Testing Minimax Play In The Field « Cheap Talk

- Wednesday, February 24, 2010

Fun article about game theory, incentives, and prediction.

Does game theory have predictive power?  The place to start if you want to examine this question is the theory of zero sum games where the predictions are robust:  you play the minimax strategy:  the one that maximizes your worst-case payoff.  (This is also the unique Nash equilibrium prediction.)

The theory has some striking and counterintuitive implications.  Here’s one.  Take the game rock-scissors-paper.  The loser pays $1 to the winner.  As you would expect, the theory says each should play each strategy with 13 probability.  This ensures that each player is indifferent among all three strategies.

Now, for the counterintuitive part, suppose that an outsider will give you an extra 50 cents if you play rock (not a zero-sum game anymore but bear with me for a minute), regardless of the other guy’s choice.  What happens now?  You are no longer indifferent among your three strategies, so your opponent’s behavior must change.  He must now play paper with higher probability in order to reduce your incentive to play rock and restore your indifference.  Your behavior is unchanged.

Things are even weirder if we change both players’ payoffs at the same time.  Take the game matching pennies.  You and your opponent hold a penny and secretly place it with either heads or tails facing up.  If the pennies match you get $1 from your opponent.  If they don’t match you pay $1.

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