Communication via a strategic mediator

This paper investigates communication between an informed expert and an uninformed principal via a strategic mediator. We demonstrate that, for any bias in the parties' preferences, there exists a strategic mediator that provides the highest expected payoff to the principal, as if the players had communicated through an optimal non-strategic mediator.     

Professional advice

This paper studies strategic communication by an expert who is concerned about appearing to be well informed. The expert is assumed to observe a private signal with a simple and particularly tractable (multiplicative linear) structure. The quality of the expert's information is evaluated on the basis of the advice given and the realized state of the world. In equilibrium of this reputational cheap-talk game, no more than two messages are effectively reported. The model is extended to consider sequential communication by experts with conditionally independent signals. In the long run, learning is incomplete and herd behavior arises.     

Correlated information, mechanism design and informational rents

Crémer and McLean (Econometrica 56 (1988) 1247-1258) obtain a sufficient and necessary condition for full surplus extraction in Bayesian-Nash equilibrium—the rank condition, which McAfee and Reny (Econometrica 60(2) (1992) 395-421) later generalize for continuous type spaces. This paper shows that, if the principal does not know how noisy is the agent's signal—or equivalently, when signals available to an agent can be ranked by Blackwell's informativeness and, an agent's informativeness is independent of others’ information, the rank condition fails to hold. Conversely, when rank condition fails and informational rents are left to an agent, the model can be interpreted as if, the principal were uncertain about the informativeness of the agent's signal.     

The art of conversation: eliciting information from experts through multi-stage communication

We examine the strategic interaction between an informed expert and an uninformed decision maker, extending the analysis of Crawford and Sobel (Econometrica 50 (1982) 1431). We modify their model to allow for more extensive communication between the two parties and show that face-to-face communication between the expert and the uninformed decision maker followed by a written report from the expert leads to improved information transmission. In (almost) all cases, there exists an equilibrium in our modified model that ex ante Pareto dominates all of the equilibria identified by Crawford and Sobel. This remains true even if the expert's bias is so great that in their model no information would be disclosed.     

Long persuasion games

This paper characterizes geometrically the sets of all Nash and perfect Bayesian equilibrium payoffs achievable with unmediated communication in persuasion games, i.e., games with an informed expert and an uninformed decisionmaker in which the expert's information is certifiable. The first equilibrium characterization is provided for unilateral persuasion games, and the second for multistage, bilateral persuasion games. As in Aumann and Hart [R.J. Aumann, S. Hart, Long cheap talk, Econometrica 71 (6) (2003) 1619-1660], we use the concepts of diconvexification and dimartingale. A leading example illustrates both geometric characterizations and shows how the expert, whatever his type, can increase his equilibrium payoff compared to all equilibria of the unilateral persuasion game by delaying information certification.     

Optimal collusion-proof auctions

We study an optimal collusion-proof auction in an environment where subsets of bidders may collude not just on their bids but also on their participation. Despite their ability to collude on participation, informational asymmetry facing the potential colluders can be exploited significantly to weaken their collusive power. The second-best auction — i.e., the optimal auction in a collusion-free environment — can be made collusion-proof, if at least one bidder is not collusive, or there are multiple bidding cartels, or the second-best outcome involves a non-trivial probability of the object not being sold. Regardless, optimal collusion-proof auction prescribes non-trivial exclusion of collusive bidders, i.e., a refusal to sell to any collusive bidder with positive probability.     

Persuasion,binary choice,and the costs of dishonesty

We study the strategic interaction between a decision maker who needs to take a binary decision but is uncertain about relevant facts and an informed expert who can send a message to the decision maker but has a preference over the decision. We show that the probability that the expert can persuade the decision maker to take the expert’s preferred decision is a hump-shaped function of his costs of sending dishonest messages.     

