Upon observing a signal, a Bayesian decision maker updates her probability distribution over the state space, chooses an action, and receives a payoff that depends on the state and the action taken. An information structure determines the set of possible signals and the probability of each...

We propose a new geometric approach for the analysis of cooperative games. A cooperative game is viewed as a real valued function $u$ defined on a finite set of points in the unit simplex. We define the \emph{concavification} of $u$ on the simplex as the minimal concave function on the simplex...

We present a model of categorization based on prototypes. A prototype is an image or template of an idealized member of the category. Once a set of prototypes is defined, entities are sorted into categories on the basis of the prototypes they are closest to. We provide a characterization of...

We suggest a model of categorization based on prototypes. A set of entities, identified with some finite dimensional Euclidian space, is partitioned into a finite number of categories. Such a categorization is said to be generated by extended prototypes if there is a set of distinguished...

Upon observing a signal, a Bayesian decision maker updates her probability distribution over the state space, chooses an action, and receives a payoff that depends on the state and the action taken. An information structure determines the set of possible signals and the probability of each...

A (TU) cooperative game is extendable if every core allocation of each subgame can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its subgames can be extended to a core allocation. We prove that strong extendability is...