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We study policy advice by several experts with noisy private information and biased preferences. We highlight a trade-off between the truthfulness of the information revealed by each expert and the number of signals from different experts that can be aggregated to reduce noise. Contrary to models with perfectly informed experts, because of this trade-off, full revelation of information is never possible. However, almost fully efficient information extraction can be obtained in two cases. First, there is an equilibrium in which the outcome converges to the first best benchmark with no asymmetric information as we increase the precision the experts' signals. Second, the inefficiency in communication also converges to zero as the number of experts increases, even when the residual noise in the experts' private signals is large and all the experts have significant and similar (but not necessarily identical) biases.

The issue of how players' model of a game may evolves over time is largely unexplored. We formalize this issue for games with perfect information, and show that small-probability model deterioration may upset the complete-model backward induction solution, possibly yielding a Pareto-improving long run distribution of play. We derive necessary and sufficient conditions for the robustness of backward induction. These conditions can be interpreted with a forward-induction logic, and are shown to be closely related to the requirements for asymptotic stability of the backward induction path under standard evolutionary dynamics.

We study decentralized trade in dynamic markets with homogeneous, non-atomic, buyers and sellers that wish to exchange one unit. In the first part of the paper we characterize equilibrium in a bargaining model with two-sided time varying outside options. In the second part we analyze a market equilibrium model in which (i) buyers and sellers are randomly matched in pairs; (ii) each buyer-seller pair bargains over the price of a good; and (iii) each agent has the option of abandoning negotiations, in which case the value of returning to the pool of unmatched agents constitutes an outside option. The second part is therefore an application of the first part in which the values of the outside options are endogenous to the model. Conditions for uniqueness of the market equilibrium are given; when it is unique it converges to the Walrasian outcome as frictions vanish. To the extent that multiplicity of market equilibria may (under some conditions) persist as frictions are removed, the limit of some sequences of equilibrium prices may converge to non-Walrasian values.

This paper presents a novel explanation of the decision by a firm to make an input within the firm rather than to out-source the production to another firm. Due to the limited attention of the manager/entrepreneur, time spent overseeing production in-house has an opportunity cost: the neglect of potential new products/markets. Outsourcing production economizes on attention, but writing and negotiating contracts also has an opportunity cost: the neglect of current operations. This paper derives the endogenous transaction costs of writing a contract with another party and shows that positive transaction costs are not sufficient for the optimal internalization of transactions. However, positive net transaction costs results in the optimal decision to produce the input internally. In addition, although there are larger firm sizes of higher value than obtainable under the optimal policy, the optimal policy maximizes the social value of each individual transaction.

Customers of network commodities face coordination problems due to adoption externalities that give rise to multiple, Pareto-ranked equilibria. We investigate the extent to which the coordination problem can be resolved by inducement schemes when agents' preferences are private information. Specifically, we show that all symmetric ``cutoff strategy'' profiles constitute the set of profiles uniquely implementable under an inducement scheme. We derive the ex ante cost of implementing each such profile and characterize simple inducement schemes of the following form that implement it: each scheme specifies a fixed fee that every adopter pays, and a fixed gross subsidy/prize to be randomly allocated to the adopters. We discuss the implications of these findings on the design of optimal schemes for different network organizers. We extend the analysis to preference revelation mechanisms and prove a revenue equivalence result and characterize optimal mechanisms, but find that unique implementation is no longer possible.

We consider a two-period portfolio problem with predictable assets returns. First-order (second-order) predictability means that an increase in the first period returns yields a first-order (second-order) stochastically dominated shift in the distribution of the second period state prices. Mean reversion in stock returns, Bayesian learning, stochastic volatility and stochastic interest rates (bond portfolios) belong to one of these two types of predictability. We first show that a first-order stochastically dominated shift in the state price density reduces the marginal value of wealth if and only if relative risk aversion is uniformly larger than unity. This implies that first-order predictability generates a positive hedging demand for portfolio risk if this condition is met. A similar result is obtained with second-order predictability under the condition that absolute prudence be uniformly smaller than twice the absolute risk aversion. When relative risk aversion is constant, these two conditions are equivalent. We also examine the effect of exogenous predictability, i.e., when the information about the future opportunity set is conveyed by signals not contained in past asset prices.

