20. Subgame perfect equilibrium: wars of attrition

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Game Theory (ECON 159)

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.

00:00 - Chapter 1. Wars of Attrition: The Rivalry Game
17:39 - Chapter 2. Wars of Attrition: Real World Examples
24:04 - Chapter 3. Wars of Attrition: Analysis
47:53 - Chapter 4. Wars of Attrition: Discussion of SPEs
01:06:54 - Chapter 5. Wars of Attrition: Generalization

Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses

This course was recorded in Fall 2007.