# Extensive Form Games

( The game of “ chicken”) Two cars are driving at each other at great speeds. If nobody changes directions, in 3 seconds they will collide and die a gruesome death, yielding payoffs of −100 for both players. At every second they have to (simultaneously) decide wether to continue or not (i.e. there are 3 periods to this game). Payoffs are as follows: If both players choose continue for each of the three periods, then they get −100. If at any period one player choses “not continue” and the other chooses “continue” the player that chose not to continue gets 0 and the other gets 100. If at some point both simultaneously choose not to continue they both get 0.

True or False: Any equilibrium has the property that one of the players chooses not to continue, but this only happens in the last period (as in the movies!).

I just wanted to double check my answer with someone.

My answer: I think that the answer is false. Because the strategy profile where player 1 plays continue at every stage and player 2 plays not continue at every stage is a subgame perfect Nash equilibrium I believe? Because based on the one shot deviation principle, there is not point in the history where player 2 can deviate from this strategy at one node profitably. And (continue, not continue) is a Nash equilibrium for the individual game. Thus, this strategy would result in a subgame perfect Nash equilibrium without getting to the third stage of this game.