Coarse matching with incomplete information

We study two-sided markets with heterogeneous, privately informed agents who gain from being matched with better partners from the other side. Our main results quantify the relative attractiveness of a coarse matching scheme consisting of two classes of agents on each side, in terms of matching surplus (output), an intermediary’s revenue, and the agents’ welfare (defined as the total surplus minus payments to the intermediary). Following Chao and Wilson (Am Econ Rev 77: 899–916, 1987) and McAfee (Econometrica 70:2025–2034, 2002), our philosophy is that, if the worst-case scenario under coarse matching is not too bad relative to what is achievable by more complex, finer schemes, a coarse matching scheme will turn out to be preferable once the various transaction costs associated with fine schemes are taken into account. Similarly, coarse matching schemes can be significantly better than random matching, while still requiring only a minimal amount of information.     

Budget-constrained sequential auctions with incomplete information

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder's type. Multiple equilibrium symmetric bidding functions may exist that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α are higher when good α is sold first.     

Exit with incomplete information about cost

This paper presents a model of output decisions by competitive firms which have incomplete information about costs. Unlike other work on this topic, our model incorporates the possibility of exit from the market after a firm has observed its unit cost. At the equilibrium expected aggregate output and the likelihood of exit depend upon the opportunity cost of staying in the market, the number of informed firms, and the intensity of competition. Uninformed firms may be better off than informed firms if exit is feasible. As a result, even if all firms face the same cost of acquiring information, informed firms may coexist with uninformed firms.     

Endogenous Stackelberg equilibria with incomplete information

In this paper, the endogenous order of quantity decision is studied in a duopoly model with incomplete information. One firm knows the state of the demand curve while the other firm remains uninformed. Firms have to commit to a quantity in one out of two periods. While, a priori, simultaneous-move Cournot equilibria are possible, only Stackelberg equilibria, with either the informed or the uninformed firm moving first, emerge endogenously.     

Cheap talk in games with incomplete information

The paper studies Bayesian games which are extended by adding pre-play communication. Let Γ be a Bayesian game with full support and with three or more players. The main result is that if players can send private messages to each other and make public announcements then every communication equilibrium outcome, q, that is rational (i.e., involves probabilities that are rational numbers) can be implemented in a sequential equilibrium of a cheap talk extension of Γ, provided that the following condition is satisfied: There exists a Bayesian Nash equilibrium s in Γ such that for each type t_i of each player i the expected payoff of t_i in q is larger than the expected payoff of t_i in s.     

A Blotto game with multi-dimensional incomplete information

We examine a multi-dimensional incomplete information Colonel Blotto game in which each player’s n-tuple of battlefield valuations is drawn from a common n-variate joint distribution function that is uniform on the non-negative orthant of the surface of a sphere.     

Incentives and incomplete information

The problem of incentives for correct revelation in a collective decision model is presented as a game with incomplete information. Two approaches to incomplete information are used, a first where the individual beliefs are not introduced and a second where they are. In the first approach it is recalled that the mechanisms for which the solution to the incentive problem is in dominant strategies lead in general to a budgetary problem for the central agency. For these mechanisms a uniqueness property is demonstrated. In the second approach it is shown that if a compatibility condition is imposed on the individual beliefs and if a Bayesian solution is given to the incentive problem, then it is possible to avoid the budgetary problem.     

Exit options in incomplete contracts with asymmetric information

This paper analyzes bilateral contracting in an environment with contractual incompleteness and asymmetric information. One party (the seller) makes an unverifiable quality choice and the other party (the buyer) has private information about its valuation. A simple deterministic exit option contract, which allows the buyer to refuse trade, achieves the first-best in the benchmark cases where either quality is verifiable or the buyer?s valuation is public information. But, when unverifiable and asymmetric information are combined, deterministic contracts are necessarily inefficient. The first-best can be achieved, however, through simple message games with stochastic terms of trade as off-equilibrium outcomes.     

A model of insurance markets with incomplete information

The paper investigates how a competitive market would allocate insurance policies if firms were not able to determine the riskiness of individual consumers. It is demonstrated that if all firms have static expectations with regard to the policy offers of other firms, no stationary equilibrium may exist. A second equilibrium concept is then introduced which incorporates a different expectation rule. Each firm assumes that any policy will be immediately withdrawn which becomes unprofitable after that firm makes its own policy offer. This equilibrium is shown to exist and some of its welfare properties are investigated.     

A model of electoral competition with incomplete information

A model of two-candidate electoral competition is developed in which voters are uncertain about the policy either candidate would implement if elected. Candidates simultaneously announce policy positions, from which voters attempt to infer the true positions the candidates would adopt. Announcing a position different from the true position is costly to the winning candidate, with these costs increasing as the difference between the true policy and the announced policy increases. A refinement of the sequential equilibrium concept is used to describe the behavior of candidates and voters.     