We provide elementary and uniform proofs of order independence for various strategy elimination procedures for finite strategic games, both for dominance by pure and by mixed strategies. The proofs follow the same pattern and focus on the structural properties of the dominance relations. They rely on Newman's Lemma established in 1942 and related results on the abstract reduction systems.

This paper studies a model of memory. The model takes into account that memory capacity is limited and imperfect. We study how agents with such memory limitations, who have very little information about their choice environment, play games. We introduce the notion of a Limited Memory Equilibrium (LME) and show that play converges to an LME in every generic normal form game. Our characterization of the set of LME suggests that players with limited memory do (weakly) better in games than in decision problems. We also show that agents can do quite well even with severely limited memory, although severe limitations tend to make them behave cautiously.

We study the decision of when to sue in a game in which multiple plaintiffs have similar cases against a single defendant. Two legal regimes are considered. In one, prior results are binding in all future cases. In contrast, under the prevalent asymmetric regime, adverse results are binding against the defendant in future actions, but a judgement adverse to one plaintiff will not be binding against another plaintiff. Some legal scholars have argued that such a system is unfair to defendants and benefits plaintiffs. Our analysis reveals, however, that an asymmetric regime may actually hurt plaintiffs in equilibrium by inducing them to wait.

We consider a single object, independent private value auction model with entry. Potential bidders are ex ante symmetric and randomize about entry. After entry, each bidder incurs a cost, then learns her private value and a set of signals that may lead to updated beliefs about other entrants' valuations. It is shown that the Vickrey auction with free entry maximizes the expected revenue. Furthermore, if the information potentially available to bidders after entry is sufficiently rich, then the Vickrey auction, up to its equivalent class, is also the only optimal sealed-bid auction.

This paper explores a multiple-object auction with the following three features: First, there is a capacity constraint, as each bidder can win at most one object from the auction. Second, the objects for sale and the bidders are located around the unit circle. A bidder's valuation of a certain object depends solely on the location of the object relative to the bidder; that is, on the distance between the object and the bidder. Third, instead of turning in separate bids on different objects, each bidder just states his location on the unit circle. His bids on different objects can then be derived from his stated location.The paper demonstrates that the Groves-Clarke logic applies to this particular setting, and it designs an auction mechanism that is ex-post efficient, under the capacity constraint, and incentive compatible. The paper also extends the Revenue Equivalence Theorem to this particular setting, using a proof different from Engelbrecht-Wiggans'(1988), by imposing less strict regularity conditions. Based on the circle setting, the paper shows that, with symmetric bidders, for any two different auction mechanisms applying the same allocation rule, the locations on the circle at which a bidder obtains the lowest expected payoff from either of these two mechanisms are the same. This location serves as the benchmark location to the circle version of the Revenue Equivalence Theorem in this paper.

This paper illustrates the effect of market size on the decision of whether or not firms should vertically integrate or disintegrate. We use a model of two successive stages of production with Cournot competition in each stage. In this model, firms choose to specialize (either upstream or downstream) or to integrate the two stages, before making their production decisions. The decision of whether or not to integrate or specialize depends on the trade-off between "escaping from" the double marginalization problem or the gain from specializing in the production stage in which the firm is more efficient. We show (using simulations) that more firms choose to be vertically integrated as the valuation of the final product or the number of consumers increases, unless the number of firms increases proportionately.

