The globe and the circle

Abstract

The geometry of the line and the circle has been used in economics for a long time to understand location choice and political positioning in democratic polity. This paper draws on some elementary ideas from geometry and game theory to extend some of the analysis to beyond lines and circles to the globe or the sphere. In the spirit of recreational geometry the paper is focused on demonstrating some abstract results concerning Nash equilibria on the globe. It is hoped that this will help us understand better the robustness of median voter theorems and why stores position themselves the way they do.