A decision maker faces an unobserved state of nature. She updates her prior on the state based on the realizations of a signal. In this note, we show that the expected posterior on any given state, taking expectation under the conditional distribution of the signal on this same state, is never...

The expected value of the log of a Bayesian’s posterior assessment of the true state of nature, computed under the probability law of the true state, is always at least as large as the log of the prior.

The problemof choosing an optimal toolkit day after day,when there is uncertainty concerning the value of different tools that can only be resolved by carrying the tools, is a multi-armed bandit problem with nonindependent arms. Accordingly, except for very simple specifications, this...

This paper addresses the problem of sequentially allocating time sensitive goods, or one-period leases on a durable good, among agents who compete through time and learn about the common component of their valuation privately through experience. I show that efficiency is unattainable, and I...

Many choice-theoretic and game-theoretic applications in Economics invoke some form of supermodularity or increasing differences for objective functions defined on lattices. These notes provide axiomatic foundations for these properties on expected-utility representations of preferences over...

A decision maker can experiment on up to two alternatives simultaneously over time. One and only one of these alternatives can produce successes, according to a Poisson process with known arrival rate; but there is uncertainty as to which alternative is the profitable one. The decision maker only...

This paper addresses the problem of sequentially allocating timesensitive goods, or one-period leases on a durable good, among agents who compete through time and learn about the common component of the value of the allocation through experience. I show that efficiency is unattainable, and I...