We provide an introduction to interactive belief systems from a qualitative and semantic point of view. Properties of belief hierarchies are formulated locally. Among the properties considered are ""Common belief in no error"" (which has been shown to have important game theoretic applications),...

The temporal updating of an agent’s beliefs in response to a flow of information is modeled in a simple modal logic that, for every date t , contains a normal belief operator B_t and a non-normal information operator I_t which is analogous to the ‘only knowing’ operator discussed in the...

We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another...

We propose a logic based on three modal operators, representing intial beliefs, information and revised beliefs. Three simple and transparent axioms are used to provide a sound and complete axiomatization of the qualitative part of Bayes'' rule. Some theorems of this logic are derived concerning...

This is the first draft of the entry “Game Theory” to appear in the Sage Handbook of the Philosophy of Social Science (edited by Ian Jarvie & Jesús Zamora Bonilla), Part III, Chapter 16.

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...

Within the class of structures introduced in [G. Bonanno, Axiomatic characterization of the AGM theory of belief revision in a temporal logic, Artificial Intelligence, 171 (2007), 144-160] we consider the subclass satisfying the property that, for every state-instant pair (omega,t), there is an...

This paper surveys the evidence, theoretical and empirical, relating to the possibility of achieving more egalitarian distributions of income than are typical in modern societies. The first four parts of the paper (Introduction, Improving efficiency an equality, The ownership of firms, and...

The "Harsanyi Doctrine" asserts that differences in individuals'' beliefs are to be attributed entirely to differences in information. In its embodiment as a Common Prior assumption it is central to the economics of information and the foundations of game theory. This paper attempts to provide a...

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.