Gershkov A, Perry M (2009) Tournaments with midterm reviews, Games and Economic Behavior 66 (1) pp. 162-190
In many tournaments investments are made over time. The question whether to conduct a review once at the end, or additionally at points midway through the tournament, is a strategic decision. If the latter course is chosen, then the designer must establish both a rule for aggregating the results of the different reviews and a rule for determining compensations. We first study the case of a fixed, exogenously given prize and then extend the analysis to the case where the prize is not fixed but may vary with the tournament's outcome. It is shown that (1) it is always optimal to assign a higher weight to the final review; (2) this weight increases with the dominance of the first-stage effort in determining the final review's outcome. When the prize is not fixed, the optimal design generates an asymmetric tournament in the second stage that favors the winner of the midterm review.
Gershkov A (2009) Optimal auctions and information disclosure, Review of Economic Design 13 (4) pp. 335-344
We characterise properties of optimal auctions if the seller may disclose information about the quality of the object for sale. We show that the seller maximizes his expected revenue by revelation of all information to all bidders and implementing a second price auction with appropriate reservation price. © Springer-Verlag 2009.
We study dominant strategy incentive compatible (DIC) and deterministic mechanisms in a social choice setting with several alternatives. The agents are privately informed about their preferences, and have single-crossing utility functions. Monetary transfers are not feasible. We use an equivalence between deterministic, DIC mechanisms and generalized median voter schemes to construct the constrained-efficient, optimal mechanism for an utilitarian planner. Optimal schemes for other welfare criteria such as, say, a Rawlsian maximin can be analogously obtained.
Gershkov A, Moldovanu B (2010) Efficient sequential assignment with incomplete information, Games and Economic Behavior 68 (1) pp. 144-154
We study the welfare maximizing assignment of several heterogeneous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially according to a Poisson or renewal process. There is a deadline after which no more objects can be allocated. We first show that the dynamically efficient allocation, characterized by Albright [Albright, S.C., 1974. Optimal sequential assignments with random arrival times. Manage. Sci. 21 (1), 60-67], is implementable by the dynamic version of VCG mechanism. We then obtain several properties of the welfare maximizing policy using stochastic dominance measures of increased variability and majorization arguments. We also propose redistribution mechanisms that 1) implement the efficient allocation, 2) satisfy individual rationality, 3) never run a budget deficit, 4) may run a budget surplus that vanishes asymptotically. © 2009 Elsevier Inc. All rights reserved.
Gershkov A, Schweinzer P (2010) When queueing is better than push and shove, International Journal of Game Theory 39 (3) pp. 409-430
We address the scheduling problem of reordering an existing queue into its efficient order through trade. To that end, we consider individually rational and balanced budget direct and indirect mechanisms. We show that this class of mechanisms allows us to form efficient queues provided that existing property rights for the service are small enough to enable trade between the agents. In particular, we show on the one hand that no queue under a fully deterministic service schedule such as first-come, first-serve can be dissolved efficiently and meet our requirements. If, on the other hand, the alternative is full service anarchy then every existing queue can be transformed into its efficient order. © Springer-Verlag 2009.
Gershkov A, Moldovanu B (2013) Non-Bayesian optimal search and dynamic implementation, Economics Letters 118 (1) pp. 121-125
We show that a non-Bayesian learning procedure leads to very permissive implementation results concerning the efficient allocation of resources in a dynamic environment where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents' values. This contrasts the rather restrictive results that have been obtained for Bayesian learning in the same environment, and highlights the role of the learning procedure in dynamic mechanism design problems. © 2012 Elsevier B.V.
A designer allocates several indivisible objects to a stream of randomly arriving agents. The long-lived agents are privately informed about their value for an object, and about their arrival time to the market. The designer learns about future arrivals from past arrivals, while agents strategically choose when to make themselves available for trade. We characterize revenue maximizing direct mechanism and offer a simple indirect mechanism that captures a substantial part of the revenues of the revenue maximizing mechanism.
Gershkov A, Toxvaerd F (2013) On Seller Estimates and Buyer Returns, Economic Theory Bulletin
This paper revisits recent empirical research on buyer credulity in arts auctions and auctions for assets in general. We show that elementary results in auction theory can fully account for some stylized facts on asset returns that have been held to suggest that sellers of assets can exploit buyers by providing biased estimates of asset values. We argue that, rather than showing that buyers are credulous, the existing evidence can serve as an indirect test of the rationality assumptions underlying auction theory.