The value of information in a principal-agent model with moral hazard: The ex post contracting case

In a principal-agent model with moral hazard, a signal about the principal?s technology — the stochastic mapping from the agent?s action to the outcome — is observed before the contract is offered. The signal is either uninformative (null information), informative and observed only by the principal (private information), or also observed by the agent (public information). We show that, from an ex ante standpoint (before the signal is observed): (i) the agent prefers private to both null and public information; (ii) the principal sometimes prefers null to both private and public information; and (iii) when the principal prefers public to null information, she prefers public to private information, whereas the agent prefers private to public information. In this last situation, we also show that (iv) for any separating equilibrium with private information, there exists a contract with public information that both strictly prefer.     

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x — and on the principal?s costs c(y) — which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal?s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal?s optimal strategy — and similarly of the strategy maximizing the expected welfare of the agents when the principal?s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang?s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.     

Informational size and incentive compatibility with aggregate uncertainty

In McLean and Postlewaite (Econometrica 56, 1992, p. 2421), we analyzed pure exchange economies with asymmetrically informed agents. We defined a notion of informational size and showed that, when the aggregate information of all agents resolves nearly all the uncertainty regarding the state of nature, the conflict between incentive compatibility and (ex post) efficiency can be made small if agents have sufficiently small informational size. This paper investigates the relationship between informational size and efficiency for the case in which nontrivial aggregate uncertainty is present, i.e., when significant uncertainty about the world persists even when the information of all agents is known.     

Comparative cheap talk

When are comparative statements credible? We show that simple complementarity conditions ensure that an expert with private information about multiple issues can credibly rank the issues for a decision maker. By restricting the expert's ability to exaggerate, multidimensional cheap talk of this form permits communication when it would not be credible in a single dimension. The communication gains can be substantial with even a couple of dimensions, and the complete ranking is asymptotically equivalent to full revelation as the number of issues becomes large. Nevertheless, partial rankings are sometimes more credible and/or more profitable for the expert than the complete ranking. Comparative cheap talk is robust to asymmetries that are not too large. Consequently, for sufficiently many independent issues, there are always some issues sufficiently symmetric to permit comparative cheap talk.     

Collusion and the organization of delegated expertise

We study the optimal design of incentive contracts for experts in different collusion environments, and explore implications for the organization of delegated expertise. We consider a principal relying on experts to gather and report two signals about a project's value. The principal can have a single expert gather both signals or two experts gather one signal each. We show that absent collusion, the multiexpert organization dominates the single expert organization. However, this ranking is reversed when the experts can collude among themselves (horizontal collusion) and with the principal (vertical collusion).     

An efficient solution to the informed principal problem

In this paper I study mechanism design by an informed principal. I show that generically this problem has an ex-post efficient solution. In the equilibrium mechanism, the informed principal appropriates all expected social surplus, with each type of her getting all expected social surplus conditional on that type. This outcome is supported as a perfect sequential equilibrium of the informed principal game when the joint probability distribution from which the agents’ types are drawn satisfies two conditions: the well-known condition of Cremer and McLean and Identifiability condition introduced by Kosenok and Severinov [Individually rational, budget-balanced mechanisms and allocation of surplus, J. Econ. Theory (2002), forthcoming]. Conversely, these conditions are necessary for an ex-post efficient outcome to be attainable in an equilibrium of the informed principal game. Under these conditions only our equilibrium outcome constitutes a neutral optimum, i.e. cannot be eliminated by any reasonable concept of blocking [R. Myerson, Mechanism design by an informed principal, Econometrica 51 (1983) 1767-1797]. Identifiability and Cremer-McLean conditions are generic when there are at least three agents, and none of them has more types than the number of type profiles of the other agents.     

