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COMPUTING SCIENCE

New Dilemmas for the Prisoner

Brian Hayes

Tit-for-Tat

2013-11HayesF1.jpgClick to Enlarge ImageAs a human predicament, Prisoner’s Dilemma is surely ancient, but as a formal game it was invented in 1950 by Merrill M. Flood and Melvin Dresher of the RAND Corporation. Interested in how human subjects deal with situations of conflict, they recruited two colleagues to play 100 matches in quick succession. Without any prearranged strategy, the players achieved mutual cooperation in 60 percent of the games.

A decade later Anatol Rapoport, a mathematician and psychologist at the University of Michigan, undertook further experiments and analysis. Then in the 1980s Robert Axelrod, also of Michigan, organized a series of IPD tournaments for computer programs. The big winner was one of the simplest strategies, called tit-for-tat, submitted by Rapoport. A tit-for-tat player always cooperates in the first round of a match and thereafter echoes the opponent’s previous move. Thus cooperation is rewarded with continued cooperation, and defection is punished by reciprocal defection.

Tit-for-tat is not an optimal strategy in the mathematical sense—guaranteed to prevail over all comers. As a matter of fact, it can never outscore an opponent; it always plays for a tie. Nevertheless, tit-for-tat performs remarkably well against a wide variety of other strategies. From the success of this simple rule Axelrod extracts some lessons for IPD players: Never be the first to defect; retaliate immediately when betrayed; relent after a single cycle of punishment.





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