We consider interactive epistemic models where individuals are described by both their ""knowledge"" and their ""beliefs."" Three intersubjective consistency conditions are examined: Intersubjective Caution (if an individual believes something to be common belief then he knows it to be common...

When we make a non-trivial prediction about the future we select, among the conceivable future descriptions of the world, those that appear to us to be most likely. Within a branching-time framework we capture this by means of two binary relations, c and p. If t1 and t2 are different points in...

The logical foundations of game-theoretic solution concepts have so far been developed within the confines of epistemic logic. In this paper we turn to a different branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play....

We provide a self-contained, selective overview of the literature on the role of knowledge and beliefs in game theory. We focus on recent results on the epistemic foundations of solution concepts, including correlated equilibrium, rationalizability in dynamic games, forward and backward induction.

The logic of common belief does not always reflect the logic of individual beliefs. In particular, the Negative Introspection property fails at the common belief level, that is, it can happen that neither is A commonly believed nor is it common belief that A is not commonly believed. Indeed...

In (Bonanno, 2013), a solution concept for extensive-form games, called perfect Bayesian equilibrium (PBE), was introduced and shown to be a strict refinement of subgame-perfect equilibrium; it was also shown that, in turn, sequential equilibrium (SE) is a strict refinement of PBE. In (Bonanno,...

This is a draft of the first half of an open access textbook on game theory. I hope to complete the entire book by the end of 2015. After teaching game theory (at both the undergraduate and graduate level) at the University of California, Davis for 25 years, I decided to organize all my teaching...

In (5) a solution concept for extensive-form games was introduced, called perfect Bayesian equilibrium (PBE), and shown to be a strict refinement of subgame-perfect equilibrium; it was also shown that, in turn, sequential equilibrium (SE) is a strict refinement of PBE. In (6) the notion of PBE...

In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the choice structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in...

We consider decision problems under complete ignorance and extend the minimax regret principle to situations where, after taking an action, the decision maker does not necessarily learn the state of the world. For example, if the decision maker only learns what the outcome is, then all she knows...