On Universal Prediction and Bayesian Confirmation

The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not always available or fail, in particular in complex situations. Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. We discuss in breadth how and in which sense universal (non-i.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. We show that Solomonoff's model possesses many desirable properties: Strong total and weak instantaneous bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the old-evidence and updating problem. It even performs well (actually better) in non-computable environments.Comment: 24 page

Equilibrium Play and Best Response in Sequential Constant Sum Games

We perform a further experiment to check the robustness of the main result in Rey Biel (2005) to sequential play. We find that Equilibrium predictions work even better when the same games are played sequentially: 85% of first movers choose the Equilibrium strategy and 85% of second movers best respond to the action taken by first movers. We conclude by identifying constant sum games as a class of games where experimental subjects' choices coincide with theory predictions and we argue that in such games distributional and reciprocal preferences do not influence subjects' decisions.Experiments, Constant Sum Games, Best Response