“Optimal Feedback in Contests,” with Jeffrey Ely (Northwestern), George Georgiadis (Kellogg), and Luis Rayo (Kellogg)
The Review of Economic Studies, 2023, 90(5), 2370–2394.
Accepted at ACM EC’21 Conference
Featured in: Kellogg Insight
We obtain optimal dynamic contests for environments where the designer monitors effort through coarse, binary signals---Poisson successes---and aims to elicit maximum effort, ideally in the least amount of time possible, given a fixed prize. The designer has a vast set of contests to choose from, featuring termination and prize allocation rules together with real-time feedback for the contestants. Every effort-maximizing contest (which also maximizes total expected successes) has a history-dependent termination rule, a feedback policy that keeps agents fully apprised of their own success, and a prize allocation rule that grants them, in expectation, a time-invariant share of the prize if they succeed. Any contest that achieves this effort in the shortest possible time must in addition be what we call second chance: once a pre-specified number of successes arrive, the contest enters a countdown phase where contestants are given one last chance to succeed.
2. “Screening in Multistage Contests,” with Lakshmi Nittala (Dayton) and Vish Krishnan (UCSD)
Manufacturing & Service Operations Management, 2023, 25(6):2249-2267.
Featured as INFORMS TIMES paper of the month in August 2023
Problem definition: Firms seek to use the contest format to source solutions from a broader network of outside solvers. We study the application of the contest approach in multi-stage settings, and show how and when screening of contestants between stages can produce improved contest outcomes. Methodology/results: We present an application-driven game-theoretic model to capture imperfections in screening using the true positive rate (Sensitivity) and the true negative rate (Specificity). Specifically, we consider a two-stage contest with a screening decision by the firm between the stages. Solvers face uncertainty about their probability of fit and the final quality of the solution is dependent on the performance across both stages. We identify two mechanisms through which screening induces greater effort, namely the encouragement effect and the competitive contest effect, and characterize how screening should be tuned to the problem setting. We find that filtering out true negatives in contests with exogenous solvers' probability of fit is optimal for solution-seeking firms. Our results indicate that in case of problems with endogenous probability of fit and less upfront complexity, coarse (imperfect) screening is beneficial in order to manage competition and stimulate greater effort, but it behooves the firm to resort to more accurate screening otherwise. We also derive nuanced results for the case when a Seeker faces screening constraints and must balance screening sensitivity and specificity. Managerial implications: Our work provides firms an additional degree of freedom, in terms of specific and sensitive screening to design and run contests and to better engage outside solvers. We derive actionable results and translate them into a managerial framework to help fine-tune the screening mechanism for improved contest performance.
3. “Dynamic Development Contests,” with Ersin Korpeoglu (UCL) and Vish Krishnan (UCSD)
Operations Research, 2023, 72(1), 43-59.
Public, private, and not-for-profit organizations find advanced technology and product development projects challenging to manage due to the time and budget pressures, and turn to their development partners and suppliers to address their development needs. We study how dynamic development contests with enriched rank-based incentives and carefully-tailored information design can help these organizations leverage their suppliers for their development projects while seeking to minimize project lead time by stimulating competition among them. We find that an organization using dynamically-adjusted flexible rewards can achieve the minimum expected project lead time at a significantly lower cost than a fixed-reward policy. Importantly, the derived flexible-reward policy pays the minimum expected reward (i.e., achieves the first best). We further examine the case where the organization may not have sufficient budget to offer a reward that attains the minimum expected lead time. In this case, the organization uses the whole reward budget and supplements it with strategic information disclosure. Specifically, we derive an optimal information disclosure policy whereby any change in the state of competition is disclosed immediately with some probability that is weakly increasing over time. Our results indicate that dynamic rewards and strategic information disclosure are powerful tools to help organizations fulfill their development needs swiftly and cost effectively.
“Mergers of Consumer Cooperatives" with Gizem Korpeoglu (TU/e)
Manufacturing & Service Operations Management, Major Revision.
Accepted at Supply Chain Management SIG conference: M&SOM, London, UK, June 2025
Problem definition: Consumer cooperatives are consumer-owned and managed enterprises that aim to achieve buyer power and maximize their members’ welfare. Recently, several cooperatives in major economies, such as the United Kingdom (UK), Italy, and Switzerland, have merged to increase their buyer power and provide lower prices for their members. We seek to understand how these mergers affect market outcomes and consumer welfare. Methodology/results: We build a game-theoretic model of a two-tier supply chain where multiple consumer cooperatives procure a product from a market on behalf of their member consumers. Multiple suppliers produce for this market and can increase their supply by incurring a scale-up cost. We show that mergers of cooperatives reduce the wholesale price, as intended. This enables consumers to allocate more of their income to purchasing other goods, which improves consumer welfare. However, the lower price also induces suppliers to reduce their production quantities, thereby causing each consumer to receive less of the supplied product, which reduces consumer welfare. We find that this underproduction is even more pronounced in industries with low scale-up costs. Thus, we show that mergers harm all consumers when the pre-merger number of cooperatives or the production scale-up cost is below a certain threshold. Otherwise, mergers benefit all consumers. We expand our results by considering horizontally and vertically differentiated cooperatives and show that our main results are robust. We also show that greater differentiation among cooperatives increases the benefit of mergers. Managerial implications: Mergers of cooperatives make a nuanced impact on consumer welfare due to their effect on wholesale prices and production incentives. Policymakers should maintain healthy competition among cooperatives to maximize consumer welfare, especially in markets with low production scale-up costs.
