We introduce a new operator on information structures which we call `knowing whether' as opposed to the standard knowledge operator which may be called `knowing that'. The difference between these operators is simple. Saying that an agent knows t h a t a certain event occurred implies that this...

We propose a new framework for bargaining in which the process follows an agenda. The agenda is represented by a family, parameterized by time, of increasing sets of joint utilities for possible agreements. This is in contrast to the single set used in the standard framework. The set at each...

We study a class of voting rules that bridge between majoritarianism and liberalism. An outcome of the vote specifies who among the voters are eligible to a certain right or qualification. Each outcome serves also as a permissible ballot. We characterize axiomatically a family of rules...

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...

We observe that the set of all priors of an agent is the convex hull of his types. A prior common to all agents exists, if the sets of the agents' priors have a point in common. We give a necessary and sufficient condition for the non-emptiness of the intersection of several closed convex...

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*...