Gershkov A, Perry M (2012) Dynamic contracts with moral hazard and adverse selection, Review of Economic Studies 79 (1) pp. 268-306
We study a novel dynamic principal-agent setting with moral hazard and adverse selection (persistent as well as repeated). In the model, an agent whose skills are his private information faces a finite sequence of tasks, one after the other. Upon arrival of each task, the agent learns its level of difficulty and then chooses whether to accept or refuse each task in turn and how much effort to exert. Although his decision to accept or refuse a task is publicly known, the agent's effort level is his private information. We characterize optimal contracts and show that the per-period utility of the agent approaches his per-period utility when his skills are publicly known, as the discount factor and the time horizon increase. © The Author 2011. Published by Oxford University Press on behalf of The Review of Economic Studies Limited.
Gershkov A, Szentes B (2009) Optimal voting schemes with costly information acquisition, Journal of Economic Theory 144 (1) pp. 36-68
A group of individuals with identical preferences must make a decision under uncertainty about which decision is best. Before the decision is made, each agent can privately acquire a costly and imperfect signal. We discuss how to design a mechanism for eliciting and aggregating the collected information so as to maximize ex-ante social welfare. We first show that, of all mechanisms, a sequential one is optimal and works as follows. At random, one agent at a time is selected to acquire information and report the resulting signal. Agents are informed of neither their position in the sequence nor of other reports. Acquiring information when called upon and reporting truthfully is an equilibrium. We next characterize the ex-ante optimal scheme among all ex-post efficient mechanisms. In this mechanism, a decision is made when the precision of the posterior exceeds a cut-off that decreases with each additional report. The restriction to ex-post efficiency is shown to be without loss when the available signals are sufficiently imprecise. On the other hand, ex-post efficient mechanisms are shown to be suboptimal when the cost of information acquisition is sufficiently small. © 2008 Elsevier Inc. All rights reserved.
Gershkov A, Li J, Schweinzer P (2009) Efficient tournaments within teams, RAND Journal of Economics 40 (1) pp. 103-119
We analyze incentive problems in team and partnership structures where the only available information to condition a contract on is a partial and noisy ranking which specifies who comes first in efforts among the competing partners. This enables us to ensure both first-best efficient effort levels for all partners and the redistribution of output only among partners. Our efficiency result is obtained for a wide range of cost and production functions. Copyright © 2009, RAND.
Gershkov A, Eyal Winter (2015) Formal vs. Informal Monitoring in Teams, American Economic Journal: Microeconomics
Gershkov A, Goeree J, Kushnir A, Moldovanu B, Shi X (2013) On the Equivalence of Bayesian and Dominant Strategy Implementation, Econometrica: journal of the Econometric Society 81 (1) pp. 197-220 Econometric Society
Gershkov A, Moldovanu B (2012) Optimal search, learning and implementation, Journal of Economic Theory 147 (3) pp. 881-909
We characterize the incentive compatible, constrained efficient policy ("second-best") in a dynamic matching environment, where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents' values. We also derive conditions on the learning process ensuring that the complete-information, dynamically efficient allocation of resources ("first-best") is incentive compatible. Our analysis reveals and exploits close, formal relations between the problem of ensuring implementable allocation rules in our dynamic allocation problems with incomplete information and learning, and between the classical problem, posed by Rothschild (1974) , of finding optimal stopping policies for search that are characterized by a reservation price property. © 2012 Elsevier Inc.
Gershkov A, Moldovanu B (2009) Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach, American Economic Journal: Microeconomics 1 (2) pp. 168-198
We study the revenue-maximizing allocation of several heterogeneous,
commonly ranked objects to impatient agents with privately known
characteristics who arrive sequentially. There is a deadline after which
no more objects can be allocated. We first characterize implementable
allocation schemes, and compute the expected revenue for any
implementable, deterministic and Markovian allocation policy. The
revenue-maximizing policy is obtained by a variational argument which
sheds more light on its properties than the usual dynamic programming
approach. Finally, we use our main result in order to derive the optimal
inventory choice, and explain empirical regularities about pricing in
clearance sales. (JEL C61, D21, D82)
Dizdar D, Gershkov A, Moldovanu B (2011) Revenue maximization in the dynamic knapsack problem, Theoretical Economics 6 (2) pp. 157-184
We analyze maximization of revenue in the dynamic and stochastic knapsack problem where a given capacity needs to be allocated by a given deadline to sequentially arriving agents. Each agent is described by a two-dimensional type that reflects his capacity requirement and his willingness to pay per unit of capacity. Types are private information. We first characterize implementable policies. Then we solve the revenue maximization problem for the special case where there is private information about per-unit values, but capacity needs are observable. After that we derive two sets of additional conditions on the joint distribution of values and weights under which the revenue maximizing policy for the case with observable weights is implementable, and thus optimal also for the case with two-dimensional private information. In particular, we investigate the role of concave continuation revenues for implementation. We also construct a simple policy for which per-unit prices vary with requested weight but not with time, and we prove that it is asymptotically revenue maximizing when available capacity and time to the deadline both go to infinity. This highlights the importance of nonlinear as opposed to dynamic pricing. © 2011 Deniz Dizdar, Alex Gershkov, and Benny Moldovanu.