2. “A Machine Learning Framework for Project Performance Prediction, Interpretation, and Inference” with Xiaochen Gao (UCSD), Vish Krishnan (UCSD), Lakshmi Nittala (Dayton), and Siqi Wang (UCSD)
Under Review.
In the knowledge economy, project performance is central to enterprise functioning, growth, and renewal. However, a significant proportion of real-world, public projects worldwide experience schedule and cost overruns. In this paper, we offer a data-driven machine-learning-based analytic pipeline to predict, interpret, and infer the nature and severity of cost or schedule overrun a project will experience. We find that a carefully curated machine learning approach can help achieve superior prediction metrics. In addition, we build a novel metric to identify and interpret at a granular level the top predictors that contribute to cost or schedule overrun and the severity of each variable. We also investigate the impact of contract pricing types and contract incentives on project performance using a double machine learning model. We confirm the influence of contract pricing on project performance but also find that existing project incentives are lacking in effectiveness in managing cost and schedule overruns. Despite popular belief, cost and performance incentives, when combined with fixed-price contracts, seem to cause additional cost and schedule overruns. However, performance incentives can mitigate cost overrun when offered with cost-plus contracts. Our analysis and results underscore the need for the government and other enterprises to collect and utilize the data for predictive and causal analysis and to develop more nuanced approaches and incentives to tackle cost and schedule overruns in real-world project settings.
3. “Curated Contests,” with Lakshmi Nittala (Dayton) and Vish Krishnan (UCSD)
Management Science, Reject & Resubmit
Firms seeking solutions to their innovation problems have attempted to use the contest format to source solutions from a broader network of solvers. However, sourcing quality solutions for complex problems has proven to be challenging as real-world contests end without satisfactory solutions for the seeker. Contestants may simply lack the resources and guidance to tackle complex innovation problems. To leverage the contest mechanism for sourcing solutions to complex problems, we propose a hybrid approach called the Curated Contest - in which firms benefit from competition among contestants but also engage in curation, by sifting and screening intermediate contestant submissions and potentially offering various forms of support for developing proof of concept and validating ideas. However, contest-curation must take into account that screening itself may be imperfect and that there may be information asymmetries between solution seekers and skeptical contestants. In the current paper, we provide guidance to the solution-seeking firm on when and how to organize such curated contests. We find that screening can stimulate additional effort from contestants. Firms can gain solver credibility by fine-tuning the reward size and other support schemes including late-stage compensation and proof of concept cost-sharing. We present a managerial framework to help design a carefully curated contest, which can help firms realize more effort from contestants.
4. “Firm Clockspeed: Toward a Theory of Relativity," with Glen Schmidt (Utah)
Final preparation for submission.
In physics, an object's speed depends on the observer's frame of reference; one observer may perceive a high speed while another observes it to be slow. Similarly, one observer might measure a firm's clockspeed based on its rapidity of product development cycles (this is the frame of reference taken in extant literature -- we denote this as the firm's perceived clockspeed) while a second observer may use economic growth as the frame of reference (we call this the absolute clockspeed) and a third observer might look at firm profit (we denote this as the firm's relative clockspeed). For example, Intel has a very fast perceived clockspeed relative to Pfizer yet both Intel and Pfizer achieve roughly the same profit and growth, with roughly the same revenue and R&D investment. To account for these three frames of reference we define the perceived, relative, and absolute clockspeed measures, and develop a model to study their interrelationships. Our work leads to a portfolio of strategies that a firm can use to increase its profit (i.e., to increase the absolute and relative clockspeed measures).
5. “Information Disclosure under Competition," with Ersin Korpeoglu (UCL), Glen Schmidt (Utah), and Vish Krishnan (UCSD)
Initial results complete.
6. “Multi-Stage Contests with Multi-Path Search,” with Ersin Korpeoglu (UCL) and Aydin Alptekinoglu (Penn State)
Initial results complete.
We prove that knowledge and information sharing in multi-stage contests with multi-path search can stimulate higher aggregate effort relative to settings with no information or knowledge sharing. We then discuss how knowledge and information should be disclosed for different project types.
“Training and Effort Dynamics in Apprenticeship,” Summer 2017
Drew Fudenberg (MIT) and Luis Rayo (Kellogg), American Economic Review 109(11), 2019
“Relational Knowledge Transfers,” Summer 2016
Luis Garicano (LSE) and Luis Rayo, American Economic Review 107(9), 2017.
“Why Organizations Fail: Models and Cases,” Summer 2015
Luis Garicano and Luis Rayo, Journal of Economic Literature 54(1), 2016.