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...

A learning process is belief affirming if for each player, the difference between her expected payoff in the next period, and the average of her past payoffs converges to zero. We show that every smooth discrete fictitious play and every continuous fictitious play is belief affirming. We also...

A standard model for a game with complete information consists of a state space with partitions, and a specification of the strategies played in each state. We show that such models are inadequate for explaining players' behavior. We propose instead extended models in which it is possible to...

Several authors have indicated a contradiction between consistent aggregation of subjective beliefs and tastes, and a Pareto condition. We argue that the Pareto condition that implies the contradiction is not compelling. Society should not necessarily endorse a unanimous choice when it is based...

Aumann(1976) 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*...

The type function of an agent, in a type space, associates with each state a probability distribution on the type space. Thus, a type function can be considered as a Markov chain on the state space. A common prior for the space turns out to be a probability distribution which is invariant under...

Shapley proved the existence of an ordinal, symmetric and efficient solution for three-player bargaining problems. Ordinality refers to the covariance of the solution with respect to order-preserving transformations of utilities. The construction of this solution is based on a special feature of...

We introduce a new solution concept for games in extensive form with perfect information: the valuation equilibrium. The moves of each player are partitioned into similarity classes. A valuation of the player is a real valued function on the set of her similarity classes. At each node a player...

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 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....