Abstract
Our aim is to design mechanisms that motivate all agents to reveal their predictions truthfully and promptly. For myopic agents, proper scoring rules induce truthfulness. However, when agents have multiple opportunities for revealing information, and take into account long-term effects of their actions, deception and reticence may appear. Such situations have been described in the literature. No simple rules exist to distinguish between the truthful and the untruthful situations, and a determination has been done in isolated cases only. This is of relevance to prediction markets, where the market value is a common prediction, and more generally in informal public prediction forums, such as stock-market estimates by analysts. We describe three different mechanisms that are strategy-proof with non-myopic considerations, and show that one of them, a discounted market scoring rule, meets all our requirements from a mechanism in almost all prediction settings. To illustrate, we extensively analyze a prediction setting with continuous outcomes, and show how our suggested mechanism restores prompt truthfulness where incumbent mechanisms fail.
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Notes
- 1.
We use the notation \(p_x\) for the density of distribution \(\varvec{p}\) at x.
- 2.
The example is true for the logarithmic scoring rule because its scores are unbounded. Every scoring rule that values exact predictions over inexact ones sufficiently will do.
- 3.
Chen et al. (2010) use the same construction to generalize from Alice-Bob-Alice to a finite-players game.
- 4.
Note that the ideal of truth-telling as dominant strategy is not attainable here, because if a player is aware of another player’s distortion, the correct Bayesian response is to compensate for the distortion.
- 5.
This formulation is different from the mechanism of prediction markets, but equivalent to it. In prediction markets, an agent replaces the current market prediction by his own. In our formulation, the agent merely announces a prediction, which, assuming the agent is truthful, becomes the market prediction by Bayesian inference. This is because all rational agents reach the same beliefs from the same data.
- 6.
Technically, an uninformative prior may be envisioned as the limit of a uniform or normal distribution as the variance goes to infinity.
- 7.
A submodularity property is required of the signal lattice, in a context described in their article.
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Ban, A. (2018). Strategy-Proof Incentives for Predictions. In: Christodoulou, G., Harks, T. (eds) Web and Internet Economics. WINE 2018. Lecture Notes in Computer Science(), vol 11316. Springer, Cham. https://doi.org/10.1007/978-3-030-04612-5_4
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