Estimation of hedonic price functions with incomplete information

Existence of persistent price dispersion suggests that some buyers find lower prices through search and information acquisition, while some sellers charge higher prices by gathering information on potential buyers. If buyers are not fully informed of the lowest price available in the market they end up paying a price higher than if they had full information. Similarly, if sellers are not fully informed about the highest price they could charge, they too suffer by receiving a price lower than had they had full information. This paper develops a hedonic price model that incorporates the effects of incomplete information on both sides of the market and obtains estimates of the discrepancies between market prices and buyers’ maximum willingness to pay and sellers’ minimum willingness to accept. Correlates of such price discrepancies are also explored. We apply the technique to a data set constructed from the American Housing Survey, and find that incomplete information has had a significant impact on housing prices.     

Revisiting games of incomplete information with analogy-based expectations

This paper studies the effects of analogy-based expectations in static two-player games of incomplete information. Players are assumed to be boundedly rational in the way they forecast their opponent's state-contingent strategy: they bundle states into analogy classes and play best-responses to their opponent's average strategy in those analogy classes. We provide general properties of analogy-based expectation equilibria and apply the model to a variety of well known games. We characterize conditions on the analogy partitions for successful coordination in coordination games under incomplete information [Rubinstein, A., 1989. The electronic mail game: Strategic behavior under ‘almost common knowledge’. Amer. Econ. Rev. 79, 385–391], we show how analogy grouping of the receiver may facilitate information transmission in Crawford and Sobel's cheap talk games [Crawford, V.P., Sobel, J., 1982. Strategic information transmission. Econometrica 50, 1431–1451], and we show how analogy grouping may give rise to betting in zero-sum betting games such as those studied to illustrate the no trade theorem.     

A note on repeated-offers bargaining with one-sided incomplete information

Summary This note analyzes a modified version of the standard repeated-offers bargaining game with one-sided incomplete information studied in Fudenberg, Levine and Tirole (1985), Gul, Sonnenschein and Wilson (1986) and Ausubel and Deneckere (1989). The modification, which is introduced in the extensive form, is that the (uninformed) seller can choose to withdraw her offer immediately after the (informed) buyer accepts it. This modification is important because it removes the (implicit) commitment assumption built into the standard model that the seller is committed not to withdraw her price offer. A main result obtained is, that whether or not there is a gap between the seller's valuation and the lowest possible buyer's valuation, any seller payoff between zero and the static monopoly profit can be supported by sequential equilibria. Thus, even in the gap case there exist equilibria that completely reverse the Coase conjecture.I thank Ian Jewitt and an anonymous referee for their helpful advice and comments.     

Unmediated communication in games with complete and incomplete information

We study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S^U(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then S^U(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e., all profiles of types have positive probability), then S^U(G) is equal to the set of communication equilibria of G.     

A learning-based model of repeated games with incomplete information

This paper tests a learning-based model of strategic teaching in repeated games with incomplete information. The repeated game has a long-run player whose type is unknown to a group of short-run players. The proposed model assumes a fraction of ‘short-run’ players follow a one-parameter learning model (self-tuning EWA). In addition, some ‘long-run’ players are myopic while others are sophisticated and rationally anticipate how short-run players adjust their actions over time and “teach” the short-run players to maximize their long-run payoffs. All players optimize noisily. The proposed model nests an agent-based quantal-response equilibrium (AQRE) and the standard equilibrium models as special cases. Using data from 28 experimental sessions of trust and entry repeated games, including 8 previously unpublished sessions, the model fits substantially better than chance and much better than standard equilibrium models. Estimates show that most of the long-run players are sophisticated, and short-run players become more sophisticated with experience.     

Representation of constitutions under incomplete information

We model constitutions by effectivity functions. We assume that the constitution is common knowledge among the members of the society. However, the preferences of the citizens are private information. We investigate whether there exist decision schemes (i.e., functions that map profiles of (dichotomous) preferences on the set of outcomes to lotteries on the set of social states), with the following properties: (i) The distribution of power induced by the decision scheme is identical to the effectivity function under consideration; and (ii) the (incomplete information) game associated with the decision scheme has a Bayesian Nash equilibrium in pure strategies. If the effectivity function is monotonic and superadditive, then we find a class of decision schemes with the foregoing properties.     

Reporting bias in incomplete information model

Company financial reports are likely to be systematically biased. In this paper, we extend the Duffie and Lando (2001) model with a skewness correction which can account for both random and directional components of reporting noise.     

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.     

Signaling via an agenda in multi-issue bargaining with incomplete information

Summary. While actual bargaining features many issues and decision making on the order in which issues are negotiated and resolved, the typical models of bargaining do not. Instead, they have either a single issue or many issues resolved in some fixed order, typically simultaneously. This paper shows that, when there is incomplete information, such an approach removes an important avenue for information transmission: the bargaining agenda itself. Compared to the standard model, pooling on offers by the informed is reduced and a signaling equilibrium arises when the agenda is determined endogenously. Signaling is carried out by use of an issue-by-issue bargaining agenda. Received: September 3, 1997; revised version: May 11, 1998