Lecture 20 - Subgame Perfect Equilibrium: Wars of Attrition

We first play and then analyze wars of attrition; the games that
afflict trench warfare, strikes, and businesses in some competitive
settings. We find long and damaging fights can occur in class in
these games even when the prizes are small in relation to the
accumulated costs. These could be caused by irrationality or by
players’ having other goals like pride or reputation. But we argue
that long, costly fights should be expected in these games even if
everyone is rational and has standard goals. We show this first in
a two-period version of the game and then in a potentially infinite
version. There are equilibria in which the game ends fast without a
fight, but there are also equilibria that can involve long fights.
The only good news is that, the longer the fight and the higher the
cost of fighting, the lower is the probability of such a fight.