Theoretical Economics ,Volume 17, Number 3 (July 2022) is now online

Theoretical Economics
Volume 17, Number 3 (July 2022)
Table of contents


Title: Equilibrium in a civilized jungle

Pages: 943-953

Authors: Ariel Rubinstein, Kemal Yildiz

Abstract: The   jungle model with an equal number of agents and objects is enriched by adding a language,   which  is a set of orderings over the set of agents. An assignment of an agent to an object is justified within a group of agents if there is an ordering according to which  that agent is the best-suited in the group. A   civilized equilibrium is an assignment  such that every agent is  the strongest  in the group of agents consisting of himself and those who wish to be assigned to the object and can be justified within this group. We  present (i) conditions under  which the equilibrium in a civilized jungle is identical to the  jungle equilibrium; (ii) a connection between the power relation and the language that is essentially necessary and sufficient for the existence of a Pareto efficient civilized equilibrium; and (iii)  an analogue to the second welfare theorem.

Keywords: Jungle equilibrium, justifiability, civilized equilibrium

JEL classification: D0, C0


Title: Surplus sharing in Cournot oligopoly

Pages: 955-975

Authors: Daniele Condorelli, Balázs Szentes

Abstract: We characterize equilibria of oligopolistic markets where identical firms with constant marginal cost compete a' la Cournot. For given maximal willingness to pay and maximal total demand, we first identify all combinations of equilibrium consumer surplus and industry profit that can arise from arbitrary demand functions. Then, as a further restriction, we fix the average willingness to pay above marginal cost (i.e., first-best surplus) and identify all possible triples of consumer surplus, industry profit and deadweight loss.

Keywords: Cournot, monopoly

JEL classification: D42, D43


Title: Informative tests in signaling environments

Pages: 977-1006

Authors: Boaz Zik, Ran Weksler

Abstract: We study a receiver's learning problem of choosing an informative test in a signaling environment. Each test induces a signaling subgame. Thus, in addition to its direct effect on the receiver's information, a test has an indirect effect through the sender's signaling strategy. We show that the informativeness of signaling in the equilibrium that a test induces depends on the relative informativeness of the test's high and low grades.
Consequently, we find that the receiver's preference relation over tests needs not comply with Blackwell's (1951) order. Our findings may shed light on phenomena such as grade inflation and information coarsening.

Keywords: Signaling games, information design, strategic learning, strategic information transmission

JEL classification: D82, D83, C72


Title: Progressive participation

Pages: 1007-1039

Authors: Dirk Bergemann, Philipp Strack

Abstract: A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived. Each buyer has private information about his arrival time and  valuation where the latter evolves according to a geometric Brownian motion. Any incentive-compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We establish that the optimal stationary allocation policy can be implemented by a simple posted price. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem which determines the first time at which the buyer participates in the mechanism.
The optimal mechanism thus induces progressive participation by each buyer: he either participates immediately or at a future random time.

Keywords: Dynamic mechanism design, observable arrival, unobservable arrival, repeated sales, interim incentive constraints, interim participation constraints, stopping problem, option value, progressive participation

JEL classification: D44, D82, D83


Title: Monotone contracts

Pages: 1041-1073

Authors: Daniel Bird, Alexander Frug

Abstract: We develop a framework for deriving dynamic monotonicity results in long-term stochastic contracting problems with symmetric information. Specifically, we construct a notion of concave separable activity that encompasses many prevalent contractual components (e.g., wage, effort, level of production, etc.).  We then provide a tight condition under which such activities manifest a form of seniority in every contracting problem in which they are present: any change that occurs in the level of the activity over time favors the agent. Our work unifies and significantly generalizes many existing results and can also be used to establish monotonicity results in other settings of interest.

Keywords: Dynamic contracting, activities, seniority

JEL classification: D86


Title: Persuasion with unknown beliefs

Pages: 1075-1107

Authors: Svetlana Kosterina

Abstract: A sender designs an information structure to persuade a receiver to take an action. The sender is ignorant about the receiver's prior, and evaluates each information structure using the receiver's prior that is the worst for the sender. I characterize the optimal information structures in this environment. I show that there exists an optimal signal with two realizations, characterize the support of the signal realization recommending approval and show that the optimal signal is a hyperbola. The lack of knowledge of the receiver's prior causes the sender to hedge her bets: the optimal signal induces the high action in more states than in the standard model, albeit with a lower probability. Increasing the sender's ignorance can hurt both the sender and the receiver.

Keywords: Bayesian persuasion, robust mechanism design

JEL classification: D8


Title: Prior-free dynamic allocation under limited liability

Pages: 1109-1143

Authors: Sylvain Chassang, Samuel Kapon

Abstract: A principal seeks to efficiently allocate a productive public resource to a number of possible users. Vickrey-Clarke-Groves (VCG) mechanisms provide a detail-free way to do so provided users have deep pockets. In practice however, users may have limited resources. We study a dynamic allocation problem in which participants have limited liability:
transfers are made ex post, and only if the productive efforts of participants are successful. We show that it is possible to approximate the performance of the pivot VCG mechanism using limited liability detail-free mechanisms that selectively ignore reports from participants who cannot make their promised payments. A complementary use of cautiousness and forgiveness achieves approximate renegotiation-proofness.  We emphasize the use of prior-free online optimization techniques to approximate aggregate incentive properties of the pivot mechanism.

