One approach to representing knowledge or belief of agents, used by economists and computer scientists, involves an infinite hierarchy of beliefs. Such a hierarchy consists of an agent's beliefs about the state of the world, his beliefs about other agents' beliefs about the world, his beliefs...

We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn...

Playersʼ beliefs may be incompatible, in the sense that player i can assign probability 1 to an event E to which player j assigns probability 0. One way to block incompatibility is to assume a common prior. We consider here a different approach: we require playersʼ beliefs to be conservative,...

For some well-known games, such as the Travelerʼs Dilemma or the Centipede Game, traditional game-theoretic solution concepts—most notably Nash equilibrium—predict outcomes that are not consistent with empirical observations. We introduce a new solution concept, iterated regret...

In earlier work (Halpern and Rêgo, 2009), we proposed a logic that extends the Logic of General Awareness of Fagin and Halpern (1988) by allowing quantification over primitive propositions. This makes it possible to express the fact that an agent knows that there are some facts of which he is...

Many different rules for decision making have been introduced in the literature. We present a single framework in which to study and compare these rules. This is done by defining expected utility with respect to general expectation structures, where a decision maker's beliefs are represented by...

I consider issues in distributed computation that should be of relevance to game theory. In particular, I focus on (a) representing knowledge and uncertainty, (b) dealing with failures, and (c) specification of mechanisms.

Many different rules for decision making have been introduced in the literature. We show that a notion of generalized expected utility proposed in 'Great Expectations. Part I' is a universal decision rule, in the sense that it can represent essentially all other decision rules.

Modica and Rustichini [Theory and Decision 37, 1994] provided a logic for reasoning about knowledge where agents may be unaware of certain propositions. However, their original approach had the unpleasant property that nontrivial unawareness was incompatible with partitional information...

Aumann has proved that common knowledge of substantive rationality implies the backwards induction solution in games of perfect information. Stalnaker has proved that it does not. Roughly speaking, a player is substantively rational if, for all vertices $v$, if the player were to reach vertex...