# Online Prediction with Selfish Experts

arXiv: https://arxiv.org/abs/1702.03615 · HTML: https://mlsanity.com/paper/1702.03615/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2017.

## Built on by (most cited first, 10 of 10)

- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Online Learning from Strategic Human Feedback in LLM Fine-Tuning](https://mlsanity.com/paper/2412.16834/) (2024)
- [Efficient Competitions and Online Learning with Strategic Forecasters](https://mlsanity.com/paper/2102.08358/) (2021)
- [Scoring Rules for Performative Binary Prediction](https://mlsanity.com/paper/2207.02847/) (2022)
- [Trading-Off Payments and Accuracy in Online Classification with Paid Stochastic Experts](https://mlsanity.com/paper/2307.00836/) (2023)
- [The Battling Influencers Game: Nash Equilibria Structure of a Potential Game and Implications to Value Alignment](https://mlsanity.com/paper/2502.01127/) (2025)
- [No-Regret Online Prediction with Strategic Experts](https://mlsanity.com/paper/2305.15331/) (2023)
- [On the price of exact truthfulness in incentive-compatible online learning with bandit feedback: A regret lower bound for WSU-UX](https://mlsanity.com/paper/2404.05155/) (2024)
- [No-regret incentive-compatible online learning under exact truthfulness with non-myopic experts](https://mlsanity.com/paper/2502.11483/) (2025)
- [Truthful Online Preference Aggregation for LLM Fine-Tuning in Mobile Crowdsourcing](https://mlsanity.com/paper/2605.24052/) (2026)

## Abstract (arXiv)

We consider the problem of binary prediction with expert advice in settings where experts have agency and seek to maximize their credibility. This paper makes three main contributions. First, it defines a model to reason formally about settings with selfish experts, and demonstrates that "incentive compatible" (IC) algorithms are closely related to the design of proper scoring rules. Designing a good IC algorithm is easy if the designer's loss function is quadratic, but for other loss functions, novel techniques are required. Second, we design IC algorithms with good performance guarantees for the absolute loss function. Third, we give a formal separation between the power of online prediction with selfish experts and online prediction with honest experts by proving lower bounds for both IC and non-IC algorithms. In particular, with selfish experts and the absolute loss function, there is no (randomized) algorithm for online prediction-IC or otherwise-with asymptotically vanishing regret.