Professor Alex Gershkov

We study a generalization of the classical monopoly insurance problem under adverse selection (see Stiglitz [1977]) where we allow for a random distribution of losses, possibly correlated with the agent's risk parameter that is private information. Our model explains patterns of observed customer behavior and predicts insurance contracts most often observed in practice: these consist of menus of several deductible-premium pairs, or menus of insurance with coverage limits-premium pairs. A main departure from the classical insurance literature is obtained here by endowing the agents with risk-averse preferences that can be represented by a dual utility functional (Yaari [1987]), or by a more general utility functional displaying Constant Risk Aversion.

We generalize the standard, private values voting model with single-peaked preferences and incomplete information by introducing interdependent preferences. Our main results show how standard mechanisms that are outcome-equivalent and implement the Con-dorcet winner under complete information or under private values yield starkly di¤erent outcomes if values are interdependent. We also propose a new notion of Condorcet winner under incomplete information and interdependent preferences, and discuss its implementation. The new phenomena in this paper arise because di¤erent voting rules (including dynamic ones) induce di¤erent processes of information aggregation and learning.

We describe and analyze the voting process leading to the compromise achieved in the Weimar Flag Controversy. We also offer a simple theoretical model that attempts to capture the main forces at work. These forces are: (1) the addition of a compromise alternative that is located between the main ideological positions on the left and on the right; (2) the interdependence of preferences that makes the compromise salient; and (3) a voting process that gradually reveals and aggregates information. Finally, we compare the theoretical insights with the observed outcome.

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 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.

We derive the revenue maximizing allocation of m units among n symmetric agents who have unit demand, and who take costly actions that influence 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

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.

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)

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 analyze the implications of introducing priority service on customers'welfare. In monopoly markets, introducing priority service can often decrease consumer surplus. This negative e¤ect exists despite an increase in e¢ ciency gains. In other words, the monopolist extracts from customers an aggregated payment higher than the total e¢ ciency gain generated by the service and hence leaves customers worse o¤ than when no priority is o¤ered at all. In duopoly markets with homogeneous customers the price competition over priority service is blocked, i.e., the equilibrium price and customers' welfare coincides with the monopoly outcome where this monopolist faces half of the market. With heterogeneous customers as well priority can reduce the aggregated consumer welfare. On the other hand, priority service can increase customers'surplus if it expands the consumption's coverage, i.e., if it introduces new customers who would not otherwise purchase the service. Furthermore, a market environment in which the dominant e¤ect of customers'indi-vidual preferences is on the value of the basic good and less on the disutility of waiting tends to be more conducive to welfare improvement due to priority service.

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.

We study auction design for bidders equipped with non-expected utility preferences that exhibit constant risk aversion (CRA). The CRA class is large and includes loss-averse, disappointment-averse, mean-dispersion and Yaari's dual preferences as well as coherent and convex risk measures. Any preference in this class displays first-order risk aversion, contrasting the standard expected utility case which displays second-order risk aversion. The optimal mechanism offers " full-insurance " in the sense that each agent's utility is independent of other agents' reports. The seller excludes less types than under risk neutrality, and awards the object randomly to intermediate types. Subjecting intermediate types to a risky allocation while compensating them when losing allows the seller to collect larger payments from higher types. Relatively high types are willing to pay more, and their allocation is efficient.

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.

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.

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 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.

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.

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.

We study issue-by-issue voting by majority and incentive compatibility in multi-dimensional frameworks where privately informed agents have preferences induced by general norms and where dimensions are endogenously chosen. We uncover the deep connections between dominant strategy incentive compatibility (DIC) on the one hand, and several geometric/functional analytic concepts on the other. Our main results are: 1) Marginal medians are DIC if and only if they are calculated with respect to coor- dinates defined by a basis such that the norm is orthant-monotonic in the associated coordinate system. 2) Equivalently, marginal medians are DIC if and only if they are computed with respect to a basis such that, for any vector in the basis, any linear combination of the other vectors is Birkho¤-James orthogonal to it. 3) We show how semi-inner products and normality provide an analytic method that can be used to nd all DIC marginal medians. 4) As an application, we derive all DIC marginal medians for lp spaces of any finite dimension, and show that they do not depend on p (unless p = 2).

We study when the voting outcome is independent of the order of issues put up for vote in a spacial multi-dimensional voting model. Agents equipped with norm-based preferences that use a norm to measure the distance from their ideal policy vote sequentially and issue-by-issue via simple majority. If the underlying norm is generated by an inner-product –such as the Euclidean norm –then the voting outcome is order independent if and only if the issues are orthogonal. If the underlying norm is a general one, then the outcome is order independent if the basis de…ning the issues to be voted upon satis…es the following property: for any vector in the basis, any linear combination of the other vectors is Birkho¤-James orthogonal to it. We prove a partial converse in the case of two dimensions: if the underlying basis fails the above property then the voting order matters. Finally, despite existence results for the two-dimensional case and for the general l p case, we show that non-existence of bases with the above property is generic.

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.

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 products.