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Content of Game Theory for Managers course includes ratiinality, prisoner dilemma, Loyal servant, assurance, credibility, stratigic subtitutes, entry, brinkmanship, negotiation, auctions, signaling, reputation etc. This file contains: Quest, Bond, Swap, Game, Clarity, Theory, Examine, Asset, Known, Section, Value, Dominant
Typology: Exercises
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Team Assignment #1: Qwest's Bond Swap
For this article, please see:
Norris, Floyd. "A Bond Swap Available Only To Big Players," The New York Times , 18 December 2002, C1.
Setup
In this homework we will examine this bond swap from a game theory point of view. In our (extremely simplified) model, each bondholder has one $ Qwest bond. We ignore interest paid on the bonds and focus only on principal repayment. (We also ignore discounting.) We simplify matters further by
(^1) Floyd Norris, while certainly an excellent reporter of facts, is not a game theorist. His analysis and conclusions may or may not be correct.
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And even if bankruptcy was viewed as being highly likely, there was certainly substantial uncertainty surrounding the exact value of Qwest's assets in the event of bankruptcy and hence uncertainty over how much bondholders would be paid back. In this section, we treat the value of Qwest's assets, X , as a random variable. To get at the important ideas of the analysis without getting bogged down in complications, we will assume that X has a very simple distribution:
The important features of this setup: Qwest is certain to go bankrupt if it can not get bondholders to tender but, if all bondholders tender, Qwest will escape bankruptcy with probability p. (If all tender, the face value of its
the special cases in which p = 0 and p = 1, respectively.
3. For which p is it a dominant strategy to tender? Hint: You will find that it is a dominant strategy to tender as long as p p* for some p* < 1.
to avoid bankruptcy through this tender offer if its chances are suf- ficiently small of escaping bankruptcy after a successful tender offer! Briefly explain (preferably without math) why this makes sense.
Up to this point, we have taken the terms of the tender offer as given. Suppose now that you are CFO of Qwest and must decide the terms of this tender offer. The CEO urges you to make the most favorable tender offer possible that is certain to succeed. (You interpret this as meaning that tendering should be a dominant strategy for bondholders.)
