Faculty & Research

Lars Stole

Lars Stole

David W. Johnson Professor of Economics

Lars Stole studies strategic pricing, contracts and incentives theory, industrial economics and game theory. Stole’s research has appeared in the American Economic Review, Econometrica, the Review of Economic Studies, the Journal of Political Economy and Games and Economic Behavior. He has made numerous contributions to the theory of strategic price discrimination and competition with contracts.

Stole has been awarded several prizes for his research, including an Alfred P. Sloan Research Fellowship, a National Science Foundation Presidential Faculty Fellowship, and an Olin Fellowship in Law and Economics from the Harvard Law School. In the past, he has lectured at MIT, CERGE/Prague, and CES/Munich, and he has served as Editor of the RAND Journal of Economics. Stole founded the Applied Theory Initiative at Booth and served as co-Director from 2009-2019.

Stole earned bachelor degrees in Political Science and Economics from the University of Illinois, a MSc in Economics from the London School of Economics, and a PhD in Economics from the Massachusetts Institute of Technology.

Outside of academia, Stole enjoys turning wood, working metal and general tinkering.


2019 - 2020 Course Schedule

Number Title Quarter
33801 Microeconomics 2019 (Fall)
33801 Microeconomics 2020 (Summer)

Other Interests



Research Activities

Economics of contracts and organizations; industrial organization; informational economics; current research focuses on price discrimination and competitive contracting.

With David Martimort and Aggey Semenov, “A Complete Characterization of Equilibria in Two-type Common Agency Screening Games,” Theoretical Economics, 13 (2018), 1151-1189.

With David Martimort, "Representing Equilibrium Aggregates in Aggregate Games with Applications to Common Agency," Games and Economic Behavior, 76 (2012), 753-772.

With David Martimort, “Market Participation in Delegated and Intrinsic Common-Agency Games,” RAND Journal of Economics (2009).

"Price Discrimination in Competitive Environments," Handbook of Industrial Organization (2008).

With David Martimort, "The Revelation and Delegation Principles in Common Agency Games," Econometrica (2002).

With Jean-Charles Rochet, "Nonlinear Pricing with Random Participation," Review of Economic Studies (2002).

For a listing of research publications, please visit the university library listing page.

New: Do Short-Term Managerial Objectives Lead to Under- or Over-Investment in Long-Term Projects
Date Posted: Dec  05, 2018
This paper studies managerial decisions about investment in long-run projects in the presence of imperfect information (the market knows less about such investments than the firm's managers) and short-term managerial objectives (the managers are concerned about the short-term stock price as well as the long-term stock price). Prior work has suggested that imperfect information and short-term managerial objectives induce managers to underinvest in long-run projects. We show that either underinvestment or overinvestment is possible, and we identify the connection between the type of informational imperfection present and the direction of the distortion. When investors cannot observe the level of investment in long-run projects, suboptimal investment will be induced. When investors can observe investment but not its productivity, however, an excessive level of investment will be induced.

REVISION: Representing Equilibrium Aggregates in Aggregate Games with Applications to Common Agency
Date Posted: Mar  02, 2015
An aggregate game is a normal-form game with the property that each player’s payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without re- quiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self- generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggre- gates of the original n-player game. We illustrate the value of this approach in common-agency games where the players’ strategy space is an infinite- dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral haz- ard versions of these games.

New: Menu Auctions and Influence Games with Private Information
Date Posted: Feb  27, 2015
We study games in which multiple principals influence the choice of a privately-informed agent by offering action-contingent payments. We characterize the equilibrium allocation set as the maximizers of an endogenous aggregate virtual-surplus program. The aggregate maximand for every equilibrium includes an information-rent margin which captures the confluence of the principals’ rent-extraction motives. We illustrate the economic implications of this novel margin in two applications: a public goods game in which players incentivize a common public good supplier, and a lobbying game between conflicting interest groups who offer contributions to influence a common political decision-maker.

