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.     

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.     

The efficiency of competitive mechanisms under private information

We consider the efficiency properties of exchange economies where privately informed traders behave strategically. Specifically, a competitive mechanism is any mapping of traders’ reports about their types to an equilibrium price vector and allocation of the reported economy. In our model, some traders may have non-vanishing impact on prices and allocations regardless of the size of the economy. Although truthful reporting by all traders cannot be achieved, we show that, given any desired level of approximation, there is such that any Bayesian-Nash equilibrium of any competitive mechanism of any private information economy with or more traders leads, with high probability, to prices and allocations that are close to a competitive equilibrium of the true economy. In particular, allocations are approximately efficient. A key assumption is that there is small probability that traders behave non-strategically.     

Trading with a common agent under complete information: A characterization of Nash equilibria

We analyze an abstract model of trading where N principals submit quantity-payment schedules that describe the contracts they offer to an agent, and the agent then chooses how much to trade with every principal. This represents a special class of common agency games with complete information. We study all the subgame perfect Nash equilibria of these games, not only truthful ones, providing a complete characterization of equilibrium payoffs. In particular, we show that the equilibrium that is Pareto-dominant for the principals is not truthful when there are more than two of them. We also provide a partial characterization of equilibrium strategies.     

Should a team be homogeneous?

Should an organization hire people with similar backgrounds or with different backgrounds? We formulate this question within the framework of team theory. The team is formed by n agents. The type of each agent is endogenous and determines his information structure and his cost for the team. We show that the sign of complementarity between jobs determines workforce homogeneity. With positive complementarities, the team should be composed of agents of the same type, while, with negative complementarities, workforce heterogeneity is optimal. These results do not rely on the restrictions on the way uncertainty is modeled or on the feasible set of agent types: they can be explained in terms of correlation between errors committed by different agents.     

“Timing Is Everything” and Marital Bliss

We first show that in a marriage market, when the stability of a matching is disturbed when a new agent joins the game, natural greedy behavior defines an equilibration procedure that converges to a stable matching for the extended problem. We then consider the iterative procedure under which agents join the game sequentially, and the natural greedy procedure is applied after the entrance of each agent. It is shown that this procedure converges to a stable matching for the original (global) problem and that for each agent, if the order of all other agents is given, he/she weakly improves his/her final outcome by deferring his/her arrival time. The agent that arrives last gets his/her optimal outcome under stable matchings. Journal of Economic Literature Classification Numbers: C78, C62.     

Proper belief revision and equilibrium in dynamic games

We present a theory of rationality in dynamic games in which players, during the course of the game, may revise their beliefs about the opponents’ utility functions. The theory is based upon the following three principles: (1) the players’ initial beliefs about the opponents’ utilities should agree on some profile u of utility functions, (2) every player should believe, at each of his information sets, that his opponents are carrying out optimal strategies and (3) a player at information set h should not change his belief about an opponent's ranking of strategies a and b if both a and b could have led to h. Scenarios with these properties are called preference conjecture equilibria for the profile u of utility functions. We show that every normal form proper equilibrium for u induces a preference conjecture equilibrium for u, thus implying existence of preference conjecture equilibrium.     

Garbling of signals and outcome equivalence

In a game with incomplete information players receive stochastic signals about the state of nature. The distribution of the signals given the state of nature is determined by the information structure. Different information structures may induce different equilibria.Two information structures are equivalent from the perspective of a modeler, if they induce the same equilibrium outcomes. We characterize the situations in which two information structures are equivalent in terms of natural transformations, called garblings, from one structure to another. We study the notion of ‘being equivalent to’ in relation with three equilibrium concepts: Nash equilibrium, agent normal-form correlated equilibrium and the belief invariant Bayesian solution.     

Competition and confidentiality: Signaling quality in a duopoly when there is universal private information

We model non-cooperative signaling by two firms that compete over a continuum of consumers, assuming each consumer has private information about the intensity of her preferences for the firms' respective products and each firm has private information about its own product's quality. We characterize a symmetric separating equilibrium in which each firm's price reveals its respective product quality. We show that the equilibrium prices, the difference between those prices, the associated outputs, and profits are all increasing functions of the ex ante probability of high safety. If horizontal product differentiation is sufficiently great then equilibrium prices and profits are higher under incomplete information about quality than if quality were commonly known. Thus, while signaling imposes a distortionary loss on a monopolist using price to signal quality, duopolists may benefit from the distortion as it can reduce competition. Finally, average quality is lower since signaling quality redistributes demand towards low-quality firms.     

EMERGENCE OF LEADERSHIP IN TEAMS*

This paper provides a simple model to explain the emergence of leadership in an unstructured team. Each agent has partial information about the productivity of the team. Each agent may invest a productive effort in one of two periods. If one agent voluntarily moves first and the other waits for the second period, and if the first‐move action successfully transmits his type, the first mover effectively exercises leadership in affecting the effort choice of the second mover. We prove that, if each agent holds stochastically independent information, leadership emerges with positive probabilities in Cho–Kreps stable outcomes.     

Partisan politics and election failure with ignorant voters

We analyze candidate competition when some voters do not observe a candidate's policy choice. Voters have a personality preference when both candidates offer the same policy. In equilibrium, the candidate with a personality advantage may get elected with a partisan policy even though his opponent's policy is preferred by all voters. The departure from the Downsian prediction is most pronounced when candidates have a weak policy preference and care mostly about winning the election. In that case, uninformed voters choose the candidate with the preferred personality even if electing this candidate implies a lower payoff on average.     

