The Social Will-Testing Game and its Solution
  We examine a two-person game we call Will-Testing in which the strategy space for both players is a real number. It has no equilibrium. When an infinitely large set of players plays this in all possible pairings, there is an equilibrium for the distribution of strategies which requires all players to use different strategies. We conjecture this solution could underlie some phenomena (like pecking orders) observed in animals. 
Leonid Gurvits, J. Stephen Judd
cs.GT q-bio.PE