Improspectives

Improv skills lead to success

Prisoner’s Dilemma, Part 3

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My previous two posts discussed the Prisoner’s Dilemma, a classic 2 x 2 game structured so each player feels compelled to violate the trust of the other player. Researcher Robert Axelrod tried to find the best strategy for playing the Prisoner’s Dilemma by holding a tournament among computer programs playing the Prisoner’s Dilemma. Every program would play every other program, a second copy of itself, and a program Axelrod created that randomly chose whether to cooperate or defect. In that first tournament, which had 14 entrants, a program by Anatol Rapoport named Tit for Tat won.

The strategy behind Tit for Tat is extremely simple: Start out by cooperating, but if the other player defects, defect on the next turn as punishment. If the other player did not defect on the next turn, the program would switch back to cooperating. So why would this program win? As Stevens points out in his course, the best the program can hope to do is to tie. It never tries to take advantage of the other player, so it will never get a higher payoff in any round than the other program. What happened was that Tit for Tat minimized its losses. It punished other programs for defecting, but it only did so once if there was just a single defection. This strategy of minimizing its own losses while minimizing the other programs’ gain due to bad behavior made Tit for Tat the best program of the bunch.

The key to the success of Tit for Tat is that it elicits cooperation. Axelrod noted that the program is nice, provokable, forgiving, and straightforward. Among humans playing the game, or for computer programs with a memory of past turns, playing Tit for Tat lets other player accurately predict the consequences of their actions. In the first Prisoner’s Dilemma tournament, the top eight programs were all nice, which meant that they were never the first to defect.

The participants included a program called JOSS, which was the same as Tit for Tat but threw in the occasional defection at random intervals. The program’s design was meant to take advantage of the occasionally high payoff from an unchallenged defection while retaining the benefits of cooperation. Unfortunately, this strategy resulted in extremely low scores because its actions weren’t predictable. One very negative consequence was that it created a series of moves versus Tit for Tat, and variations of Tit for Tat, in which each program defected on alternate turns and led to dismally low scores.

In Axelrod’s analysis of the first tournament, he noted that there were three strategies not included in the tournament but that, if submitted, would have won. With these results made available to potential entrants, along with randomizing the number of rounds each pair of strategies competed against each other to invalidate “late round” tactics, he ran a second tournament. This new competition attracted 62 entries. Tit for Tat won again. From the results, it’s easy to see that there is a penalty for being the first to defect. Axelrod wrote:

What seems to have happened is an interesting interaction between people who drew one lesson and people who drew another from the first round. Lesson One was: “Be nice and forgiving.” Lesson Two was more exploitative: “If others are going to be nice and forgiving, it pays to try to take advantage of them.” The people who drew Lesson One suffered in the second round from those who drew Lesson Two….The reason is that in trying to exploit other rules, they often eventually got punished enough to make the whole game less rewarding for both players than pure mutual cooperation would have been.

The lessons for improv and business are obvious, so I won’t belabor them. I would point out that the Prisoner’s Dilemma is an inherently grim scenario, so it’s best not to get into this type of situation in the first place. Because each player faces potential catastrophe if they don’t protect themselves, you can allow the players to communicate and not guarantee cooperation.

Next up: further insights into the nature of competition in the Prisoner’s Dilemma scenario.

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