Fundamental Agreement: A new foundation for the Harsanyi Doctrine

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 framework for the Harsanyi Doctrine (in an incomplete information framework) based on two qualitative properties of individuals'' belief hierarchies: Fundamental Agreement and Shared Worlds. A general notion of "agreeing to disagree" about "belief indices" satisfying a Bayesian Sure-Thing Principle is introduced and illustrated by a range of examples and subsequently characterized as equivalent to a local version of the Common Prior assumption. Fundamental Agreement is defined as the absence of any such (implicit) agreement to disagree. The non-trivial gap between this and Harsanyi Consistency proper is bridged by a novel Shared Worlds condition, which requires individuals'' beliefs about what is commonly believed to be equal. Common belief in the conjunction of Fundamental Agreement and Shared Worlds is then shown to be equivalent to Harsanyi Consistency. On the technical level, this paper is probably the first to (have to) seriously confront the failure of the common belief operator to satisfy the axiom of "Negative Introspection."