the absurd observers

Friday, March 18, 2005

TNR screws up game theory


Thomas Mann argues in The New Republic that game theory suggest democrats ought not compromise on social security because tit-for tat has been proven to be the most effective strategy in delaing with the prisoner's dilemma:

The lesson for Democrats? If they believe that Bush's single-minded embrace of personal accounts is a defection from a cooperative game to deal with the solvency of Social Security (and it is), they should respond in kind: by withholding any specific proposals on benefit reductions and revenue increases until the President withdraws his insistence on personal accounts. If Bush's interest in solvency is genuine, he will then have no choice but to bargain.

Aside form transforming a game with two options (cooperate and trust the other party to do the same or don't cooperate) into one with a thrid option (negotiate), Mann completely ignores the reason why tit-for tat is an effective strategy in certain circumstances.

Becasue I am too lazy to explain the basics of the prisoners dilemma, I refer you to a page that explains it.

As anyone who has studied game theory knows, tit-for-tat is the most effective strategy for ongoing interactions with a variety of different players. The basic stategy is to cooperate first and then imitate whatever the other player's last move was. If his last move was to defect, a player using tit-for-tat defects, if it was to cooperate, then a player using tit-for-tat cooperates. This strategy works when there are numerous other players because it protects against exploitation by those who defect, but gains the benefits of cooperation if other players cooperate.

Tit-for-tat is not a flawless strategy, however, it is merely the best strategy amongst many different ones. If there are only two players, then it is quite possible another strategy will be most successful. The success of any given strategy will depend on the strategy employed by the other player.

Let us assume that Bush is purusing a strategy of reverse tit for tat. This leads him to defect first and then imitate democrats prior move. If democrats follow tit for tat, then every time Bush defects, they will cooperate and vice versa. The result will be the least efficient outcome for all parties involved. Certainly that would not be the ideal strategy.

By contrast, if Democrats follo an always cooperate strategy, then only on social security will the country loose and on all other issues, both parties will be better served.

Obviously no one actually pursues such simple strategies in politics, but hopefully this illustrates why Mann's attempted application of game theory to politics is worthless.


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