Distributed Prediction Markets modeled by Weighted Bayesian Graphical Games

We consider a novel, yet practical setting of prediction markets called distributed prediction markets, where the aggregated price of a security of an event in one prediction market is affected dynamically by the prices of securities of similar events in other, simultaneously running prediction markets. We focus on the problem of decision making facing a market maker to determine the price of a security within such a setting. We propose a formal framework based on graphical games called a weighted Bayesian graphical game (WBGG) to model the distributed prediction market setting and to capture the local interactions between multiple market makers. We then describe a distributed message passing algorithm based on NashProp algorithm to calculate the Bayes-Nash equilibrium in a WBGG. We provide analytical results including convergence and incentivizing truthful revelation among market makers. Our experimental results show that market makers that consider the influence of other market makers in a distributed prediction market setting while using our proposed WBGG-based algorithm obtain higher utilities and set prices more accurately in comparison to market makers using a greedy strategy to set prices or those that do not consider the influence of other market makers. We also observe that extreme sizes of the neighborhood of a market maker have an adverse impact on its utilities.