It is generally agreed that the minimax solution to a two-person zero-sum matrix game is intuitively satisfactory. Now in many applications of game theory, a game is not described a priori in matrix (or "normal" or "strategic") form, but rather in extensive form, i.e., by its rules. A game...

In recent decades, subjective probabilities have been increasingly applied to an adversary's choices in strategic games (SGs). In games against nature (GANs), the subjective probability of a state can be elicited from lotteries yielding utility 1 if that state obtains, 0 otherwise. But in SGs,...

This document contains four separate analyses, each with a different author, of the "Gans" committee report on the Bible codes (DP 364 of the Center for the Study of Rationality, June 2004). The analyses appear in alphabetical order of the authors' names. Three of the authors were members of the...

Modern game theory was born in 1928, when John von Neumann published his Minimax Theorem. This theorem ascribes to all two-person zero-sum games a value–what rational players may expect–and optimal strategies–how they should play to achieve that expectation. Seventyseven years later,...

Consciousness is the last great frontier of science. Here we discuss what it is, how it differs fundamentally from other scientific phenomena, what adaptive function it serves, and the difficulties in trying to explain how it works. The emphasis is on the adaptive function.

In recent decades, the concept of subjective probability has been increasingly applied to an adversary’s choices in strategic games. A careful examination reveals that the standard construction of subjective probabilities does not apply in this context. We show how the difficulty may be...