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Full-Text Articles in Economics
Optimal Design For Social Learning, Yeon-Koo Che, Johannes Hörner
Optimal Design For Social Learning, Yeon-Koo Che, Johannes Hörner
Cowles Foundation Discussion Papers
This paper studies the design of a recommender system for organizing social learning on a product. To improve incentives for early experimentation, the optimal design trades off fully transparent social learning by over-recommending a product (or “spamming”) to a fraction of agents in the early phase of the product cycle. Under the optimal scheme, the designer spams very little about a product right after its release but gradually increases the frequency of spamming and stops it altogether when the product is deemed sufficiently unworthy of recommendation. The optimal recommender system involves randomly triggered spamming when recommendations are public — as …
Learning To Disagree In A Game Of Experimentation, Alessandro Bonatti, Johannes Hörner
Learning To Disagree In A Game Of Experimentation, Alessandro Bonatti, Johannes Hörner
Cowles Foundation Discussion Papers
We analyse strategic experimentation in which information arrives through fully revealing, publicly observable “breakdowns.” With hidden actions, there exists a unique equilibrium that involves randomization over stopping times. This randomization induces belief disagreement on the equilibrium path. When actions are observable, the equilibrium is pure, and welfare improves. We analyse the role of policy interventions such as subsidies for experimentation and risk-sharing agreements. We show that the optimal risk-sharing agreement restores the first-best outcome, independent of the monitoring structure.
Career Concerns With Coarse Information, Alessandro Bonatti, Johannes Hörner
Career Concerns With Coarse Information, Alessandro Bonatti, Johannes Hörner
Cowles Foundation Discussion Papers
This paper develops a model of career concerns. The worker’s skill is revealed through output, wage is based on expected output, and so on assessed ability. Specifically, effort increases the probability that a skilled worker achieves a one-time breakthrough. Effort levels at different times are strategic substitutes. Equilibrium effort (and, if marginal cost is convex, wage) is single-peaked with seniority. The agent works too little, too late. Both delay and underprovision of effort worsen if effort is observable. If the firm commits to wages but faces competition, the optimal contract features piecewise constant wages as well as severance pay.
Career Concerns And Market Structure, Alessandro Bonatti, Johannes Hörner
Career Concerns And Market Structure, Alessandro Bonatti, Johannes Hörner
Cowles Foundation Discussion Papers
This paper analyzes the impact of market structure on career concerns. Effort increases the probability that a skilled agent achieves a one-time breakthrough. Wages are based on assessed ability and on expected output. For any wage, the agent works too little, too late. Under short-term contracts, effort and wages are single-peaked with seniority, due to the strategic substitutability of effort levels at different times. Both delay and underprovision of effort worsen if effort is observable. Commitment to wages by competing firms mitigates these inefficiencies. In that case, the optimal contract features piecewise constant wages and severance pay.
Incentives For Experimenting Agents, Johannes Hörner, Larry Samuelson
Incentives For Experimenting Agents, Johannes Hörner, Larry Samuelson
Cowles Foundation Discussion Papers
We examine a repeated interaction between an agent, who undertakes experiments, and a principal who provides the requisite funding for these experiments. The agent’s actions are hidden, and the principal, who makes the offers, cannot commit to future actions. We identify the unique Markovian equilibrium (whose structure depends on the parameters) and characterize the set of all equilibrium payoffs, uncovering a collection of non-Markovian equilibria that can Pareto dominate and reverse the qualitative properties of the Markovian equilibrium. The prospect of lucrative continuation payoffs makes it more expensive for the principal to incentivize the agent, giving rise to a dynamic …
Incentives For Experimenting Agents, Johannes Hörner, Larry Samuelson
Incentives For Experimenting Agents, Johannes Hörner, Larry Samuelson
Cowles Foundation Discussion Papers
We examine a repeated interaction between an agent, who undertakes experiments, and a principal who provides the requisite funding for these experiments. The agent’s actions are hidden, and the principal, who makes the offers, cannot commit to future actions. We identify the unique Markovian equilibrium (whose structure depends on the parameters) and characterize the set of all equilibrium payoffs, uncovering a collection of non-Markovian equilibria that can Pareto dominate and reverse the qualitative properties of the Markovian equilibrium. The prospect of lucrative continuation payoffs makes it more expensive for the principal to incentivize the agent, giving rise to a dynamic …
Incentives For Experimenting Agents, Johannes Hörner, Larry Samuelson
Incentives For Experimenting Agents, Johannes Hörner, Larry Samuelson
Cowles Foundation Discussion Papers
We examine a repeated interaction between an agent, who undertakes experiments, and a principal who provides the requisite funding for these experiments. The repeated interaction gives rise to a dynamic agency cost — the more lucrative is the agent’s stream of future rents following a failure, the more costly are current incentives for the agent, giving the principal an incentive to reduce the continuation value of the project. We characterize the set of recursive Markov equilibria. We also find that there are non-Markov equilibria that make the principal better off than the recursive Markov equilibrium, and that may make both …
Incentives For Experimenting Agents, Johannes Hörner, Larry Samuelson
Incentives For Experimenting Agents, Johannes Hörner, Larry Samuelson
Cowles Foundation Discussion Papers
We examine a repeated interaction between an agent, who undertakes experiments, and a principal who provides the requisite funding for these experiments. The repeated interaction gives rise to a dynamic agency cost — the more lucrative is the agent’s stream of future rents following a failure, the more costly are current incentives for the agent, giving the principal an incentive to reduce the continuation value of the project. We characterize the set of recursive Markov equilibria. We show that there are non-Markov equilibria that make the principal better off than the recursive Markov equilibrium, and that may make both players …
Collaborating, Alessandro Bonatti, Johannes Hörner
Collaborating, Alessandro Bonatti, Johannes Hörner
Cowles Foundation Discussion Papers
This paper examines moral hazard in teams over time. Agents are collectively engaged in an uncertain project, and their individual efforts are unobserved. Free-riding leads not only to a reduction in effort, but also to procrastination. The collaboration dwindles over time, but never ceases as long as the project has not succeeded. In fact, the delay until the project succeeds, if it ever does, increases with the number of agents. We show why deadlines, but not necessarily better monitoring, help to mitigate moral hazard.
