Abstract
We study the computation of equilibria in prediction markets in perhaps the most fundamental special case with two players and three trading opportunities. To do so, we show equivalence of prediction market equilibria with those of a simpler signaling game with commitment introduced by Kong and Schoenebeck [18]. We then extend their results by giving computationally efficient algorithms for additional parameter regimes. Our approach leverages a new connection between prediction markets and Bayesian persuasion, which also reveals interesting conceptual insights.
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Notes
- 1.
This is a slight departure from the formalization of the game in [18]. There, Alice did not automatically observe Bob’s signal, causing complications in the case where Bob’s report \(\mathbf {p}_{S,B}\) could be the same for two different outcomes \(b,b' \in \mathcal {B}\).
- 2.
Such a signaling scheme is also called an experiment by Kolotilin et al. [17]. We remark that their model is a special case of the general model we described here, with independent A, B and binary receiver actions.
- 3.
Note that if \(\lambda > 1\) in the \(\lambda \)-nice condition, or if \(\beta > 1\) in the \((\alpha ,\beta )\)-local Hölder continuity condition, then G is identically zero so we are not interested in those trivial cases.
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Anunrojwong, J., Chen, Y., Waggoner, B., Xu, H. (2019). Computing Equilibria of Prediction Markets via Persuasion. In: Caragiannis, I., Mirrokni, V., Nikolova, E. (eds) Web and Internet Economics. WINE 2019. Lecture Notes in Computer Science(), vol 11920. Springer, Cham. https://doi.org/10.1007/978-3-030-35389-6_4
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