Twofold Multiprior Preferences and Failures of Contingent Reasoning

We propose a model of incomplete \textit{twofold multiprior preferences}, in which an act \(f\) is ranked above an act \(g\) only when \(f\) provides higher utility in a worst-case scenario than what \(g\) provides in a best-case scenario. The model explains failures of contingent reasoning, captured through a weakening of the state-by-state monotonicity (or dominance) axiom. Our model gives rise to rich comparative statics results, as well as extension exercises, and connections to choice theory. We present an application to second-price auctions.