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Econ110_Section6 - Section 6 Wars of Attrition and Some...

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Section 6: Wars of Attrition and Some Odds and Ends Daniel Egel October 13, 2008 1 War of Attrition I: A Simple Example The following is stolen from one of the previous midterms for this course. To give you a taste of what an exam question might look like... Two firms, S and T , are locked in a war of attrition to determine the next DVD format. The winner of the contest will become the industry standard and win a profit of $5 billion. S is much weaker financially and only has resources of $7 billion. Every year that the firms fight costs S $1 billion. T has a great deal of financial backing and total resources of $50 billion. But it is a complex organization and fighting very long will force painful and very costly adjustments. The per-period costs of fighting for T are: 1 billion in the first round, 1 billion in the second round, 6 billion in the third round, 6 billion in the fourth round, and 1 billion per round thereafter. A firm can fight only as long as it has resources. The tree below specifies the first six rounds of the game. fight quit (0 , 5) T fight quit (4 , - 1) S fight quit T fight quit S fight quit T fight ... quit S 1.1 Questions 1. How many rounds can each firm fight? 2. Complete the tree by adding additional rounds if needed and filling in the payoffs. 3. What is the backwards-programming equilibrium? Does S or T win the format war? 2 War of Attrition II: Three Equilibria 2.1 Setup We have a very simple set-up analogous to what we did in class.
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