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Prisoner’s Dilemma, Part 4

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I’ve spent the last few posts talking about the Prisoner’s Dilemma, where two individuals must decide whether or not to cooperate. There’s a harsh penalty for having one’s trust violated, so the most risk-averse strategy is to violate the other player’s trust. RobertAxelrod’s analysis gives us a number of results that we can use both in the realm of improv and in the realm of business. He enumerated these five principles in The Evolution of Cooperation:

  • Enlarge the shadow of the future
  • Change the payoffs
  • Teach people to care about each other
  • Teach reciprocity
  • Improve negotiation abilities

Enlarging the shadow of the future simply means taking a long view of your interactions. When you form an improvisational comedy group, you should plan to have many performances over a number of months or years. This sort of ongoing interaction, like any other relationship, requires nurturing and mutual trust. Just like saving for retirement, the more you set aside in terms of money or trust at the start, the higher your return and, as the years go by, the interest accumulates. The same principle holds for business interactions. Americans on the West Coast tend to change jobs a lot more often than folks on the East Coast, but many of us stay within the same industry and interact with our colleagues from previous jobs frequently. Within a company, you’ll find that fostering a spirit of cooperation on your team will help you generate better results. Hopefully that conclusion won’t be too surprising.

The next question is how to reward different behaviors. In the classic Prisoner’s Dilemma payoff matrix, the only logical choice is to defect. Doing so limits the damage that would be caused by trusting another individual whose rational calculus would push them to defect. In business, anyone who sees their business as a series of one-time relationships will not be all that keen on building a trusting relationship with their business partners. In the entertainment industry, it said that you haven’t really sold someone until you’ve done business with them twice. If they’re not willing to rehire you, it means that they don’t trust you based on their experience with you.

Teaching people to care about each other can be tricky, particularly if you have individuals who are not prone to trusting relationships with others. Sociopaths, who don’t empathize with other individuals at all, are a particular problem. I’m not a psychologist, so I can’t tell you how to deal with them, but there are a number of online resources that you can use to see where to go and what to do. For individuals who do have feelings toward others, you can use teambuilding exercise rewards and the warm afterglow of successful shows or projects to develop a sense of camaraderie.

In the improv world, in which interactions in local groups are reasonably equal, you don’t often have that much trouble with these relationships. Yes, every so often members of the group will disagree intensely, but if everything is in place and the relationship is solid, it’s likely that you will get through the difficulties. In a business in which promotions, internal awards, and raises are at issue, the stakes are quite a bit higher. Managers need to keep everyone’s wants, needs, and desires in mind as they manage their projects.

One of the best ways to ensure people are satisfied is to give them work they care about and reward them for doing good jobs. The nature of those rewards will vary based on your business and the resources available to you, but rewards and recognition, even if only at the personal level, go a long way toward making those relationships more solid.

Axelrod also recommends that you learn to teach reciprocity. A willingness to respond to offers of cooperation allows teams to make much more progress than a loose collection of individuals would be able to. The form that reciprocity takes depends upon your organization. For businesses, providing a bit of after-hours help for others on their part of a project after they have done the same for you is a perfect example. In the improv world, we can try to “set up players for the slam.” Just as volleyball players run through the bump, set, spike sequence to go from defense to offense, improvisers can do their fellow players a favor by giving them straight lines, by allowing them to be the focus of the scene, and by staying off the stage when their presence is not strictly necessary. All these actions are judgment calls that improve with experience, but managers can improve their odds, both in the performance and business worlds, by bringing on individuals who are predisposed toward these behaviors.

Finally, you should improve your negotiation skills. Negotiation is the art of the compromise, and there are very few solutions that will meet everyone’s wants and desires. Some folks have to compromise, some more than others, and good leaders and team members will find ways to negotiate for what they feel is necessary and compromise when it’s called for.

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.

Prisoner’s Dilemma, Part 2

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In my previous post, I described the Prisoner’s dilemma, a classic 2 x 2 game structured so the players are coerced into violating the trust of the other player. The strategy for a single round of the Prisoner’s dilemma is to defect, selling out the other player and eliminating the prospect of a huge negative outcome for yourself. But what about playing the game multiple times, perhaps many times?

Improv groups and businesses are meant it to be long-lived entities. The group I’m with, ComedySportz Portland, was founded in 1993 – as of this writing, we’ve been around for 19 years. I like to joke that it means we’ve lasted 38 times longer than the average improv group. Sure, there are plenty of groups that have been around for a long time, but there are quite a few more that have blown up in very short order.

