Draw the Tree, Start From the End

The board’s chicken game and thrown-away steering wheel showed that a threat only counts if it would really be carried out. This lesson gives you the tool that checks that by hand: draw who moves when, and solve from the last move backward.

Before you start. Every game so far had players choosing at the same moment, so a grid held it. From Coordination, Schelling Points & Credible Threats you have the credible threat: a threat works only if carrying it out would actually be in your interest when the moment comes. And from Nash on a Number Line you have two sellers choosing amounts, settling at 30 litres each. Here one player moves first and the other sees it before replying.