Dynamic Pari-mutuel Market

    In a pari-mutuel wagering game, players wager money on the outcome of an uncertain future event, competing against each other to earn a portion of the total pool of money wagered by all players. Players can purchase at any time an outcome-contingent equal share of the pool for a constant price, say $1. We describe and analyze the game induced by the dynamic pari-mutuel market (DPM) mechanism, a dynamic-cost variant of the pari-mutuel wagering mechanism. As before, traders compete for a share of the total money wagered, however the cost of a single share varies dynamically with time according to a cost function that depends on wagering activity so far, thus allowing traders to sell their shares prior to the determination of the outcome for profits or losses. From a trader’s perspective, the mechanism resembles a continuous double auction with a market maker always willing to except both buy and sell orders at some price. We derive a particularly natural cost function called the share-ratio cost function, which equates the ratio of prices of any two outcomes with the ratio of number of shares outstanding for the two outcomes. We prove that the share-ratio cost function induces an arbitrage-free mechanism and ensures that wagers on the correct outcome can never lose money. We examine trader strategies in the DPM game. We analyze real traders’ behaviors in a live system implementing the DPM in a public game.