What makes some groups stay together and others break apart? One thing that can make it happen is taking advantage of the other individuals in your group, whether by not making good on your promises or by not cooperating during scenes. Some examples of not cooperating can include making personal comments at another player’s expense, such as about their weight, height, or the choices that they made; denying other players’ choices during a scene or game; or showing up late (or not at all) to a rehearsal or performance. Taking advantage of the goodwill of your fellow players is extremely shortsighted. Forming a successful group is incredibly difficult, so you should do your best to ensure the group you’re with carries on, or at least that you don’t burn any bridges if you do decide to leave.

As Robert Axelrod noted in his book, The Evolution of Cooperation, and Scott Stevens noted in his Games People Play course for The Great Courses, the more likely it is for the game to continue, the more incentive you have to continue cooperating throughout the entire game. The same consideration applies to business relationships. Con artists can get money out of their victims and disappear knowing that, if their luck holds, they will never have to encounter that individual again. For business professionals, you have to take the opposite approach. Even though many of us change jobs and industries, it’s very likely that we will encounter the same individuals during our work lives. We should cultivate the best relationships we can. In game theoretic terms, that means we should cooperate whenever possible.

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.

Coordinating to Win Big in the Stag Hunt

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This series of posts talks about game theory and applications of the classic 2 x 2 games to improv and business. I’d previously discussed Chicken and Battle of the Sexes–next up is the Stag Hunt.

The Stag Hunt game is also called the Assurance Game or the Coordination Game. The basic idea behind the Stag Hunt is that the players can increase their payoff by cooperating. Following one traditional way to state the game’s conditions, I’ll define cooperation as a situation in which two individuals can increase their immediate payoffs by working together.

In its traditional form, the Stag Hunt posits that there are two hunters. The hunters can either choose to hunt for a stag, which has a very high but uncertain payoff, or a hare, which has a small and reliable payoff. Every time you hunt for a hare you will catch one and get a small payoff. On the other hand, if you hunt for stag and the other hunter goes after a hare, you will get nothing, and the other hunter will get the hare. You get a stag only if both of you decide to go after it. That’s why this game is also called the Coordination Game: You must coordinate your efforts to get the highest possible return.

The following matrix displays the payoffs for the Stag Hunt.

A graphic showing the payoff matrix for the Stag Hunt game.

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.

Obviously the best possible outcome is for you and the other player to go for the stag every round, but adopting that strategy is difficult when you don’t know the payoffs in advance and can’t communicate during the game. The best solution, both in business and in improv, is to find a way to communicate, even if it means making taking several moves to try different choices and observe the payoffs. Then, if you make a choice that leads to the big payoff, you trust that the other player will cooperate and repeat the move.

Next time: Do humans play this game better than chimpanzees?

Battle of the Sexes

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In my previous two posts, I discussed the classic game of Chicken, where the loser is the first person to give way to the other. Another classic game is the Battle of the Sexes, which imagines a situation in which neither player can get their preferred outcome, but the worst possible outcome is disagreeing. Let’s say you and your partner are invited to a party, and the host has asked you to bring beer or wine, but not both. Now also assume that you can’t get in contact with your partner. It’s the lack of coordination that makes these 2 x 2 games interesting and aggravating.

For the sake of argument, let’s assume that you are a beer drinker and your partner prefers wine. For you, the best possible outcome is if both you and your partner decide to bring beer. The second best outcome is if both of you decide to bring wine, and tied for the worst are when you and your partner bring different beverages. The problem is that you have no way to decide whether to bring beer or wine. If you base your decision on your partner’s preferences, you will bring wine. On the other hand, if you think that your partner will go along with your choice, you will bring beer. There’s no way to place one of those two options over the other. What’s worse is that your partner has exactly the same problem.

In terms of improv, you’ll find the Battle of the Sexes occurring when there is a lack of communication before you start playing a scene or game. Every improv group plays games differently, even when they’re based on the same familiar pattern. If you’re playing in the city as a guest player, there might be two different ways of playing the same game. If there is a lack of communication, such as if you go over to one side of the stage to pick up a costume piece before conferring with your playing partners, whoever starts might not have the same idea about how to play the game as everyone else. If your scene partners play one game, and you’re playing another, a train wreck ensues. It’s easy enough to fix once everything gets underway – either you or your playing partners can adapt, but there might be an awkward moment or two at the start. At that point, you just hope the audience either doesn’t notice or forgives you.

In business, you’ll find that the Battle of the Sexes game is played out during sales calls and engineering meetings. Everyone has a preferred solution for implementing a change or creating a product. Any time there are multiple pathways to creating a product or finishing a project, you should be in close communication to ensure that the solution you’re pursuing doesn’t contradict what someone else is doing.