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....

This survey captures the main contributions in the area described by the title that were published up to 1997. (Unfortunately, it does not capture all of them.) The variations that are the subject of this chapter are those axiomatically characterized solutions which are obtained by varying...

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?...

There are four types of dominance depending on whether domination is strict or weak and whether the dominating strategy is pure or mixed. Letting d vary over these four types of dominance, we say that a player is d-dominance rational when she does not play a strategy that is d-dominated relative...