A Balanced Diplomacy Tournament

We present a design for a seven-game tournament of the 7-player board game \emph{Diplomacy}, in which each player plays each country one time and each pair of players shares a border either 4 or 5 times. It is impossible for each pair of players to share a border the same number of times in such a tournament, and so the tournament presented is the most “balanced” possible in this sense. A similarly balanced tournament can be constructed for a generalized version of the game involving an arbitrary number of countries. We also present an infinite family of graphs that cannot be balanced.