Rational Search with Learning (Job Market Paper)
I explore Bayes rational search for prizes (such as wages or prices) with learning. A searcher Sam is impatient and pays a cost for every search. He draws prize offers from a distribution with an uncertain mean, where observed draws constitute informative signals of the true mean via a location family with the monotone likelihood ratio property. A higher draw is myopically more inviting, but also raises expectations of better future draws. I show that a logconcave prior on the mean prize guarantees that a standard reservation rule is optimal. By contrast, in a highly uncertain environment with a heavy-tailed prior distribution, a sufficiently patient Sam accepts some prizes below those he rejects. I show that if Sam searches long enough, a reservation policy is once again optimal. With a prior over finitely many possible means, reservation policy failures arise with enough dispersion.
Why Sell Loot Boxes?
with Rodrigo Yañez
A monopolist sells an indivisible good to risk-averse consumers with unit demand who share a common valuation but differ in wealth. By selling a lottery that delivers the good stochastically, the firm effectively makes the good divisible. When consumers can purchase the lottery repeatedly, they optimally choose their number of attempts and hence their overall probability of receiving the good. Richer consumers choose more attempts, so the repeated lottery screens consumers by wealth and can generate more revenue than does a posted price. This repeated lottery is nevertheless dominated by a menu of one-shot lotteries. We show that selling bundles of a virtual currency that consumers then spend on lotteries closes the gap, rationalizing why this selling scheme is prevalent in video games.
Rational Snowballing in Financial Markets
This explores the Glosten-Milgrom market maker model with an uncertain fundamental distribution. A buy raises the next bid and ask prices, but also encourages the next trader about the fundamental. This paper studies whether trades make subsequent trades in the same direction more or less likely. I prove that with a logconcave noise density, buying discourages a subsequent buy, and selling likewise discourages another sell. In contrast, heavy-tailed noise leads to trade “snowballing,” where same side trades grow more likely over time. With two possible fundamental values, I show that equilibrium trading strategies, and thus trading probabilities, are time-invariant.