Preventing Arbitrage from Collusion When Eliciting Probabilities

We consider the design of mechanisms to elicit probabilistic forecasts when agents are strategic and may collude with one another. Chun and Shachter [2011] have shown that when agents may form coalitions, many known mechanisms for elicitation permit arbitrage, allowing the coalition members to guarantee themselves higher payments by misreporting their beliefs. We consider two approaches to protect against colluding agents. First, we present a novel strictly proper mechanism that does not admit arbitrage provided that the reports of the agents are bounded away from 0 and 1, a common assumption in many settings. Second, we discover weakly proper mechanisms that are fully arbitrage free for general beliefs. We show that a subclass of these mechanisms satisfies an appealing and natural intermediate guarantee, in between weak and strict, that preserves many of the advantages of strictly proper mechanisms.