Non-myopic strategies in prediction markets

Abstract

One attractive feature of market scoring rules [Hanson, Information Systems Frontiers, 2003] is that they are myopically strategyproof: It is optimal for a trader to report her true belief about the likelihood of an event provided that we ignore the impact of her report on the profit she might garner from future trades. This does not rule out the possibility that traders may profit by first misleading other traders through dishonest trades and then correcting the errors made by other traders. In this paper, we describe a new approach to analyzing non-myopic strategies and the existence of myopic equilibria. We first use a simple model with two partially informed traders in a single information market to gain insight into the conditions under which different equilibrium behavior emerges. We prove that, under generic conditions, the myopically optimal strategy profile is not a weak Perfect Bayesian Equilibrium (PBE) strategy for the logarithmic market scoring rule. We show that our results extend to multiple traders and signals. We propose a simple discounted market scoring rule that reduces the opportunity for bluffing strategies. We show that in any weak PBE, myopic or otherwise, the market price converges to the optimal price, and the rate of convergence can be bounded in terms of the discounting parameter.