Efficient Dynamic Auctions, Dirk Bergemann, Juuso Välimäki
Efficient Dynamic Auctions, Dirk Bergemann, Juuso Välimäki
Cowles Foundation Discussion Papers
We consider the truthful implementation of the socially efficient allocation in a dynamic private value environment in which agents receive private information over time. We show that a suitable generalization of the Vickrey-Clark-Groves mechanism, based on the marginal contribution of each agent, leads to truthtelling in every period. A leading example of a dynamic allocation model is the sequential auction of a single good in which the current winner of the object receives additional information about her valuation. We show that a modified sequential second price auction in which only the current winner makes a positive payment leads to truthtelling. …
Bandit Problems, Dirk Bergemann, Juuso Välimäki
Bandit Problems, Dirk Bergemann, Juuso Välimäki
Cowles Foundation Discussion Papers
We survey the literature on multi-armed bandit models and their applications in economics. The multi-armed bandit problem is a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. This classic problem has received much attention in economics as it concisely models the trade-off between exploration (trying out each arm to find the best one) and exploitation (playing the arm believed to give the best payoff).
Informational Herding And Optimal Experimentation, Lones Smith, Peter Norman Sorensen
Informational Herding And Optimal Experimentation, Lones Smith, Peter Norman Sorensen
Cowles Foundation Discussion Papers
We show that far from capturing a formally new phenomenon, informational herding is really a special case of single-person experimentation — and ‘bad herds’ the typical failure of complete learning. We then analyze the analogous team equilibrium, where individuals maximize the present discounted welfare of posterity. To do so, we generalize Gittins indices to our non-bandit learning problem, and thereby characterize when contrarian behaviour arises: (i) While herds are still constrained efficient, they arise for a strictly smaller belief set. (ii) A log-concave log-likelihood ratio density robustly ensures that individuals should lean more against their myopic preference for an action …
Competitive Experimentation With Private Information, Giuseppe Moscarini, Francesco Squintani
Competitive Experimentation With Private Information, Giuseppe Moscarini, Francesco Squintani
Cowles Foundation Discussion Papers
We study a winner-take-all R&D race where firms are privately informed about the uncertain arrival rate of the invention. Due to the interdependent-value nature of the problem, the equilibrium displays a strong herding effect that distinguishes our framework from war-of-attrition models. Nonetheless, equilibrium expenditure in R&D is sub-optimal when the planner is sufficiently impatient. Pessimistic firms prematurely exit the race, so that the expected discounted amount of R&D activity is inefficiently low. This result stands in contrast to the overinvestment in research that is typical of winner-take-all R&D races without private information. We conclude that secrecy in R&D inefficiently slows …
Entry And Vertical Differentiation, Dirk Bergemann, Juuso Välimäki
Entry And Vertical Differentiation, Dirk Bergemann, Juuso Välimäki
Cowles Foundation Discussion Papers
This paper analyzes the entry of new products into vertically differentiated markets where an entrant and an incumbent compete in quantities. The value of the new product is initially uncertain and new information is generated through purchases in the market. We derive the (unique) Markov perfect equilibrium of the infinite horizon game under the strong long run average payoff criterion. The qualitative features of the optimal entry strategy are shown to depend exclusively on the relative ranking of established and new products based on current beliefs. Superior products are launched relatively slowly and at high initial prices whereas substitutes for …
Entry And Vertical Differentiation, Dirk Bergemann, Juuso Välimäki
Entry And Vertical Differentiation, Dirk Bergemann, Juuso Välimäki
Cowles Foundation Discussion Papers
This paper analyzes the entry of new products into vertically differentiated markets where an entrant and an incumbent compete in quantities. The value of the new product is initially uncertain and new information is generated through purchases in the market. We derive the (unique) Markov perfect equilibrium of the infinite horizon game under the strong long run average payoff criterion. The qualitative features of the optimal entry strategy are shown to depend exclusively on the relative ranking of established and new products based on current beliefs. Superior products are launched relatively slowly and at high initial prices whereas substitutes for …
Experimentation In Markets, Dirk Bergemann, Juuso Välimäki
Experimentation In Markets, Dirk Bergemann, Juuso Välimäki
Cowles Foundation Discussion Papers
We present a model of entry and exit with Bayesian learning and price competition. A new product of initially unknown quality is introduced in the market, and purchases of the product yield information on its true quality. We assume that the performance of the new product is publicly observable. As agents learn from the experiments of others, informational externalities arise. We determine the Markov Perfect Equilibrium prices and allocations. In a single market, the combination of the informational externalities among the buyers and the strategic pricing by the sellers results in excessive experimentation. If the new product is launched in …