1 A NOTE ON THE SUBTLETIES OF BAYESIAN INFERENCE Giacomo Bonanno 1 Department of Economics, University of California, Davis, CA 95616-8578. U.S.A. e-mail: gfbonanno@ucdavis.edu July, 1996 The Bayesian approach plays a central role in economics, decision theory and game theory. Bayesianism is usually characterized as the philosophical view that probability can be interpreted subjectively and that the rational way to assimilate information into one’s structure of beliefs is by a process called “conditionalization”. Thus Bayesianism has a static part and a dynamic part. The former asserts that a coherent set of beliefs can be represented by a probability function over sentences or events (see De Finetti, 1937, Ramsey, 1931, Savage, 1954, and, for a recent survey, Hammond, in press). The dynamic part of Bayesian theory asserts that rational change of beliefs, in response to new evidence, goes by conditionalization: if the individual starts with a subjective probability distribution P o and observes E, where P o (E) > 0, then her new beliefs should be given by the probability distribution P n defined as follows: for every event A, P n (A) = P A E P E o o ( ) ( ) ∩ . The conditionalization rule thus says that the correct way to accommodate a piece of information into a belief set is by revising the initial subjective probabilities according to Bayes’ rule. We refer to this as “Bayesian inference”. There is an ongoing debate in the philosophical 1 I am grateful to Klaus Nehring for helpful comments and to Ignacio Ortuno-Ortin for bringing Nalebuff’s contribution to my attention.