Tuesday, April 30, 2013

Dilemma 22: Chicken


Other non-zero-sum games exist. Consider this:
(A,B)            |  nice      mean
nice       |  2,2   |   1,3   |   
A              -|--------|---------|   
mean       |  3,1   |   0,0   |   

This game, “Chicken”, is similar to Dilemma, except that the values of “lose” amd “draw” are interchanged. Now draw is the worst outcome, and lose is the lesser evil. Unlike Dilemma, this game has two Nash equilibria; win/lose and lose/win. This fact weakens exploitation but strengthens intimidation.
This is the general Chicken payoff matrix:

(A,B)            |  nice      mean
           |                     W  =  Win
       ----|--------|---------|       T  =  Truce
nice       |  T,T   |   L,W   |  D  =  Draw
A              -|--------|---------|       L  =  Lose
mean       |  W,L   |   D,D   |      
          -|--------|---------|  where D<L<T<W

It is often presented as a war game; Car Wars, involving irresponsible adolescents in high-powered vehicles. In Car Wars Chicken, two cars approach each other in the same lane at high velocity. The first driver to swerve out is not, as you might expect, lauded for sanity, but jeered for lack of bravado. To “chicken out” is a loss in this stupid game; to chicken others out is to win.
Chicken is a contest of stubbornness, aggression, and intimidation. Like Dilemma, this game rewards mutual cooperation, yet offers tempting opportunities for exploitation. In Dilemma the dialog is between cooperation and competition; in Chicken the dialog is between rationality and irrationality. There is little a loser can do ... except threaten a draw, which is the worst outcome for both players. This is a stubborn, unreasonable bargaining position; but that’s just what Chicken favors.
Dilemma and Chicken both enforce harmony via reciprocity, in the long run. Chicken’s long run is longer and costlier; for Chicken is a metaphor for that most anti-social of games, War.

My father relates this anecdote of wartime Chicken:
During the early 40’s he was trucking high explosives for a certain Army project. It was a hazardous job, made more hazardous by the presence of Chicken players on the road. Many times he found some joker homing in on him; but my father assures me that he never paid the slightest attention to such fools. He just kept on driving as if they weren’t in his lane, and pretty soon they weren’t. That was my Dad!
Those guys didn’t have a chance. After all, he was trucking those explosives for the Manhattan Project!
So my father said to me. From this story I deduce (with horror and awe) that it’s a miracle that I even exist!


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