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 (2018). 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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