Subsidized Prediction Mechanisms for Risk-Averse Agents

In this article, we study the design and characterization of sequential prediction mechanisms in the presence of agents with unknown risk aversion. We formulate a collection of desirable properties for any sequential forecasting mechanism. We present a randomized mechanism that satisfies all of these properties, including a guarantee that it is myopically optimal for each agent to report honestly, regardless of her degree of risk aversion. We observe, however, that the mechanism has an undesirable side effect: each agent's expected reward, normalized against the inherent value of her private information, decreases exponentially with the number of agents. We prove a negative result showing that this is unavoidable: any mechanism that is myopically strategyproof for agents of all risk types, while also satisfying other natural properties of sequential forecasting mechanisms, must sometimes result in a player getting an exponentially small expected normalized reward.