Keywords: Dynamic allocation, renegotiation-proofness, lending, limited liability, VCG, approachability, online optimization, cautiousness, forgiveness

JEL classification: D82


Title: Participation constraints in discontinuous adverse selection models

Pages: 1145-1181

Authors: David Martimort, Lars A. Stole

Abstract: We present a set of necessary and sufficient conditions for a class of optimal control problems with pure state constraints for which the objective function is linear in the state variable but the objective function is only required to be upper semi-continuous in the control variable.   We apply those conditions to  economic environments in contract theory where discontinuities in objectives prevail.  Examples of applications include nonlinear pricing of   digital goods and nonlinear pricing under competitive threat.

Keywords: Optimal control, non-smooth optimization, convex analysis, type-dependent participation constraints, principal-agent models

JEL classification: D82, D86


Title: Quid pro quo: friendly information exchange between rivals

Pages: 1183-1223

Authors: Andreas Blume, In-Uck Park

Abstract: We show that information exchange via disclosure is possible in equilibrium even when it is certain that whenever one party learns the truth, the other loses. The  incentive to disclose results either from an expectation of disclosure being reciprocated -- the quid pro quo motive -- or from the possibility of learning from the rival's failure to act in response to a disclosure -- the screening motive.  Alternating and gradual disclosures are generally indispensable for information exchange and the number of disclosure rounds grows without bound if the agents' initial information becomes sufficiently diffuse -- in that sense, the less informed agents are the more they talk.  Patient individuals can achieve efficiency by means of continuous alternating disclosures of limited amounts of information. This provides a rationale for protracted dialogues.

Keywords: Alternating information disclosure, dynamic communication, two-sided incomplete information

JEL classification: C72, C73, D82, D83


Title: Value-based distance between information structures

Pages: 1225-1267

Authors: Fabien Gensbittel, Marcin Pęski, Jérôme Renault

Abstract: We define the distance between two information structures as the largest possible difference in value across all zero-sum games. We provide a tractable characterization of distance and use it to discuss the relation between the value of information in games versus single-agent problems, the value of additional information, informational substitutes, complements, or joint information. The convergence to a countable information structure under value-based distance is equivalent to the weak convergence of belief hierarchies, implying, among other things, that for zero-sum games, approximate knowledge is equivalent to common knowledge. At the same time, the space of information structures under the value-based distance is large:
there exists a sequence of information structures where players acquire increasingly more information, and \varepsilon>0 such that any two elements of the sequence have distance of at least \varepsilon. This result answers by the negative the second (and last unsolved) of the three problems posed by J.F. Mertens in his paper “Repeated Games”, ICM 1986.

Keywords: Value of information, universal type space

JEL classification: C7


Title: Mislearning from censored data: The gambler's fallacy and other correlational mistakes in optimal-stopping problems

Pages: 1269-1312

Authors: Kevin He

Abstract: I study endogenous learning dynamics for people who misperceive intertemporal correlations in random sequences. Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are "good enough," so predecessors' experiences contain negative streaks but not positive streaks. When agents wrongly expect systematic reversals (the "gambler's fallacy"), they understate the likelihood of consecutive below-average draws, converge to over-pessimistic beliefs about the distribution's mean, and stop too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. I also analyze how other misperceptions of intertemporal correlation interact with endogenous data censoring.

Keywords: Misspecified learning, gambler’s fallacy, Berk-Nash equilibrium, endogenous data censoring, fictitious variation

JEL classification: D83, D91


Title: Heterogeneity in decentralized asset markets

Pages: 1313-1356

Authors: Benjamin Lester, Pierre-Olivier Weill, Julien Hugonnier

Abstract: We study a canonical model of decentralized exchange for a durable good or asset, where agents are assumed to have time-varying, heterogeneous utility types.  Whereas the existing literature has focused on the special case of two types, we allow agents' utility to be drawn from an arbitrary distribution.  Our main contribution is methodological: we provide a solution technique that delivers a complete characterization of the equilibrium, in closed form, both in and out of the steady state.  This characterization offers a richer framework for confronting data from real-world markets, and reveals a number of new economic insights.  In particular, we show that heterogeneity magnifies the impact of frictions on equilibrium outcomes, and that this impact is more pronounced on price levels than on price dispersion and welfare.

Keywords: Over-the-counter markets, search frictions, bargaining, heterogeneity, price dispersion

JEL classification: G11, G12, G21


Title: Simple contracts with adverse selection and moral hazard

Pages: 1357-1401

Authors: Daniel Gottlieb, Humberto Moreira

Abstract: We study a principal-agent model with moral hazard and adverse selection. Risk-neutral agents with limited liability have arbitrary private information about the distribution of outputs and the cost of effort. We show that under a multiplicative separability condition, the optimal mechanism offers a single contract. This condition holds, for example, when output is binary. If the principal's payoff must also satisfy free disposal and the distribution of outputs has the monotone likelihood ratio property, the mechanism offers a single debt contract. Our results generalize if the output distribution is "close" to multiplicatively separable. Our model suggests that offering a single contract may be optimal in environments with adverse selection and moral hazard when agents are risk neutral and have limited liability.

Keywords: Principal-agent problem, contract theory, mechanism design

JEL classification: D82, D86


Title: Experimentation in Organizations

Pages: 1403-1450

Authors: Sofia Moroni

Abstract: We consider a moral hazard problem in which a principal provides incentives to a team of agents to work on a risky project. The project consists of two milestones of unknown feasibility. While working unsuccessfully, the agents’ private beliefs regarding the feasibility of the project decline. This learning requires the principal to provide rents to prevent the agents from procrastinating and free-riding on others’
discoveries. To reduce these rents the principal stops the project inefficiently early and gives identical agents asymmetric experimentation assignments. The principal prefers to reward agents with better future contract terms or task assignments rather than monetary bonuses.

Keywords: Principal-agent, moral hazard, experimentation, exponential bandit, contests

JEL classification: D82, D83, D86