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“President Obama faces a deadline of March 31 to decide the fate of G.M.,” i.e., whether to give GM additional loans or let GM go through a managed bankruptcy (The New York Times, March 16, 2009). Fate of GM March 2009 The New York Times (March 16, 2009): “The face-off with … … has quickly become a high-stakes game of chicken.” Washington Post (Feb. 13, 2009): Quotes Senator Corker as saying, “In a way, it's a game of chicken.” Wall Street Journal (March 31, 2009): “Now the great game of chicken begins…”

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Game of Chicken Two cars drive toward each other If neither car swerves, both drivers sustain damage to themselves and their cars If only one person swerves, this person is known forever more as “Chicken”

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SwerveStraight Swerve Straight

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-5, -5 0, 0 -1, +1 +1, -1

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Ron Gettelfinger

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Ron Gettelfinger -5, -5 0, 00, 0 -1, +1 +1, -1 ____________ _________

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In the game of chicken above, both players going straight is not a Nash Equilibrium because at least one player would have preferred to swerve. In the game of chicken, both players swerving is not a Nash Equilibrium because at least one player would have preferred to go straight. However, when one player swerves and one player goes straight, this is a Nash Equilibrium because neither player can improve their outcome by changing their action. Two (pure strategy) Nash Equilibriums 0

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Because the loss of swerving is so trivial compared to the crash that occurs if nobody swerves, the reasonable strategy would seem to be to swerve before a crash is likely. Yet, knowing this, if one believes one's opponent to be reasonable, one may well decide not to swerve at all, in the belief that he will be reasonable and decide to swerve, leaving the other player the winner. This unstable situation can be formalized by saying there is more than one Nash equilibrium, which is a pair of strategies for which neither player gains by changing his own strategy while the other stays the same. (In this case, the pure strategy equilibria are the two situations wherein one player swerves while the other does not.) Wikipedia, http://en.wikipedia.org/wiki/Chicken_%28game%29

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StraightSwerve Straight 0, 020, 6 Swerve 5, 2710, 9 GM owes the Unions more than $20 billion GM owes bondholders $27 billion

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Suppose the union leader puts 6 red marbles and 4 white ones and will pick one--if it is red, he won’t swerve from demanding complete payment of $20 billion to the retirees’ health fund, if it is white he will swerve and agree to substantially less. Let p equal the probability that the union drives straight towards the bankruptcy wall. Hence, What is the expected payment to the bondholders for each alternative decision? p = 0.6 & (1-p) = 0.4 Bondholders drive straight.6(0)+.4(27)= $10.8 billion Bondholders swerve.6(6)+.4(9)= $3.6 billion + $2.8 billion = $7.2 billion If the bondholders know the union’s strategy, they are better off driving straight.

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Suppose the union leader puts 6 red marbles and 4 white ones and will pick one--if it is red, he won’t swerve from demanding complete payment of $20 billion to the retirees’ health fund, if it is white he will swerve and agree to substantially less. Let p equal the probability that the union drives straight towards the bankruptcy wall. Hence, What is the value of p at which the bondholders would be indifferent between driving straight for the bankruptcy wall and swerving? p = 0.6 & (1-p) = 0.4 p(0) + (1-p)(27) = p(6) + (1-p)(9) 27-27p = 6p + 9 – 9p 27-9 = 6p – 9p + 27p 24p = 18 p = 18/24 = 0.75 The Union wants to convince the bondholders that there is more than a 75% probability that they will drive straight into the bankruptcy wall.

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Sequential game: First, the union commits to driving into the bankruptcy wall Bondholders are better off swerving!!

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Two (pure strategy) Nash Equilibriums One mixed strategy Nash equilibrium: Strong incentive for each bargainer to pre-commit Probability of driving straight into bankruptcy wall Bondholdersq = Unionp =

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What type of good is saving General Motors? Nonrival in consumption… union workers and bond holders jointly consume it. Nonexcludable…. You can’t exclude someone who didn’t help save the company..

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Games, Strategies, and Decision Making By Joseph Harrington, Jr. First Edition Chapter 4: Stable Play: Nash Equilibria in Discrete Games with Two or Three.

Games, Strategies, and Decision Making By Joseph Harrington, Jr. First Edition Chapter 4: Stable Play: Nash Equilibria in Discrete Games with Two or Three.

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