Revealed preference analysis of expected utility maximization under prize-probability trade-offs

We provide a revealed preference characterization of expected utility maximization in binary lotteries with prize-probability trade-offs. This characterization applies to a wide variety of decision problems, including first price auctions, crowdfunding games, posted price mechanisms and principal agent problems. We start by characterizing optimizing behavior when the empirical analyst exactly knows either the probability function of winning or the decision maker’s utility function. Subsequently, we provide a statistical test for the case where the utility function is unknown and the probability function has to be estimated. Finally, we consider the situation with both the probability function and utility function unknown. We show that expected utility maximization has empirical content when these functions satisfy log-concavity assumptions. We demonstrate the empirical usefulness of our theoretical findings through an application to an experimental data set.

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