Gershkov A, Moldovanu B (2012) Dynamic allocation and pricing: A mechanism design approach, International Journal of Industrial Organization 30 (3) pp. 283-286
This paper illustrates the benefits of applying mechanism design techniques to questions in revenue management, in particular to dynamic allocation and pricing problems. It is demonstrated that the solution to a sequential stochastic assignment problem under complete information can also be implemented under incomplete information by a variation of the Vickrey-Clarke-Groves mechanism. More generally, we argue that the mechanism design focus on implementable allocations rather than on prices yields many valuable insights about dynamic RM models. Finally, we also briefly survey some of the recent literature on dynamic mechanism design. © 2011 Elsevier B.V. All rights reserved.
Gershkov A, Moldovanu B (2009) Learning about the future and dynamic efficiency, American Economic Review 99 (4) pp. 1576-1587
Gershkov Alexander, Moldovanu B, Shi X (2016) Optimal voting rules, The Review of Economic Studies 84 (2) pp. 688-717
Oxford University Press
We derive the incentive compatible and ex-ante welfare maximizing (i.e., utilitarian) mechanism for settings with an arbitrary number of agents and alternatives where the privately informed agents have single-crossing and single-peaked preferences. The optimal outcome can be implemented by modifying a sequential voting scheme, due to Bowen (1943), and used in many legislatures and committees. The modiÖcation uses a áexible majority threshold for each of several alternatives, and allows us to replicate, via a single sequential procedure, the entire class of anonymous, unanimous and dominant strategy incentive compatible mechanisms. Our analysis relies on the elegant characterization of this class of mechanisms for single-peaked preferences by Moulin (1980) and, subsequently, for single-crossing preferences by Saporiti (2009).
We study the role of information exchange, leadership, and coordination in team and partnership structures. For this purpose, we view individuals jointly engaging in productive processes?a ?team??as endowed with individual and privately held information on the joint production process. Once each team member decides on whether or not to share his private information truthfully, he chooses which effort to exert in the joint production process. This effort, however, is not contractible: only the realized output (or profit) of the team can be observed. Our central question is whether or not incentives can be provided to a team in this environment such that team members communicate their private information and exert efficient productive efforts on the basis of this communication. Our main result shows that there exists a simple ranking-based contract that implements both desiderata in a wide set of situations.
We study a multi-dimensional collective decision under incomplete information.
Agents have Euclidean preferences and vote by simple majority on each
issue (dimension), yielding the coordinate-wise median. Judicious rotations of
the orthogonal axes ñthe issues that are voted upon ñlead to welfare improvements.
If the agentsí types are drawn from a distribution with independent
marginals then, under weak conditions, voting on the original issues is not optimal.
If the marginals are identical (but not necessarily independent), then
voting Örst on the total sum and next on the di§erences is often welfare superior
to voting on the original issues. We also provide various lower bounds on
incentive e¢ ciency: in particular, if agentsítypes are drawn from a log-concave
density with I.I.D. marginals, a second-best voting mechanism attains at least
88% of the Örst-best e¢ ciency. Finally, we generalize our method and some
of our insights to preferences derived from distance functions based on inner
We derive the revenue maximizing allocation of m units among n symmetric agents
who have unit demand, and who take costly actions that in
uence their values before
participating in the mechanism. The allocation problem with costly actions can be
represented by a reduced form model where agents have convex, non-expected utility
preferences over the interim probability of receiving an object. Both the uniform m+1
price auction and the discriminatory pay-your-bid auction with reserve price constitute
symmetric revenue maximizing mechanisms. Contrasting the case with exogenous valuations,
the optimal reserve price reacts to both demand and supply. We also identify
a condition under which the optimal mechanism is indeed symmetric, and illustrate the
structure of the optimal asymmetric mechanism when the condition fails. The main
tool in our analysis is an integral inequality, due to Fan and Lorentz (1954), involving
majorization, super-modularity and convexity.