The schelling diagram: On binary choice with externalities

Abstract

In his work, Micromotives and Macrobehavior, T. C. Schelling introduces a useful diagram for representing binary choice games with externalities. The main contention of this article is that Schelling's presentation is ambiguous between two different types of diagram. Although superficially similar, the diagrams are conceptually quite distinct, and confusion between them is liable to mislead interpretation of binary choice situations. A complete classification of two-person games is given, with some brief discussion of equilibrium points, and the role of communication in reaching those points. Generalization to the n-person case is noted where it is straightforward. A case is argued for a strong connection between choice theory and choice situations. The aim is to render a useful construction clearer and more accessible.