A Mechanism-Design Approach to Speculative Trade

When agents hold non-common priors over an unverifiable state of nature which affects the outcome of their future actions, they have an incentive to bet on the outcome. We pose the following question: what are the limits on the agents' ability to realize gains from speculative bets when their prior belief is private information? We apply a 'mechanism design' approach to this question, in the context of a pair of models: a principal-agent model in which the two parties bet on the agent's future action, and a market model in which traders bet on the future price. We characterize interim-efficient bets in these environments, and their implementability as a function of fundamentals. In general, implementability of interim-efficient bets diminishes as the costs of manipulating the bet's outcome become more uneven across states or agents.