We introduce the concepts of joint games and compatibility. In a joint game, members of the grand coalition have the option to split and maximize their total worths, over different games. In order to determine whether the grand coalition will remain intact, we introduce the notion of...

Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential signals that stochastically depend on the actual state of nature. These signal not only provide the players with partial information about the state of nature but also serve...

In a decision problem with uncertainty a decision maker receives partial information about the actual state via an information structure. After receiving a signal he is allowed to withdraw and get 0. We say that one structure is weakly better than another if it may never happen that the latter...

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...