In this paper we try to explain how price discrimination can cause bilateral trade patterns of the type seen under countertrade agreements. We interpret countertrade as a form of transaction bundling, which can discriminate between potential trading partners, and we combine characteristics from two explanations as to the existence of countertrade: Price discrimination through transaction bundling, and adverse selection arising from the uncertainty in the quality of the goods produced by trading partners in a less developed country (LDC) leading to a partner preference from the side of the Western (DC) firm. Our paper shows that the trade volume prospects of a firm in a LDC can be considerably enhanced if a countertrade transaction is bundled, and that such gains in trade become greater (relative to the case of no bundling), the greater the degree of quality uncertainty in the good it sells. It is also shown that it is profit maximising for a firm in a DC to offer mixed bundling for the exchange transaction, and that the profits derived from such bundling are a decreasing function of both the degree of uncertainty in the good sold by the firm in the LDC, and the marginal cost of the good sold by firm in the DC.

I consider the problem of an independent inventor attempting to sell a cost-reducing innovation in an oligopoly setting. There are N potential buyers and the inventor possesses private information regarding the value of the invention. A revealing equilibrium is characterized in which the inventor’s demand signals the value of the invention to each potential buyer. I find that both the inventor’s demand and his continuation value increase as the number of firms left in the sequence of potential buyers increases. I also find that a firm’s probability of rejecting the inventor’s demand is higher the sooner the firm is approached in the sequence.

In a model of bank lending characterized by asymmetric information, we show that banks may use an interim monitoring technology strategically to soften price competition, even though the borrowers face no moral hazard problem. The interim monitoring technology can also be used to alleviate adverse selection. The equilibria that emerge resemble those in vertical product differentiation models. We also show that because of the strategic use of interim monitoring, a bank may forego the use of a costless and perfect ex-ante screening technology.

A socially optimal structure of application and renewal fees for patents would encourage the maximal number of applications while reducing effective patent length. We find, however, that when patent offices are required to be self-funding, resource constraints can distort this fee structure. Specifically, a financially constrained, but welfare-oriented, patent office will tend to raise initial application fees while lowering renewal fees. This creates two detriments to social welfare as it discourages the filing of some patents while extending the effective life of others.

In a number of evolutionary models the presence of mutations, or random components of choice, serve to refine predictions of long-run behavior. We analyze the effects of mutation rates that vary because of the presence of imitation. A full characterization of long-run outcomes is provided for familiar coordination and congestion games, and also a number of other games not previously considered within the evolutionary framework. Our results are often quite distinct from those in the literature. We apply these tools to a series of economic applications, including market games, where imitation can explain excess volatility of prices, and location games, where it leads to greater uniformity in choices.

When evaluating the rationality of a player in a game one has to examine counterfactuals such as "what would happen if the player were to do what he does not do?" In this paper I develop a model of a normal form game where counterfactuals of this sort are evaluated as in the philosophical literature (cf. Lewis, 1973; Stalnaker, 1968). According to this method one evaluates a statement like ``what would the player believe if he were to do what he does not do'' at the world that is closest to the actual world where the hypothetical deviation occurs. I show that in this model common knowledge of rationality need not lead to rationalizability. I also present assumptions that allow rationalizability to follow from common knowledge of rationality. These assumptions suggest that rationalizability may not rely on weaker assumptions about belief consistency than Nash equilibrium.

This paper examines incentives for information disclosure in a oligopolistic market when buyers are unsure of the existence of that information. Previous empirical and theoretical work has shown that mandatory disclosure laws can be binding when buyers do not know whether the information exists. This paper shows that the information unraveling result is strengthened by competition not only because a market with more firms is increasingly likely to have at least one firm with quality high enough to want to disclose it (thus starting the information unraveling result) but also because firms reveal information that makes themselves look bad if they can make their competitors look worse. This results in prisoner's dilemma style incentives to reveal that ensures full disclosure as the number of firms goes to infinity.

We propose a new theory of choice between lotteries, which combines an 'economic' view of decision making - based on a rational, though incomplete, ordering - with a 'psychological' view - based on heuristics. This theory can explain observed violations of EU theory, namely all cyclical patterns of choice as well as violations of independence.

With indivisible shareholdings and simultaneous shareholder decision-making, the existing takeover literature provides a reasonable profit only in asymmetric equilibria. We allow the raider to approach shareholders sequentially and thereby find a unique equilibrium that produces the same outcome.