Andrés Perea (Maastricht)
Common belief in rationality in games with unawareness
Abstract: This talk will be about static games with unawareness, where players may be unaware of some of the choices that can be made. That is, different players may have different views on the game. We propose an epistemic model that encodes players' belief hierarchies on choices and views, and use it to formulate the basic reasoning concept of common belief in rationality. We also design a recursive elimination procedure that yields for every possible view the choices that can rationally be made under common belief in rationality.
Some Finitely Additive (Statistical) Decision Theory or How Bruno de Finetti might have channeled Abraham Wald
Abstract: We examine general decision problems with loss functions that are bounded below. We allow the loss function to assume the value infinity. No other assumptions are made about the action space, the types of data available, the types of non-randomized decision rules allowed, or the parameter space. By allowing prior distributions and the randomizations in randomized rules to be finitely additive, we prove very general complete class and minimax theorems. Specifically, under the sole assumption that the loss function is bounded below, we show that every decision problem has a minimal complete class and all admissible rules are Bayes rules. We also show that every decision problem has a minimax rule and a least-favorable distribution and that every minimax rule is Bayes with respect to the least-favorable distribution. Some special care is required to deal properly with infinite-valued risk functions and integrals taking infinite values. The talk is based on the paper, "What Finite Additivity Can Add to Decision Theory" -- Mark Schervish (CMU) Teddy Seidenfeld (CMU) Rafael Stern (Universidade Federal De São Carlos), and Jay Kadane (CMU), forthcoming in Statistical Methods and Applications.
Jan Sprenger (Turin)
Conditional Degrees of Belief and Bayesian Inference with Idealized Models
Abstract: Bayesian reasoners standardly interpret the probability of a statistical hypothesis, p(H), as their subjective degree of belief that this hypothesis is true. This "textbook Bayesianism", however, does not square well with the practice of statistical inference in science. In this contribution, I expound this dilemma and I develop a solution based on what I call the suppositional analysis of conditional degrees of belief. As I show, the analysis has important repercussions for all of Bayesian inference, including our interpretation of Bayes's Theorem.