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...

A valuation for a board game is an assignment of numeric values to different states of the board. The valuation reflects the desirability of the states for the player. It can be used by a player to decide on her next move during the play. We assume a myopic player, who chooses a move with the...

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....

Several axioms concerning probabilistic beliefs are examined here, and the relations between them are established, using belief spaces that generalize Harsanyi type spaces. Two axioms concerning high-order probabilistic beliefs are investigated in particular. The first is the triviality axiom,...

That people estimate quantities, or have beliefs about them, is a daily observable phenomenon. People also quantify their beliefs, at least in theory, by ascribing to them probability numbers. It is shown that quantified beliefs and estimations give rise to the same model, that of a type space,...

In two famous and popular puzzles a participant is required to compare two numbers of which she is shown only one. In the first one there are two envelopes with money in them. The sum of money in one of the envelopes is twice as large as the other sum. An envelope is selected at random and...

According to the standard definition, a Bayesian agent is one who forms his posterior belief by conditioning his prior belief on what he has learned, that is, on facts of which he has become certain. Here it is shown that Bayesianism can be described without assuming that the agent acquires any...

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...