A necessary and sufficient condition for the existence of a common prior for several players is given in terms of the players' present beliefs only. A common prior exists, if for each random variable it is common knowledge that all its iterated expectations converge to the same value; this value...

A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. We show that, if beliefs given a union of two databases are a convex combination of beliefs given each of the databases, the...

In two famous and popular puzzles a participant is required to compare two numbers of which she is shown only one. The first puzzle is known as the paradox of the double sum, the second, due to Cover is known as "which is the larger number". Although the puzzles have been discussed and explained...

Harsanyi's utilitarianism is extended here to Savage's framework. We formulate a Pareto condition that implies that both society's utility function and its probability measure are linear combinations of those of the individuals. An indiscriminate Pareto condition has been shown to contradict...

In their seminal paper, Mertens and Zamir (1985) proved the existence of a universal Harsanyi type space which consists of all possible types. Their method of proof depends crucially on topological assumptions. Whether such assumptions are essential to the existence of a universal space remained...

The literary source of the main ideas in Aumann's article "Backward Induction and Common Knowledge of Rationality" is exposed and analyzed. The primordial archetypal images that underlie both this literary source and Aumann's work are delineated and are used to explain the great emotive impact...

The three notions studied here are Bayesian priors, invariant priors and introspection. A prior for an agent is Bayesian, if it agrees with the agent's posterior beliefs when conditioned on them. A prior is invariant, if it is the average, with respect to itself, of the posterior beliefs....

Aumann has shown that agents who have a common prior cannot have common knowledge of their posteriors for event E if these posteriors do not coincide. But given an event E, can the agents have posteriors with a common prior such that it is common knowledge that the posteriors for E do coincide?...