New: The Economics of Liquidated Damage Clauses in Contractual Environments with Private Information
Date Posted: Feb  21, 2014
This paper considers trading environments in which buyers are privately informed about their valuations and sellers are privately informed about the expected value of outside trading opportunities. Outside opportunities are stochastic, however, and future realized shocks may make bilateral trade between a buyer and a seller inefficient. In this environment, there is a role for using liquidated damage clauses as a screening device in optimal contracts, whether designed by the seller, designed by the buyer or designed by a third-party. In all such design settings, liquidated damages are set below the buyer's valuation. Excessive liquidated damage clauses are never optimal in this trading environment and may be a symptom of another contracting distortion or failure. These findings provide a partial rationalization for why courts may strike down liquidated damage clauses when they are excessive, but not when they are insufficient to compensate the harmed party.

New: Licensing and Technology Transfer
Date Posted: Feb  21, 2014
Government mandated technology transfers from the developer of a product to a second source offer a potential gain of reduced information rents and procurement costs, even when such transfers are otherwise inefficient. This paper models the tradeoff between information extraction and inefficient transfers in the context of an optimally-designed procurement auction in which an incumbent supplier bids against a potential second-source firm. In the optimal auction, the incumbent firm is given stronger incentives to bid aggressively by transferring technology when the bids from the competing firms are close and the transfer is not otherwise too inefficient.

New: Fixed-Equilibrium Rationalizability in Signaling Games
Date Posted: Feb  19, 2014
This paper studies equilibrium refinements in signaling games through an examination of rationalizability in derived games obtained by replacing the equilibrium path with a sure outcome that yields the equilibrium payoff to all players. The informed player chooses between the sure payoff and sending an out-of-equilibrium signal from the original game. Whether or not the strategy of choosing the sure payoff is rationalizable is related to the iterated intuitive condition (divinity) when the original game is viewed as having imperfect (incomplete) information. Our results also demonstrate the significance of testing out-of-equilibrium signals as a set rather than individually.

New: Information Expropriation and Moral Hazard in Optimal Second-Source Auctions
Date Posted: Feb  19, 2014
Government mandated technology transfers from the developer of a product to a second source offer a potential gain of reduced information rents and procurement costs. To provide appropriate incentives, technology must sometimes be transferred even when the second source is less efficient than the first. Additionally, when developer moral hazard exists with respect to investments in cost-reducing technology, the optimal auction will make the developer's success in the auction more sensitive to the developing firm's announced costs.

New: Nonlinear Pricing and Oligopoly
Date Posted: Feb  19, 2014
We consider the general problem of price discrimination with nonlinear pricing in an oligopoly setting where firms are spatially differentiated. We characterize the nature of optimal pricing schedules, which in turn depends importantly upon the type of private information the customer possesses – either horizontal uncertainty regarding brand preference or vertical uncertainty regarding quality preference. We show that as competition increases, the resulting quality distortions decrease, as well as price and quality dispersions. Additionally, we indicate conditions under which price discrimination may raise social welfare by increasing consumer surplus through encouraging greater entry.

New: Mandated Countertrade as a Strategic Commitment
Date Posted: Feb  18, 2014
Mandated countertrade is a policy to restrict unilateral imports. A country’s government thereby in effect commits domestic firms not to purchase from a foreign trading partner unless there are reciprocal sales. We argue that the policy may be a rational response to fundamental contracting failures, our key assumption being that sellers are incompletely informed about buyers’ valuations. In line with observed practices, the analysis suggests that an optimal mandated countertrade policy will target high mark-up imports and low mark-up exports. Implications for global welfare are ambiguous and depend upon the extent of a double coincidence of wants.

New: Organizational Design and Technology Choice Under Intrafirm Bargaining
Date Posted: Feb  18, 2014
We consider a wide number of applications of an intrafirm bargaining game within organizations where employees and the firm engage in wage negotiations. Under our presumption that contracts cannot bind employees to the organization, the resulting stable wage and profit profiles give rise to an objective function for the firm that places weight on inframarginal profits in an economically significant manner. We in turn employ this methodology to explore applications of organizational design, hiring and capital decisions, training and cross-training, the importance of labor and asset specificity, managerial hierarchies, preferences for unionization, responses to competition, and internal capital budgeting.

New: Price Discrimination in Competitive Environments
Date Posted: Feb  18, 2014
This chapter surveys recent theoretical developments in the intersection of price discrimination and imperfect competition, emphasizing how the introduction of competition fundamentally alters some well-established results derived from models of monopoly pricing.

