Matching with noise and the acceptance curse

This paper explores matching with both search and information frictions. Specifically, everyone observes only a noisy signal of the true type of any potential mate. In this context, matching decisions must incorporate not only information about a partner's attribute conveyed by the noisy signal, but also—as in the winner's curse in auction theory—information about a partner's type contained in his or her acceptance decision.We show that there exists an equilibrium exhibiting a stochastic positive assorting of types, generalizing [Becker, J. Polit. Economy 81 (1973) 813-846]. In equilibrium, selection is adverse: being accepted reduces an agent's estimate of a potential partner's type, a phenomenon that we call the acceptance curse effect.     

Intertemporal pricing in markets with differential information

Summary This paper provides a theory of intertemporal pricing in a small market with differential information about the realizations of a stochastic process which determines demand. We study the sequential equilibria in stationary strategies of the stochastic game between a seller and buyer. The seller has zero cost of producing one unit of a non-durable good in all market periods. The buyer's value for the good is a random variable governed by a simple Markov process. At the beginning of each period the unit's value is determined by nature and is privately revealed to the buyer. The seller posts a single price offer each period, which the buyer either accepts or rejects. Only two types of price paths emerge in equilibrium: either prices are constant, or they have persistent cycles between a low and a high value. In both cases, however, prices are sticky in the sense that changes in price are less frequent than changes in the economy's fundamentals.We thank John Rust and Asher Wolinsky for helpful comments. We also gratefully acknowledge financial support from NSF grant SES 89-09242.     

Contractual distortions in a market with frictions

This paper analyses contract design in a decentralized market environment with frictions. While principals (e.g., firms) have all contractual power, their market power is constrained as agents (e.g., workers) can choose to wait and search for better offers. We find that results depend crucially on how market frictions affect agents’ utilities. With type-independent costs of search and waiting, equilibrium contracts are always first-best. If agents are impatient and discount future payoffs, however, distortions vanish only gradually. In the latter case, we also characterize equilibrium offers and show that the market exhibits two types of externalities, both of which are absent in the case of type-independent costs of search.     

The tradeoff between risk sharing and information production in financial markets

The production of information in financial markets is limited by the extent of risk sharing. The wider a stock's investor base, the smaller the risk borne by each shareholder and the less valuable information. A firm which expands its investor base without raising capital affects its information environment through three channels: (i) it induces incumbent shareholders to reduce their research effort as a result of improved risk sharing, (ii) it attracts potentially informed investors, and (iii) it may modify the composition of the base in terms of risk tolerance or liquidity trading. Implications for individual firms and the market as a whole are derived.     

The relative contributions of private information sharing and public information releases to information aggregation

We calculate learning rates when agents are informed through public and private observation of other agents' actions. We characterize the evolution of the distribution of posterior beliefs. If the private learning channel is present, convergence of the distribution of beliefs to the perfect-information limit is exponential at a rate equal to the sum of the mean arrival rate of public information and the mean rate at which individual agents are randomly matched with other agents. If, however, there is no private information sharing, then convergence is exponential at a rate strictly lower than the mean arrival rate of public information.     

From posteriors to priors via cycles

We present new necessary and sufficient conditions for checking if a set of players' posteriors may come from a common prior. A simple diagrammatic device calculates the join and meet of players' knowledge partitions. Each cycle in the diagram has a corresponding cycle equation. Posteriors are consistent with a common prior if and only if all cycle equations are satisfied. We prove that in games of two players, where the join partition has only singletons, a common prior exists if each player's distribution of beliefs over the elements of her opponent's partition is independent of her own private information.     

A Walrasian Rubinstein and Wolinsky model

We provide a full dynamic analysis of a continuous-time variant of Rubinstein and Wolinsky (1985) matching and bargaining model with unbalanced flows of buyers and sellers. The focus is on the price limit as the frictions of search are removed. It is found that a necessary and sufficient condition for the limit price to be Walrasian at all times is the alignment of the initial buyer and seller stocks with the flows.     

THIRD PARTIES, INFORMATION DISCLOSURE AND MONITORING INCENTIVES

Within an incomplete contract setting, the paper analyses the role of third parties in ameliorating incentive problems arising in the context of financial contracts with costly verification and lender's bargaining power. Contrary to the findings of the bilateral lender–borrower relationship, characterised by no information revelation and possibly a breakdown of the market, it is shown that, in the presence of third parties, an optimal contract exists featuring partial information revelation and random monitoring. The importance of third parties is therefore not limited to improving efficiency, as it is when the contract offer comes from the informed party, but to ensure project realisation, and thus to ensure that the surplus that can arise from the project does not get lost.     

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.     

Perturbed communication games with honest senders and naive receivers

This paper studies communication games in which the sender is possibly honest (tells the truth) and the receiver is possibly naive (follows messages as if truthful). The characterization of message-monotone equilibria in the perturbed games explain several important aspects of strategic communication including sender exaggeration, receiver skepticism and message clustering. Surprisingly, the strategic receiver may respond to more aggressive claims with more moderate actions. In the limit as the probabilities of the non-strategic players approach zero, (i) the limit equilibrium corresponds to a most-informative equilibrium of the limit (Crawford-Sobel) game; (ii) only the top messages are sent.     

