Selling to a naive agent with two rationales ∗

A seller is selling an object to an agent who uses two rationales to compare pairs of outcomes (allocation probability, transfer) pairs. Each rationale is generated by quasilinear preference over the outcome space, and hence, can be represented by a valuation. However, the agent faces a budget constraint when making decisions using the first rationale. The agent compares any pair of outcomes using his pair of valuations in a lexicographic manner: first, he compares using the valuation corresponding to the first rationale; then, he compares using the valuation corresponding to the second rationale if and only if the first rationale cannot compare (due to budget constraint). We show that the optimal mechanism is either a posted price mechanism or a mechanism involving a pair of posted prices (a menu of three outcomes). In the latter case, the optimal mechanism involves randomization and pools types in the middle. JEL Codes: D82, D40, D90