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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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     

Virtual utility and the core for games with incomplete information

The core is extended to games with incomplete information. The feasible set is characterized by incentive-compatible mechanisms. Blocking is organized at the interim stage by an incentive-compatible mediation plan. Membership of the blocking coalition itself may be determined randomly by the blocking mediator. Nonemptiness of an interim fine core is proven for games with a balanced structure, independent types, and sidepayments. An offer of severance payments may be needed to inhibit blocking. Core allocations are characterized in terms of virtual-utility scales that generalize the weighted-utility scales of the inner core. Mechanisms that achieve core allocations are coalitionally durable.     

Regulating a risk-averse firm under incomplete information

We examine the optimal regulatory policy for a risk-averse firm when the firm is imperfectly informed about its efficiency parameter for a project at the time of contracting. The firm’s risk aversion shifts the optimal regulatory policy from a fixed-price contract to a cost-plus contract. The optimal regulatory policy entails undereffort by an inefficient firm as in Laffont and Tirole (J Polit Econ 94(3):614–641, 1986) and the effort distortion increases as the firm becomes more risk-averse. Further, the regulator benefits from sequential contracting with the firm where the firm chooses contract terms gradually as it acquires information, albeit the benefit diminishes as the firm becomes more risk-averse.      

Alternating-offer bargaining over menus under incomplete information

Summary. This paper considers bargaining with one-sided private information and alternating offers where an agreement specifies both a transfer and an additional (sorting) variable. Moreover, both sides can propose menus. We show that for a subset of parameters the alternating-offer game has a unique equilibrium where efficient contracts are implemented in the first period. This stands in sharp contrast to the benchmarks of contract theory, where typically only the uninformed side proposes, and bargaining theory, where typically the agreement only specifies a transfer. Received: September 10, 2001; revised version: March 25, 2002 RID="*" ID="*" I benefitted from discussions with Benny Moldovanu, Holger Müller, and Roland Strausz, and from comments made by an anonymous referee.     

The evolution of conventions under incomplete information

Summary. We formulate an evolutionary learning process with trembles for static games of incomplete information. For many games, if the amount of trembling is small, play will be in accordance with the games (strict) Bayesian equilibria most of the time. This supports the notion of Bayesian equilibrium. Often the process will select a specific equilibrium. We study an extension to incomplete information of the prototype conflict known as Chicken and find that the equilibrium selection by evolutionary learning may well be in favor of inefficient Bayesian equilibria where some types of players fail to coordinate.Received: 17 March 2003, Revised: 3 December 2003, JEL Classification Numbers: C72.     

Computationally restricted unmediated talk under incomplete information

Summary. We show the role of unmediated talk with computational complexity bounds as both an information transmission and a coordination device for the class of two-player games with incomplete information and rational parameters. We prove that any communication equilibrium payoff of such games can be reached as a Bayesian-Nash equilibrium payoff of the game extended by a two phase universal mechanism of interim computationally restricted pre-play communication. The communication protocols are designed with the help of modern cryptographic tools. A familiar context in which our results could be applied is bilateral trading with incomplete information.Received: 9 September 2002, Revised: 14 March 2003, JEL Classification Numbers: C72. Correspondence to: Amparo UrbanoWe wish to thank financial aid from the Valencian Institute of Economic Research (IVIE) and partial support by DIGCYT under project PB95 - 1074. A previous version of this work appears as IVIE Working Paper WP-AD 99-07, under the title: "Unmediated talk under incomplete information".     

Macroeconomic implications of voucher privatization in a model with incomplete information

Voucher privatization implies a significant wealth transfer from state to private agents who, in turn, would increase consumption. This paper investigates the consequences of this wealth effect on the macroeconomic equilibrium in a high unemployment economy. The model builds on a two-stage sequential game between the government and private agents. We verify the existence of a pooling equilibrium in which private agents cannot guess whether a policy of fast privatization will be continued in the future or not. This configuration presents an endogenous probability of privatization slowdown; as a consequence, the wealth effect is moderated and the genuine fast privatizer government bears an “undue” credibility cost in terms of employment     

Belief-free equilibria in games with incomplete information: Characterization and existence

We generalize the results of Hörner and Lovo (2009) [15] to N-player games with arbitrary information structure. First, we characterize the set of belief-free equilibrium payoffs under low discounting as the set of feasible payoffs that are individually rational, jointly rational, and incentive compatible. Second, we provide necessary and sufficient conditions on the information structure for this set to be non-empty.     

Correlated equilibria, incomplete information and coalitional deviations

This paper proposes new concepts of strong and coalition-proof correlated equilibria where agents form coalitions at the interim stage and share information about their recommendations in a credible way. When players deviate at the interim stage, coalition-proof correlated equilibria may fail to exist for two-player games. However, coalition-proof correlated equilibria always exist in dominance-solvable games and in games with positive externalities and binary actions.