New: The Economics of Multidimensional Screening
Date Posted: Feb  18, 2014
This chapter, which corresponds to an invited lecture at the Seventh World Congress of the Econometric Society, surveys recent theoretical developments in the use of multidimensional screening models in such applications as contract theory and pricing strategies.

New: Involuntary Unemployment and Intrafirm Bargaining with Replacement Workers: Reply
Date Posted: Feb  18, 2014
This note responds to a comment by de Fontenay and Gans "Organizational Design and Technology Choice under Intrafirm Bargaining: Comment," on the possibility of replacement workers, published in the American Economic Review, March 2003.

New: Barter Relationships
Date Posted: Feb  18, 2014
We offer a simple economic model of repeated barter to explore current economic exchange in Russia: individuals trade with each other in a dynamic environment where the threat of dissolving the relationship constrains the incentives to cheat. We show how the value of future interactions affects the willingness of individuals to trade with each other; only when rates of interaction are large can trust compensate for an absence of money. Moreover, when trading relationships are asymmetric – either in the trading partners' values for each other's goods or in their relative bargaining power – the resulting barter allocations are distorted, as goods must be used for liquidity reasons. When third-party middlemen exist who can facilitate barter, they command a premium for their services, and have preferences for improved liquidity which may or may not correspond with the other traders in the barter economy. Fourth, we demonstrate that the restriction of trading to tight trading networks may ...

New: The Non-Monetary Nature of Gifts
Date Posted: Feb  15, 2014
This paper addresses the prevalence of non-monetary gifts over more highly valued and efficient monetary transfers in social relationships. We demonstrate that under a wide variety of circumstances, inefficient non-monetary gifts will be offered by a donor in lieu of cash in order to signal the donor's quality of information about the recipient's preferences. This result emerges because gift giving is inefficient relative to cash, and not because of any arbitrary assumptions regarding communication. In particular, the donor has available the strategy of offering cash and saying what he would have purchased. Nonetheless, there is still an important equilibrium role for buying gifts.

New: Nonlinear Pricing with Random Participation
Date Posted: Feb  15, 2014
The canonical selection contracting programme takes the agent's participation decision as deterministic and finds the optimal contract, typically satisfying this constraint for the worst type. Upon weakening this assumption of known reservation values by introducing independent randomness into the agents' outside options, we find that some of the received wisdom from mechanism design and nonlinear pricing is not robust and the richer model which allows for stochastic participation affords a more general empirical specification. We develop a multidimensional methodology for addressing this class of problems, providing two important applications to nonlinear pricing. First, with nonlinear pricing by a monopolist the familiar "no-distortion-at-the-top" result persists, but in tandem with the surprising conclusion that there is either no distortion at the bottom or bunching. Second, in a simple model of product differentiated duopolists competing with nonlinear pricing we show that, ...

New: Selecting Equilibria in Common Agency Games
Date Posted: Feb  15, 2014
We characterize equilibrium payoffs of a delegated common agency game in a public good context where principals use smooth contribution schedules. We prove that under complete information, payoff vectors of equilibria with truthful schedules coincide with the set of smooth equilibrium payoffs, including non-truthful schedules. We next consider whether the presence of arbitrarily small amounts of asymmetric information is enough to refine this payoff set. Providing that the extensions of the equilibrium schedules beyond the equilibrium point are flatter than truthful schedules, the set of equilibrium payoffs is strictly smaller than the set of smooth (equivalently, truthful) equilibrium payoffs. Interestingly, some forms of asymmetric information do not sufficiently constrain the slopes of the extensions and fail to refine the payoff set. In the case of a uniform distribution of types and arbitrary out-of-equilibrium contributions, the refinement has no bite. If, however, one ...

New: Intrafirm Bargaining Under Nonbinding Contracts
Date Posted: Feb  15, 2014
We present a new methodology for studying the problem of intra-firm bargaining, based on the notion that contracts cannot commit the firm and its agents to wages and employment. We develop and analyse a general non-cooperative multilateral bargaining framework between the firm and its employees and consider outcomes which are immune to renegotiations by any party. Equilibrium firm profits are characterizable as both a weighted average of a neo-classical (non-bargaining) firm's profits and a generalization of Shapley value for a corresponding cooperative game. Furthermore, the resulting payoffs induce economically significant distortions in the firm's input and organizational-design decisions.

