Price of information in games of chance

Abstract

We consider a game where $N$ players bet on the outcome of a biased coin and share the entry fees pot if successful. We assume that one player holds information about past outcomes of the game, which they may either use exclusively to improve their betting strategy or offer to sell to another player. We determine analytically the optimal price curves for the data seller and the prospective buyer. We find a sharp transition in the number $N$ of players that separates a phase where the transaction is always profitable for the seller from one where it may not be. In both phases, different regimes are possible, depending on the "quality" of information being put up for sale: we observe symbiotic regimes, where both parties collude effectively to rig the game in their favor, competitive regimes, where the transaction is unappealing to the data holder as it overly favors a competitor for scarce resources, and even prey-predator regimes, where the data holder is eager to give away bad-quality data to undercut a competitor. Our framework can be generalized to more complex settings and constitutes a flexible tool to address the rich and timely problem of pricing information in games of chance.Comment: 18 pages, 6 figure