Bounded Rationality in Wagering Mechanisms

David Pennock, Vasilis Syrgkanis, Jennifer Wortman Vaughan
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:495-504, 2016.

Abstract

Wagering mechanisms allow decision makers to inexpensively collect forecasts from groups of experts who reveal their information via bets with one another. Such mechanisms naturally induce a game in which strategic considerations come into play. What happens in the game depends on the reasoning power of the experts. At one extreme, if experts are fully rational, no-trade theorems imply no participation. At the other extreme, if experts ignore strategic considerations, even the least informed will wager as if his beliefs are correct. Economists have analyzed the former case and decision theorists the latter, but both are arguably unrealistic. In this paper, we adopt an intermediate model of bounded rationality in wagering mechanisms based on level-k reasoning. Under this model, overconfidence allows some participation to be sustained, but experts who realize they are at a relative disadvantage do bow out. We derive conditions on the particular wagering mechanism used under which participation is unbiased, and show that unbiasedness always implies truthful reports. We show that if participation is unbiased, then participation rates unavoidably fall as players’ rationality increases, vanishing for large k. Finally, we zoom in on one particular information structure to give a complete characterization specifying the conditions under which mechanisms are unbiased and show how to maximize participation rates among all unbiased mechanisms.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-pennock16a, title = {Bounded Rationality in Wagering Mechanisms}, author = {Pennock, David and Syrgkanis, Vasilis and Vaughan, Jennifer Wortman}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {495--504}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/pennock16a/pennock16a.pdf}, url = {https://proceedings.mlr.press/r14/pennock16a.html}, abstract = {Wagering mechanisms allow decision makers to inexpensively collect forecasts from groups of experts who reveal their information via bets with one another. Such mechanisms naturally induce a game in which strategic considerations come into play. What happens in the game depends on the reasoning power of the experts. At one extreme, if experts are fully rational, no-trade theorems imply no participation. At the other extreme, if experts ignore strategic considerations, even the least informed will wager as if his beliefs are correct. Economists have analyzed the former case and decision theorists the latter, but both are arguably unrealistic. In this paper, we adopt an intermediate model of bounded rationality in wagering mechanisms based on level-k reasoning. Under this model, overconfidence allows some participation to be sustained, but experts who realize they are at a relative disadvantage do bow out. We derive conditions on the particular wagering mechanism used under which participation is unbiased, and show that unbiasedness always implies truthful reports. We show that if participation is unbiased, then participation rates unavoidably fall as players’ rationality increases, vanishing for large k. Finally, we zoom in on one particular information structure to give a complete characterization specifying the conditions under which mechanisms are unbiased and show how to maximize participation rates among all unbiased mechanisms.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Bounded Rationality in Wagering Mechanisms %A David Pennock %A Vasilis Syrgkanis %A Jennifer Wortman Vaughan %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-pennock16a %I PMLR %P 495--504 %U https://proceedings.mlr.press/r14/pennock16a.html %V R14 %X Wagering mechanisms allow decision makers to inexpensively collect forecasts from groups of experts who reveal their information via bets with one another. Such mechanisms naturally induce a game in which strategic considerations come into play. What happens in the game depends on the reasoning power of the experts. At one extreme, if experts are fully rational, no-trade theorems imply no participation. At the other extreme, if experts ignore strategic considerations, even the least informed will wager as if his beliefs are correct. Economists have analyzed the former case and decision theorists the latter, but both are arguably unrealistic. In this paper, we adopt an intermediate model of bounded rationality in wagering mechanisms based on level-k reasoning. Under this model, overconfidence allows some participation to be sustained, but experts who realize they are at a relative disadvantage do bow out. We derive conditions on the particular wagering mechanism used under which participation is unbiased, and show that unbiasedness always implies truthful reports. We show that if participation is unbiased, then participation rates unavoidably fall as players’ rationality increases, vanishing for large k. Finally, we zoom in on one particular information structure to give a complete characterization specifying the conditions under which mechanisms are unbiased and show how to maximize participation rates among all unbiased mechanisms. %Z Reissued by PMLR on 04 October 2026.
APA
Pennock, D., Syrgkanis, V. & Vaughan, J.W.. (2016). Bounded Rationality in Wagering Mechanisms. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:495-504 Available from https://proceedings.mlr.press/r14/pennock16a.html. Reissued by PMLR on 04 October 2026.

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