New: Restricting the Means of Exchange within Organizations
Date Posted: Feb  15, 2014
This paper considers why firms often ban monetary exchange between their employees, while encouraging these trades through other means, such as through the reciprocation of favours or barter. Despite classical inefficiencies associated with non-monetary exchange, we illustrate two themes as to why non-monetary trade may be preferred to allowing money. First, the use of non-monetary trade may affect the allocation of rents in surplus-enhancing ways, as agents respond strategically to the existence of these rents. Second, non-monetary trade improves the ability of agents to impose sanctions on those who act dishonestly.

New: Competitive Nonlinear Pricing
Date Posted: Feb  15, 2014
We study competitive nonlinear pricing in a model involving simultaneously horizontal and vertical product differentiation. It is a particular case of a more general model of optimal contracting with uncertain participation that we study elsewhere (Rochet-Stole (1997)).

New: Monetizing Social Exchange
Date Posted: Feb  15, 2014
We address the role of monetizing trades in an environment when reciprocal trade acts as the alternative means of exchange and opportunism is possible. We illustrate that money has three roles: (i) money enable trade on contractible goods, (ii) money aids trade in non-contractible goods through the use of voluntary transfers, and (iii) money possibly induces inefficient pricing and production decisions. We show a number of cases where allowing trades to be monetized reduces welfare and also illustrate how an inefficient instantaneous means of exchange can sometimes increase trade more than pure money. Finally, analogous to the role of barter in facilitating efficient exchange, we illustrate that otherwise classically inefficient restrictions on trading may have a similar desirable effect.

New: Market Participation in Delegated and Intrinsic Common-Agency Games
Date Posted: Feb  15, 2014
We study how competition in nonlinear pricing between two principals (sellers) affects market participation by a privately-informed agent (consumer). When participation is restricted to all-or-nothing ("intrinsic" agency), the agent must choose between both principals' contracts and selecting her outside option. When the agent is afforded the additional possibilities of choosing only one contract ("delegated" agency), competition is more intense. The two games have distinct predictions for participation. Intrinsic agency always induces more distortion in participation relative to the monopoly outcome and equilibrium allocations are discontinuous for the marginal consumer. Under delegated agency, relative to monopoly market participation increases (resp. decreases) when contracting variables are substitutes (resp. complements) on the intensive margin. Equilibrium allocations are continuous for the marginal consumer and the range of product offerings is identical to both the first-best ...

New: Mergers, Employee Hold-Up and the Scope of the Firm: An Intrafirm Bargaining Approach to Mergers
Date Posted: Feb  15, 2014
We explore the scope of the firm in a setting where employee wage contracts are nonbinding and firms cannot contract with one another on their respective employment decisions. Specifically, we consider two divisions that have scope for beneficial interaction, and examine whether it is best for them, given this incomplete contracting environment, to produce jointly within the same firm or to interact over the market. Employing a multilateral bargaining framework, we analyze how employee wages, firm profits and employment levels are altered by merger when employees have some hold-up power. Among other results, our analysis suggests that merged production is more likely when the optimal contributions by the two firms to joint production are more unequal (leading to productive and bargaining externalities), while nonintegration is more likely the greater the productive gains to joint interaction between the firms (despite such gains being equally realizable under both merger and ...

New: Public Contracting in Delegated Agency Games
Date Posted: Feb  14, 2014
We study games of public delegated common agency under asymmetric information. Using tools from non-smooth analysis and optimal control, we derive best responses and characterize equilibria (both continuous and discontinuous) using self-generating optimization programs of which any equilibrium allocation must be a solution. Special attention is given to common agency games in which each principal's payoff is a linear function of the agent's action. In such games the self-generating optimization program reduces to the maximization of the principals' "aggregate" virtual surplus in which the agent's marginal valuation is replaced by a confluence of "virtual" valuations that reflect common agency problems. In all equilibria, we illustrate that there are two distinct sources of inefficiencies: inefficient contracting by a given coalition of active principals and inefficient activity by principals. One noteworthy subset of equilibrium allocations are maximal in the range of actions that ...

