different sorts of situation. Two examples which concern decision making under risk are: (i) when an individual, prior to making a decision, consults a number of experts who differ in their assessments of the probabilities of alternative states of nature; (ii) when the individuals constituting a society have to make a joint decision on the basis of identical utility functions but, again, differing assessments of the probabilities of alternative states of nature.2 We illustrate (i) above by means of a simple example: An individual consults two legal experts, who give him their probability judgements concerning the success or failure (there are just two possible outcomes) of proposed litigation. Scenario 1: The individual knows that litigation will succeed if judge J presides and barrister B defends, but will not succeed otherwise. From the experts' probability judgements the individual is able to infer that one expert has received a message that judge J will preside, and the other a message that barrister B will defend. (Either message, or both, may be false.) Given these messages, the individual updates in Bayesian fashion the prior probabilities he assigns to success and failure. Scenario 2: Success or failure depends on interpretation of the law. Pooling the information on which the experts' probability judgements are based is, we suppose, impracticable. (Perhaps they meet to discuss the case and cannot agree.) Aggregation of probability judgements in situations such as Scenario 1 (and according to axioms which we discuss in the next section) is clearly a wrong procedure which may lead to totally erroneous results. In situations such as Scenario 2 such aggregation may however have a useful role. Formulae for aggregating probability judgements have been discussed by, among others, Wagner (1982), Bordley (1982), Genest, Weerahandi, and Zidek (1984), and Fishburn and Rubinstein (1984). In this paper we generalize some results contained in the latter two papers, before going on to consider paradoxes. An early, Arrow-type impossibility result, based on rather strong assumptions, is due to Dalkey (1972). In Section 2 notation and axioms are introduced, and some results given. In Section 3 three propositions are stated and proved.
Several partners jointly own an asset that may be traded among them. Each partner has a valuation for the asset; the valuations are known privately and drawn independently from a common probability distribution. We characterize the set of all incentive-compatible and interim-individually-rational trading mechanisms, and give a simple necessary and sufficient condition for such mechanisms to dissolve the partnership ex post efficiently. A bidding game is constructed that achieves such dissolution whenever it is possible. Despite incomplete information about the valuation of the asset, a partnership can be dissolved ex post efficiently provided no single partner owns too large a share; this contrasts with Myerson and Satterthwaite's result that ex post efficiency cannot be achieved when the asset is owned by a single party.
John H. Kagel, Ronald M. Harstad, Dan Levin, Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study, Econometrica, Vol. 55, No. 6 (Nov., 1987), pp. 1275-1304
This paper provides sufficient conditions for the equilibrium price system and a vector of exogenously specified state variable processes to form a diffusion process in a pure exchange economy. The conditions involve smoothness of agents' utility functions and certain nice properties of the aggregate endowment process and the dividend processes of traded assets. In place of the dynamic programming, a martingale representation technique is utilized to characterize equilibrium portfolio policies. This technique is useful even when there does not exist a finite dimensional Markov structure in the economy and thus the Markovian stochastic dynamic programming is not applicable. A gents are shown to hold certain hedging mutual funds and the riskless asset. In contrast to earlier results, the market portfolio does not have a special role in hedging, since the markets are dynamically complete. When there exists a finite dimensional Markov system in the economy, the dimension of the hedging demand identified through the Markovian dynamic programming may be much larger than that identified by the martingale method. Copyright 1987 by The Econometric Society.