Delay and information aggregation in stopping games with private information

We consider equilibrium timing decisions in a model with a large number of players and informational externalities. The players have private information about a common payoff parameter that determines the optimal time to invest. They learn from each other in real time by observing past investment decisions. We develop new methods of analysis for such large games, and we give a full characterization of symmetric equilibria. We show that the equilibrium statistical inferences are based on an exponential learning model. Although the beliefs converge to truth, learning takes place too late. Ex-ante welfare is strictly between that without observational learning and that with full information.     

A model of collateral, investment, and adverse selection

This paper characterizes the relationship between entrepreneurial wealth and aggregate investment under adverse selection. Its main finding is that such a relationship need not be monotonic. In particular, three results emerge from the analysis: (i) pooling equilibria, in which investment is independent of entrepreneurial wealth, are more likely to arise when entrepreneurial wealth is relatively low; (ii) separating equilibria, in which investment is increasing in entrepreneurial wealth, are most likely to arise when entrepreneurial wealth is relatively high and; (iii) for a given interest rate, an increase in entrepreneurial wealth may generate a discontinuous fall in investment.     

Competition among auctioneers in large markets

We analyse a multistage game of competition among auctioneers. First, the auctioneers commit to some reserve prices; second, the bidders enter one auction, if any; and finally, the auctions take place. We show that for any finite set of feasible reserve prices, each auctioneer announces a reserve price equal to his production cost if the numbers of auctioneers and bidders are sufficiently large, though finite. Our result supports the idea that optimal auctions may be quite simple. Our model also confirms previous results for some “limit” versions of the model by McAfee (Econometrica 61 (1993) 1281-1312), Peters (Rev. Econ. Stud. 64 (1997) 97-123), and Peters and Severinov (J. Econ. Theory 75 (1997) 141-179).     

Signaling in markets with two-sided adverse selection

Summary. The paper analyzes an economy with two-sided adverse selection, focusing on equilibria that satisfy a refinement based on the notion of strategic stability. In the familiar case of one-sided adverse selection, agents reveal all of their private information as long as the contract space is rich enough. However, with two-sided adverse selection, the sufficient conditions for separation are much stronger. Received: September 3, 1999; revised version: December 3, 1999     

The communication requirements of social choice rules and supporting budget sets

The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any minimally informative way to verify that a given alternative is in the choice rule is by verifying a “budget equilibrium”, i.e., that the alternative is optimal to each agent within a “budget set” given to him. Therefore, any communication mechanism realizing the choice rule must find a supporting budget equilibrium. We characterize the class of choice rules that have this property. Furthermore, for any rule from the class, we characterize the minimally informative messages (budget equilibria) verifying it. This characterization is used to identify the amount of communication needed to realize a choice rule, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisible-good economies, and stable many-to-one matchings.     

Strategic argumentation

I analyze a game between an uninformed decision maker and a possibly biased expert. The expert receives a set of arguments, and each argument favors one of two alternatives. He can disclose each argument credibly, but cannot prove whether he has disclosed everything. In all equilibria, the biased expert sends messages containing arguments both for and against his preferred alternative. However, the decision maker is not influenced by the unfavorable arguments revealed by the biased expert. The latter is able to convince the decision maker to choose the biased expert?s preferred alternative only if he reveals sufficiently many favorable arguments.     

Optimal search auctions

We study the design of profit maximizing single unit auctions under the assumption that the seller needs to incur costs to contact prospective bidders and inform them about the auction. With independent bidders’ types and possibly interdependent valuations, the seller's problem can be reduced to a search problem in which the surplus is measured in terms of virtual utilities minus search costs. Compared to the socially efficient mechanism, the optimal mechanism features fewer participants, longer search conditional on the same set of participants, and inefficient sequence of entry.     

Income distribution, efficiency and rationing

This paper studies the impacts of income distribution on the efficiency of trade mechanism and rationing of agents who are priced out of trade in a dynamic search model with two-sided asymmetric information. Buyers and sellers have asymmetric information about valuations and incomes respectively. In such a frictional environment, the effects of several variants of changes in income distribution on efficiency of trading mechanism and the population of rationed buyers and sellers are elaborated.     

Coordination failure in repeated games with private monitoring

Players coordinate continuation play in repeated games with public monitoring. We investigate the robustness of such equilibrium behavior with respect to ex-ante small private-monitoring perturbations. We show that with full support of public signals, no perfect public equilibrium is robust if it induces a “regular” 2×2$2\times 2$ coordination game in the continuation play. This regularity condition is violated in all belief-free equilibria. Indeed, with an individual full rank condition, every interior belief-free equilibrium is robust. We also analyze block belief-free equilibria and point out that the notion of robustness is sensitive to whether we allow for uninterpretable signals.