Optimal use of correlated information in mechanism design when full surplus extraction may be impossible

We study the mechanism design problem when the principal can condition the agent's transfers on the realization of ex post signals that are correlated with the agent's types. Crémer and McLean [Econometrica 53(1985) 345-361; 56(1988) 1247-1257], McAfee and Reny [Econometrica 60(2)(1992) 395-421], and Riordan and Sappington [J. Econ. Theory, 45(1988) 189-199] studied situations where the signals are such that full surplus can be extracted from every agent type. We study optimal utilization of the signals when there are fewer signals than types and the Riordan and Sappington conditions do not always hold. For some special cases, we show the level of surplus that can be extracted, and identify the agent types who obtain rent.     

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.     

Unemployment insurance with hidden savings

This paper studies the design of unemployment insurance when neither the searching effort nor the savings of an unemployed agent can be monitored. If the principal could monitor the savings, the optimal policy would leave the agent savings-constrained. With a constant absolute risk-aversion (CARA) utility function, we obtain a closed form solution of the optimal contract. Under the optimal contract, the agent is neither saving nor borrowing constrained. Counter-intuitively, his consumption declines faster than implied by Hopenhayn and Nicolini (1997) [1]. The efficient allocation can be implemented by an increasing benefit during unemployment and a constant tax during employment.     

Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly

The seller of N distinct objects is uncertain about the buyer's valuation for those objects. The seller's problem, to maximize expected revenue, consists of maximizing a linear functional over a convex set of mechanisms. A solution to the seller's problem can always be found in an extreme point of the feasible set. We identify the relevant extreme points and faces of the feasible set. We provide a simple algebraic procedure to determine whether a mechanism is an extreme point. We characterize the mechanisms that maximize revenue for some well-behaved distribution of buyer's valuations.     

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).     

A dynamic theory of war and peace

In every period, an aggressive country seeks concessions from a non-aggressive country with private information about their cost. The aggressive country can force concessions via war, and both countries suffer from limited commitment. We characterize the efficient sequential equilibria. We show that war is necessary to sustain peace and that temporary wars can emerge because of the coarseness of public information. In the long run, temporary wars can be sustained only if countries are patient, if the cost of war is large, and if the cost of concessions is low.     

Reputation and exogenous private learning

Short-run competitors in the chain store game receive noisy signals of the long-run incumbent firm's type. The history of signals, which in the limit is fully revealing, is observable to the competitors but possibly not to the incumbent. As long as there is sufficient noise in the signals, then in any equilibrium a patient weak incumbent obtains a payoff strictly higher than her minmax payoff.     

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.     

Dynamic coordination with individual learning

We study coordination in dynamic global games with private learning. Players choose whether and when to invest irreversibly in a project whose success depends on its quality and the timing of investment. Players gradually learn about project quality. We identify conditions on temporal incentives under which, in sufficiently long games, players coordinate on investing whenever doing so is not dominated. Roughly speaking, this outcome occurs whenever players? payoffs are sufficiently tolerant of non-simultaneous coordination. We also identify conditions under which players coordinate on the risk-dominant action. We provide foundations for these results in terms of higher order beliefs.     

Optimal contracting with dynastic altruism: Family size and per capita consumption

We use a Barro–Becker model of endogenous fertility, in which parents are subject to idiosyncratic shocks that are private information (either to labor productivity or taste for leisure), to study the efficient degree of consumption inequality in the long run. The planner uses the trade-off between family size and future consumption and leisure, to provide incentives for workers to reveal their shocks. We show that in this environment, the optimal dynamic contract no longer features immiseration in consumption. We also discuss the implications of the model on the long run properties of family size in the optimal contract and show that the long run trend in dynasty size can be either positive or negative depending on parameters.     

On the first-order approach in principal-agent models with hidden borrowing and lending

We provide sufficient conditions for the validity of the first-order approach for two-period dynamic moral hazard problems where the agent can save and borrow secretly. The first-order approach is valid if the following conditions hold: (i) the agent has non-increasing absolute risk aversion utility (NIARA), (ii) the output technology has monotone likelihood ratios (MLR), and (iii) the distribution function of output is log-convex in effort (LCDF). Moreover, under these three conditions, the optimal contract is monotone in output. We also investigate a few possibilities of relaxing these requirements.     

Bayesian learning and convergence to Nash equilibria without common priors

Summary. Consider an infinitely repeated game where each player is characterized by a “type” which may be unknown to the other players in the game. Suppose further that each player's belief about others is independent of that player's type. Impose an absolute continuity condition on the ex ante beliefs of players (weaker than mutual absolute continuity). Then any limit point of beliefs of players about the future of the game conditional on the past lies in the set of Nash or Subjective equilibria. Our assumption does not require common priors so is weaker than Jordan (1991); however our conclusion is weaker, we obtain convergence to subjective and not necessarily Nash equilibria. Our model is a generalization of the Kalai and Lehrer (1993) model. Our assumption is weaker than theirs. However, our conclusion is also weaker, and shows that limit points of beliefs, and not actual play, are subjective equilibria. Received: March 3, 1995; revised version: February 17, 1997     

Quality undersupply and oversupply

I analyze a market in which a price-taking buyer buys a variable-quality good from a population of sellers, contrasting the case where quality is a seller's private information to that where it is public information. Average quality traded under private information can be either higher (quality oversupply) or lower (quality undersupply) than under public information, depending on sellers’ preferences. We are likely to see quality undersupply if (i) sellers’ preferences exhibit substitutability between the variable-quality good and the numéraire good, and/or (ii) sellers view the numéraire good as a luxury good relative to the variable-quality good. Reverse arguments hold for quality oversupply.     

Negotiation and take it or leave it in common agency

This paper contrasts models of common agency in which principals compete in incentive contracts (that is, they make take it or leave it offers) with models where principals offer agents menus of incentive contracts from which the final contract is negotiated. It is shown that pure strategy equilibria in incentive contracts are robust to the possibility that principals might offer menus. In addition, a no-externalities condition is given such that any pure strategy equilibrium allocation with menus can be supported with competition in incentive contracts. The no-externalities condition is restrictive, but it is shown that it applies in most well-known common agency problems, including, for example, the Bertrand pricing problem.