New: Necessary and Sufficient Conditions for Optimal Control Problems with Linear State, Semicontinuous Lagrangians
Date Posted: Feb  14, 2014
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 otherwise only restricted to be upper semi-continuous in the control variable.

New: A Theory of Contracts with Limited Enforcement
Date Posted: Feb  14, 2014
We present a Theory of Contracts under costly enforcement in the context of a dynamic relationship between an uninformed buyer and a seller who is privately informed on his persistent cost at the outset. Public enforcement relies on remedies for breach. Private enforcement comes from severing relationships. We first characterize aggregate enforcement constraints ensuring that trading partners do not breach contracts unduly. Whether a long-term contract is enforceable does not depend on the distribution of penalties for breach between the buyer and the seller. While under complete information, the optimal contract would remain stationary, non-stationarity might arise under asymmetric information. Enforcement constraints are time-dependent and easier to satisfy as time passes. Indeed, a high-cost seller may be tempted to trade high volumes at high prices at the beginning of the relationship before breaching the contract later on. Yet, such take-the-money-and-run strategy becomes less ...

New: Do Short-Term Managerial Objectives Lead to Under- or Over-Investment in Long-Term Projects
Date Posted: Jan  06, 2007
This paper studies managerial decisions about investment in long-run projects in the presence of imperfect information (the market knows less about such investments than the firm's managers) and short-term managerial objectives (the managers are concerned about the short-term stock price as well as the long-term stock price). Prior work has suggested that imperfect information and short-term managerial objectives induce managers to underinvest in long-run projects. We show that either ...

The Revelation and Delegation Principles in Common Agency Games
Date Posted: Sep  01, 2004
In the context of common agency adverse-selection games we illustrate that the revelation principle cannot be applied to study equilibria of the multi-principal games. We then demonstrate that an extension of the taxation principle - what we term the delegation principle - can be used to characterize the set of all common agency equilibria.

Common Agency Equilibria with Discrete Mechanisms and Discrete Types
Date Posted: Sep  01, 2004
This paper characterizes the equilibrium sets of an intrinsic common agency game with discrete types and direct revelation mechanisms. After presenting a general algorithm to find the pure-strategy equilibria of this game, we use it to characterize these equilibria when the two principals control activities which are complements in the agent's objective function. Some of those equilibria may entail allocative inefficiency. For the case of substitutes, we demonstrate non-existence of such ...

Barter, Liquidity and Market Segmentation
Date Posted: Sep  01, 2004
This paper explores the private and social benefits from barter exchange in a monetized economy. We first prove a no-trade theorem regarding the ability of firms with double-coincidences-of-wants to negotiate improvements in trade among themselves relative to the market outcomes. We then demonstrate that in the presence of liquidity shocks, introducing a non-monetary exchange avoids this limitation and enhances trade by (1) generating liquidity and (2) by segmenting the market place into ...

Contractual Externalities and Common Agency Equilibria
Date Posted: Sep  01, 2004
This paper characterizes the equilibrium sets of an intrinsic common agency game with direct externalities between principals both under complete and asymmetric information. Direct externalities arise when the contracting variable of one principal affects directly the other principal's payoff. Out-of-equilibrium messages are used by principals to precommit themselves to distort their strategic behavior. We characterize pure-strategy symmetric equilibria arising in such games under complete ...

Non-Monetary Exchange Within Firms and Industry
Date Posted: May  12, 2000
This paper considers why non-monetary means of exchange, such as barter and the reciprocation of favors, are chosen by firms despite the usual benefits of monetary transactions. We consider the chosen means of exchange when both monetary and non-monetary exchange mechanisms are available. We illustrate three potential reasons for the emergence of non-monetary trade. First, a willingness to barter may reveal information that cannot be revealed solely through monetary trade. Second, ...

Impetuous Youngsters and Jaded Old-Timers: Acquiring a Reputation for Learning
Date Posted: Feb  01, 1998
This paper examines individual decision making when decisions reflect on people's ability to learn. We address this problem in the context of a manager making investment decisions on a project over time. We show that in an effort to appear as a fast learner, the manager will exaggerate his own information; but ultimately, he becomes too conservative, being unwilling to change his investments on the basis of new information. Our results arise purely from learning about competence rather than ...

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