Improspectives

Improv skills lead to success

Archive for October 2012

Prisoner’s Dilemma, Part 1

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The Prisoner’s Dilemma is perhaps the classic 2 x 2 game. The scenario is simple enough to explain, but it seems impossible to find a way out of the dilemma. Here’s the situation: You and a fellow criminal have been apprehended, and the police want at least one of you to give evidence against the other guy. They tell you that if neither of you talks, they have enough evidence to put each of you in jail for a relatively short time. On the other hand, if you give up the other guy and he refuses to talk, he will be convicted and sentenced to a long term, and you will go free. Of course, if you don’t talk and he does, the same thing happens to you. If you both talk, you will each get a sentence that’s worse than you would get if you were the only one to defect but not as bad as when you didn’t defect and your partner in crime did.

You can summarize the Prisoner’s Dilemma payoffs using the following 2 x 2 grid.

Graphic showing the payoff grid for the Prisoner's Dilemma.

The central question is: What is the best way to play this game?

Obviously, it’s in your best interest to cooperate. If both you and the other person cooperate (that is, you cooperate with each other and don’t talk), you will get a sentence of only one year and minimize the negative payoff. The problem is that if the other individual knows that you are going to cooperate, he has no incentive to play along. He should defect (turn you in and get away with no jail time at all). To avoid the possibility of a longer jail term, you should also turn in the other person, giving him a medium sentence and assuring that you don’t get the longest possible term.

So the strategy for playing the Prisoner’s Dilemma exactly once is to always defect. You don’t get the best possible payoff, but you do prevent yourself from getting the worst possible outcome. The same considerations work for improv and business. If you never plan on performing or working with someone again, what they think of you and what they might do to you in the future is irrelevant. You could choose to defect by breaking a promise or paying an invoice late and move on with your life knowing that the other individual or business won’t be able to exact revenge. But what if you play game multiple times? That’s what’s called an Iterated Prisoner’s Dilemma.

Next time: the Prisoner’s Dilemma and ongoing relationships.

Stag Hunt Across Species

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In the Stag Hunt, also known as the Assurance Game or the Coordination Game, two hunters have the option of going after a hare or a stag. If a hunter targets a hare, he will get one for a small payoff every day. If both hunters go after a stag, they will each receive a much larger payoff, but if you target a stag and the other hunter goes after a hare, you will get nothing. Your choice as a player is whether to go for the reliable but small payoff or the larger, riskier payoff.

As with most of the other classic 2 x 2 games, we assume that the two hunters can’t communicate. At least, not so that they can coordinate their efforts before they choose which strategy to follow on a given day. What they can see, however, are the payoffs both for themselves and for the other hunter after they play a round of the game. This situation leads to some very interesting outcomes, especially when you consider it across species.

The authors of a paper titled “Responses to the Assurance Game in Monkeys, Apes, and Humans,” using equivalent procedures, tested whether capuchin monkeys, chimpanzees, or humans would perform better at the Assurance Game. The research team chose these three sets of primates because they all show tendencies toward cooperation in their natural environment. What made their research interesting was that they did not allow the humans to talk while they were being tested.

As you might expect, the humans performed better at the task than either the chimpanzees or the capuchin monkeys, but the difference was not as large as one might expect. Specifically, the researchers found that the humans who discovered the hare-hare approach thought that they had beaten the game and were always getting a reliable payoff. Game theorists call this approach the risk dominant strategy. Once the players achieve a reliable outcome, they tend not to move away from it and explore alternate possibilities.

The paper’s authors summarized their results this way:

Finally, despite being the species for which the highest frequency of pairs achieved the payoff dominant outcome, even among humans fewer than 20% in pairs did so (this increases to 27% when borderline pairs are included). An additional 38% of pairs achieved the risk dominant outcome (hare-hare), and 12% matched their partner. It is worth reiterating that despite success of humans compared with the other primates, a nontrivial proportion of pairs failed to achieve the payoff-dominant outcome. This underscores the difficulty of finding outcomes when the typical human procedures (instructions, payoff matrices, pretest for understanding) are absent, common handicaps for nonhuman species.

Obtaining the highest possible payoff from any venture, whether it is in improv or in business, means taking risks. Even in this artificial situation, in which communication was limited, some pairs of humans managed to find the payoff-dominant outcome for the Stag Hunt experiment. The problem was that many of them did not. As the authors of the study note, this is most likely a case of humans being risk averse. In an improv context, being risk averse might mean always asking for the same type of suggestions or doing the same type of scene, regardless of which suggestion you get. Some so-called improv groups even get a single suggestion from the audience, use it once by stating it during their scene, and then do the rest of the scene according to a script. It’s a cheat, one that takes a lot of the fun out of doing your performances unless you change the script every night, but it does reduce the risk of having something terribly wrong and not entertaining your audience. Over time, however, taking larger risks will yield greater rewards as long as you have competent individuals on the stage with you.