Mean-preserving contractions are critical for studying Bayesian models of information design. We introduce the class of bi-pooling policies, and the class of bi-pooling distributions as their induced distributions over posteriors. We show that every extreme point in the set of all...

In his seminal work, Nash (1950) derives a solution for two-person bargaining problems, within a cooperative setup. Nash assumes that the result of disagreement is known to both players and is not stochastic. We study the same problem, where the last assumption is relaxed. We provide a set of...

Bayesian Statisticians, decision theorists, and game theorists often use Bayesian representations to describe the probability distribution governing the evolution of a stochastic process. Generally, however, one given distribution has infinitely many different Bayesian representations. This...

The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v(S) of a coalition S is a function f of ?(S) where ? is a vector measure. Special classes of...