In order to identify expertise, forecasters should not be tested by their calibration score, which can always be made arbitrarily small, but rather by their Brier score. The Brier score is the sum of the calibration score and the refinement score; the latter measures how good the sorting into...

Although there exist learning processes for which the empirical distribution of play comes close to Nash equilibrium it is an open question whether the players themselves can learn to play equilibrium strategies without assuming that they have prior knowledge of their opponents' strategies...

Information theory offers a coherent perspective on model selection. As in Rissanen's original application of information theory to model selection, our perspective arises from viewing a model as a component of a compressed representation of data in a two-part code. The first part of such a code...

Over the past few years many proofs of calibration have been presented (Foster and Vohra (1991, 1997), Hart (1995), Fudenberg and Levine (1995), Hart and Mas-Colell (1996)). Does the literature really need one more? Probably not, but this algorithim for being calibrated is particularly simple...

We propose a framework for reconciling frequentist and subjectivist views of probability. In an environment with repeated trails we show that beliefs about the possible states of nature can be represented by probabilities. Second, these probabilities will correspond to long run frequencies. In...

A learning rule is uncoupled if a player does not condition his strategy on the opponent's payoffs. It is radically uncoupled if a player does not condition his strategy on the opponent's actions or payoffs. We demonstrate a family of simple, radically uncoupled learning rules whose...

We provide an axiomatic characterization of the measure of riskiness of gambles (risky assets) introduced by Foster and Hart (2009). The axioms are based on the concept of "wealth requirement."