ENTRY AND QUALITY SIGNALLING WHEN ONLY SOME CONSUMERS ARE INFORMED OF THE ENTRANT'S QUALITY

This paper focuses on competition between an incumbent and an entrant when only the entrant's quality is unknown to (some) consumers. The incumbent may or may not know the entrant's quality. The model reveals a separating equilibrium where the entrant's high price signals its high quality when the proportion of informed consumers is at some intermediate value. The case in which the incumbent knows the entrant's quality generates two additional equilibria. When the proportion of informed consumers is large enough, firms choose their prices as in the complete information case. The entrant's high price in combination with the incumbent's low price signals the entrant's high quality. When the proportion of informed consumers is at some intermediate value, the incumbent's high price signals the entrant's low quality, while its low price signals the entrant's high quality. Interestingly, we find that entry may be facilitated with informational product differentiation.     

Subjective probabilities on “small” domains

The Savagian choice-theoretic construction of subjective probability does not apply to preferences, like those in the Ellsberg Paradox, that reflect a distinction between risk and ambiguity. We formulate two representation results—one for expected utility, the other for probabilistic sophistication—that derive subjective probabilities but only on a “small” domain of risky events. Risky events can be either specified exogenously or in terms of choice behavior; in the latter case, both the values and the domain of probability are subjective. The analysis identifies a mathematical structure—called a mosaic—that is intuitive for both exogenous and behavioral specifications of risky events. This structure is weaker than an algebra or even a λ-system.     

Corrigendum to “Reserve price signaling” [J. Econ. Theory 135 (1) (2007) 253-268]

We find an error in [H. Cai, J. Riley, L. Ye, Reserve price signaling, J. Econ. Theory 135 (1) (2007) 253-268]. The existence of the separating signaling equilibrium is not challenged, but the related comparative statics, while valid in the case without informational externalities between bidders, do not generalize to the case with informational externalities as claimed by the authors. General results on the influence of the number of bidders are obtained in a linear specification of the informational externalities.     

ASYMMETRIC INFORMATION AND EXCHANGE OF INFORMATION ABOUT PRODUCT DIFFERENTIATION

We introduce asymmetric information about consumers’ transportation costs (i.e., the degree of product differentiation) in the model of Hotelling. When transportation costs are high, both firms have lower profits with asymmetric information than with perfect information. Contrarily, if transportation costs are low, both firms may prefer the asymmetric information scenario (the informed firm always prefers the informational advantage, while the uninformed firm may or may not prefer to remain uninformed). Information exchange is ex‐ante advantageous for both firms, but ex‐post damaging if transportation costs turn out to be low. If the information is unverifiable, the informed firm does not represent a reliable source of information, since it always prefers to announce that transportation costs are high and there is no contract that induces truthful revelation.     

Optimal limited authority for principal

This article studies a principal-agent problem where the only commitment for the uninformed principal is to restrict the set of decisions she makes following a report by the informed agent. We show that an ex ante optimal equilibrium for the principal corresponds to a finite partition of the state space, and each retained decision is ex post suboptimal for the principal, biased toward the agent?s preference. Generally an optimal equilibrium does not maximize the number of decisions the principal can credibly retain. Compared to no commitment, limited authority improves the quality of communication from the agent. As a result, it can give the principal a higher expected payoff than delegating the decision to the agent.     

Nonmanipulable Bayesian testing

This paper considers the problem of testing an expert who makes probabilistic forecasts about the outcomes of a stochastic process. I show that, as long as uninformed experts do not learn the correct forecasts too quickly, a likelihood test can distinguish informed from uninformed experts with high prior probability. The test rejects informed experts on some data-generating processes; however, the set of such processes is topologically small. These results contrast sharply with many negative results in the literature.     

Aggregate information cascades

We introduce a new model of aggregate information cascades where only one of two possible actions is observable to others. Agents make a binary decision in sequence. The order is random and agents are not aware of their own position in the sequence. When called upon, they are only informed about the total number of others who have chosen the observable action before them. This informational structure arises naturally in many applications. Our most important result is that only one type of cascade arises in equilibrium, the aggregate cascade on the observable action. A cascade on the unobservable action never arises.