Knowledge that Transforms

We analyze a nonlinear pricing model where the seller controls both product pricing (screening) and buyer information about their own values (persuasion). We prove that the optimal mechanism always consists of finitely many signals and items, even with a continuum of buyer values. The seller optimally pools buyer values and reduces product variety to minimize informational rents. We show that value pooling is optimal even for finite value distributions if their entropy exceeds a critical threshold. We also provide sufficient conditions under which the optimal menu restricts offering to a single item.

Pay-as-bid (or discriminatory or multiple-price) auctions are used to sell homogenous goods such as treasury securities and commodities.We prove the uniqueness of their pure-strategy Bayesian Nash equilibrium and establish a tractable representation of equilibrium bids for symmetrically-informed bidders.Analyzing design, we show that supply transparency and full disclosure are revenue-maximizing in pay as bid, though not necessarily in uniform-price (or single-price) auctions, the main alternative auction format.Pay as bid raises weakly more revenue than uniform price and may lead to higher welfare.Our results provide an explanation for the revenue equivalence observed in empirical studies of treasury auctions.

The measurement of intelligence should identify and measure an individual’s subjective confidence that a response to a test question is correct. Existing measures do not do that, nor do they use extrinsic financial incentive for truthful responses. We rectify both issues and show that each matters for the measurement of intelligence, particularly for women. Our results on gender and confidence in the face of risk have wider applications in terms of the measurement of “competitiveness” and financial literacy. Contrary to received literature, women are more intelligent than men, compete when they should in risky settings, and are more literate.

We study what changes to an agent's decision problem increase her value for information. We prove that information becomes more valuable if and only if the agent's reduced-form payoff in her belief becomes more convex. When the transformation corresponds to the addition of an action, the requisite increase in convexity occurs if and only if a simple geometric condition holds, which extends in a natural way to the addition of multiple actions. We apply these findings to two scenarios: a monopolistic screening problem in which the good is information and delegation with information acquisition.