“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 GMMarch 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…”

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”

Swerve Straight

Swerve

Straight

-5, -5

0, 0 -1, +1

+1, -1

Ron Gettelfinger

Ron Gettelfinger

-5, -5

0, 0 -1, +1

+1, -1

____________ ____________

____________

_________

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

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

Straight Swerve

Straight 0 , 0 20 , 6

Swerve 5 , 27 10 , 9

GM owes the Unions more than $20 billion

GM owes bondholders $27 billion

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.

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.

Sequential game: First, the union commits to driving into the bankruptcy wall

Bondholders are better off swerving!!

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

Bondholders q =

Union p = 4/3

3/2

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..