The Mixed Strategy Equilibria and Adaptive Dynamics in the Bar Problem

This paper looks at an N-person coordination game which is called, by Brian Arthur, the bar problem. We look at the mixed strategy equilibria and show that there is a unique purely mixed strategy equilibrium in which all players play non-degenerated mixed strategies. We also examine some simple dynamics that might evolve the system to that equilibrium by conducting some preliminary numerical experiments. The results show that under usual initial conditions the system will converge to the unique mixed strategy equilibrium.