Abstract
Team formation is ubiquitous in many sectors: education, labor markets, sports, etc. A team’s success depends on its members’ latent types, which are not directly observable but can be (partially) inferred from past performances. From the viewpoint of a principal trying to select teams, this leads to a natural exploration-exploitation trade-off: retain successful teams that are discovered early, or reassign agents to learn more about their types? We study a natural model for online team formation, where a principal repeatedly partitions a group of agents into teams. Agents have binary latent types, each team comprises two members, and a team’s performance is a symmetric function of its members’ types. Over multiple rounds, the principal selects matchings over agents and incurs regret equal to the deficit in the number of successful teams versus the optimal matching for the given function. Our work provides a complete characterization of the regret landscape for all symmetric functions of two binary inputs. In particular, we develop team-selection policies that, despite being agnostic of model parameters, achieve optimal or near-optimal regret against an adaptive adversary.
Extended version with proofs can be found at https://arxiv.org/abs/2210.05795.
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Notes
- 1.
Except in the last round, where known (0, 0)-teams may be played; however, no (1, 1)-teams are played in this round.
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Acknowledgments
We would like to thank anonymous reviewers for useful feedback. Part of the work was done when SB and ME were visiting the Simons Institute for the Theory of Computing for the semester on Data-Driven Decision Processes; they also acknowledge support from the NSF under grants ECCS-1847393 and CNS-195599, and the ARO MURI grant W911NF1910217. DK acknowledges support from ARO MURI grant ARO W911NF1810208.
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Eichhorn, M., Banerjee, S., Kempe, D. (2022). Online Team Formation Under Different Synergies. In: Hansen, K.A., Liu, T.X., Malekian, A. (eds) Web and Internet Economics. WINE 2022. Lecture Notes in Computer Science, vol 13778. Springer, Cham. https://doi.org/10.1007/978-3-031-22832-2_5
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