Two bars compete with each other and can charge a price of $2, $4 or $5 for a beer.

The customer base consists of tourists and natives.

6,000 tourists pick a bar randomly (equivalent to every other tourist will stop by one specific bar) and 4,000 natives select the lowest price bar (otherwise they evenly split). Marginal costs are zero.

What is the equilibrium of this pricing game, and how much profits do the bars make?