Removing arbitrage from wagering mechanisms

Abstract

We observe that Lambert et al.'s [2008] family of weighted score wagering mechanisms admit arbitrage: participants can extract a guaranteed positive payoff by betting on any prediction within a certain range. In essence, participants leave free money on the table when they ``agree to disagree,'' and as a result, rewards don't necessarily go to the most informed and accurate participants. This observation suggests that when participants have immutable beliefs, it may be possible to design alternative mechanisms in which the center can make a profit by removing this arbitrage opportunity without sacrificing incentive properties such as individual rationality, incentive compatibility, and sybilproofness. We introduce a new family of wagering mechanisms called no-arbitrage wagering mechanisms that retain many of the positive properties of weighted score wagering mechanisms, but with the arbitrage opportunity removed. We show several structural results about the class of mechanisms that satisfy no-arbitrage in conjunction with other properties, and provide examples of no-arbitrage wagering mechanisms with interesting properties.