Insider trading with public and shared information

We study the impact of public information and shared information on traders' trading behavior in the context of Kyle's (1985) speculative market. We suppose that there are four types of traders in our model: one insider, M outsiders, liquidity traders, and market makers. We explicitly describe the unique linear Nash equilibrium and find that public information harms the insider but benefits the outsiders and noise traders. Also, the market is more efficient because of the existence of public information.     

The role of independence in the Green-Lin Diamond-Dybvig model

Green and Lin study a version of the Diamond-Dybvig model with a finite number of agents, independence (independent determination of each agent's type), and sequential service. For special preferences, they show that the ex ante first-best allocation is the unique equilibrium outcome of the model with private information about types. Via a simple argument, it is shown that uniqueness of the truth-telling equilibrium holds for general preferences—and, in particular, for a constrained-efficient allocation whether first-best or not. The crucial assumption is independence.     

Informed principal with correlation

In this paper we analyze an adverse selection model with one principal and one agent, who are both risk neutral and have private information. We assume that the private information of the principal is correlated with that of the agent. The main result of the paper is that the principal can extract a larger share of the surplus from the agent than in the case where her information is public. The principal can design such a contract because she exploits the fact that her type is an informative signal on the agent's one. We fully characterize the equilibrium of the game in which different types of principal offer the same menu of contracts that leaves the agent uninformed about the principal's type. This gives more freedom to the principal when setting the transfers because the agent's constraints need to hold only at an interim stage.     

PRODUCTS LIABILITY WHEN CONSUMERS VARY IN THEIR SUSCEPTIBILITY TO HARM AND MAY MISPERCEIVE RISK

This article examines products liability when consumers have private information about their susceptibilities to product‐related harm. In this case, it is efficient for consumers to self‐select their purchases, with those especially prone to harm refraining from purchase. Achieving this outcome requires consumers to bear their own harm, given that producers cannot observe consumer types. When consumers also misperceive risk, the problem becomes more complicated because accurate signaling of risk requires that firms bear liability. A trade‐off therefore emerges between imposing liability on firms versus consumers. This article characterizes the choice among liability rules in the presence of this trade‐off. (JEL K13, L15)     

Rates of information aggregation in common value auctions

We study the rates at which transaction prices aggregate information in common value auctions under the different information structures in Wilson (Rev. Econ. Stud. 44 (1977) 511) and Pesendorfer and Swinkels (Econometrica 65 (1997) 1247). We consider uniform-price auctions in which k identical objects of unknown value are auctioned to n bidders, where both n and k are allowed to diverge to infinity, and k/n converges to a number in [0,1). The Wilson assumptions lead to information aggregation at a rate proportional to , but the price aggregates information at a rate proportional to in the PS setting. We also consider English auctions, and investigate whether the extra information revealed in equilibrium improves convergence rates in these auctions.     

Will Self‐Managed Superannuation Fund Investors Survive?

The relative risk aversion coefficient that characterises the representative self‐managed superannuation fund (SMSF) investor reveals not only how much that investor dislikes risk but also other information about the investor's economic characteristics, including how his or her allocations to risky assets change as his or her wealth changes. Determination of the relative risk aversion coefficient for the average SMSF investor reveals a value of 5.05. This value is too high to be consistent with logarithmic utility. This is significant because it implies that SMSF investors may be too risk averse to maximise the expected growth rate of wealth share accumulation. We are left to consider a very important question: Will SMSF investors survive?     

Sequential location equilibria under incomplete information

Summary We consider a simple model of incomplete information in location theory. Two firms compete in a two stage framework: a sequential location stage and a price competition stage. Firm 1 knows both its own constant marginal cost technology and that of Firm 2, whereas the latter has incomplete information about firm 1's technology. The location stage turns out to be a monotonic signaling game and theunique D1 equilibrium is a pure strategy separating equilibrium if firm 1's cost advantage is below some bound, and otherwise a pooling equilibrium if the prior probability that Firm 1 is of the low cost type is high, or a semi-pooling equilibrium if it is low. This surprising result is due to the fact that the location gap between the two types of Firm 1 is bounded because of natural economic reasons, which may prevent the separation of the two types. Hence, incomplete information matters: the equilibrium locations differ quite significantly from the full information equilibrium locations.We would like to thank an anonymous referee for very helpful comments and also the participants in seminars at GREQE (Marseille), Université de Montréal, UBC, HEC (Paris), in the Location Theory session of the World Congress of the Econometric Society (Barcelona) and in the Game Theory Conference at the University of Western Ontario for their comments. We remain, of course, solely responsible for the content of the paper. Financial support from FCAR (Québec), SSHRCC (Canada) and CNRS (France) is gratefully acknowledged.     

Pivots versus signals in elections

We consider a two-period model of elections in which voters have private information about their policy preferences. A first-period vote can have two types of consequences: it may be pivotal in the first election and it provides a signal that affects candidates' positions in the second election. Pivot events are exceedingly unlikely, but when they occur the effect of a single vote is enormous. In contrast, vote totals always have some signaling effect, but the effect of a single vote is small. We investigate which effect - pivot or signaling - drives equilibrium voting behavior in large electorates.     

Increasing Dominance with No Efficiency Effect

I uncover a new force towards increasing dominance (the property whereby, in dynamic games, the leader tends to increase his or her lead in expected terms). The new effect results from the strategic choice of covariance in races. I assume that players must choose not the amount of resources to spend but how to allocate those resources. I show that, in equilibrium, the laggard chooses a less promising path, in effect trading off lower expected value for lower correlation with respect to the leader. This results in increasing dominance and holds true even if no joint-payoff (or efficiency) effect is present. Journal of Economic Literature Classification Numbers: C7, L1.