Two players play an unknown zero-sum repeated game. Before the game starts one player may receive signals, whose nature is specified by an information structure, regarding the game actually played. We characterize when one information structure is better for the maximizer than another. We also...

A geometric approach, analogous to the approach used in the additive case, is proposed to determine the conditional expectation with non- additive probabilities. The conditional expectation is then applied for (i) updating the probability when new information becomes available; and (ii) defining...

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...

A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform measure.

Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential stochastic signals that depend on the actual state of nature. These signals provide the players with partial information about the state of nature and may also serve as a...

Aumann 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 $E$...

Real world players often increase their payoffs by voluntarily committing to play a fixed strategy, prior to the start of a strategic game. In fact, the players may further benefit from commitments that are conditional on the commitments of others. This paper proposes a model of conditional...

Subjective utility maximizers, in an infinitely repeated game, will learn to predict opponents' future strategies and will converge to play according to a Nash equilibrium of the repeated game. Players' initial uncertainty is placed directly on opponents' strategies and the above result is...