• 2010-08-11
• economics,
• psychology

Prisoner's Dilemma

Definition #

In game theory, the prisoner's dilemma refers to a situation in which two parties can:

1. cooperate (each gains a moderate amount),
2. defect (each looses a moderate amount), or
3. one defects (gains a large amount), the other cooperates (looses a large amount).

Summary #

Background #

During the summer, I took a course on negotiating. On the last day of class, the professor announced we would be doing a large-scale group negotiation. He split the class into two large groups of 12 people each and provided everyone with the following information:

Each group represents a store in a town where commerce is forbidden on Sunday. For various reasons, the two stores are now considering being open on Sundays with the following ramifications:

• If both stores are closed, each makes $20,000 during the week.
• If both stores are open, the town will fine each store $20,000 for that week.
• If only one store is open, that store will make $40,000 during the week and will actually take business away from the other store for a week, so the the closed store looses $40,000 for that week.

For those of you playing along at home, here is the payoff matrix:

The two group convene in separate classrooms where for each of the next 12 "weeks" a new representative must exit the room with a sign that says "Open" or "Closed." The two representatives have the option of negotiating for up to one minute except after weeks 4 and 8 when they must negotiate. This is because on weeks 4, 8, and 12, the profits and losses double, triple, and quadruple, respectively.

Game Play #

As the twelve members of my group finished reading the assignment I pointed out that this was, indeed, the classic prisoner's dilemma game in which we can maximize our gains by cooperating, although there are short-term gains in defecting.

A fellow classmate (let's call him Bob) responded saying he did not care; he just wanted to win. I pointed out that there are a few ways of defining win in this particular circumstance. Did he mean that we should try to make as much money as we could? No. He wanted to make sure we made more money than the other team. Okay, I said, but let's focus on the short-term goal here on figuring out whether or not we should be open for week 1.

Eventually, we came to a consensus that we should be open week 1 as a precaution. As the first representative to go out, I displayed our "Open" sign to the amazement of the other team representative. I made a deal, offering to be closed for the remaining 11 weeks (as my team had proposed), and the other representative agreed—provided that they were allowed to open the following week while we remained closed. Deal.

When I returned, the discussion picked up on a theme that might be described as "When Should We Screw Them?" Several people agreed that "we have to screw them sometime," but I was at a loss to explain my position that we should not screw them. In the meantime, we were being pressed to send out representatives for the following weeks, and we continued to abide by the agreement laid out in the first week.

Both teams remained closed for weeks 2, 3, 4, 5, 6, and 7. Our group became more passionate. We tried to define what our interests were. While we could not agree what the expression "maximize your profits" (as written in the instructions) meant, we did agree on the following two principles:

1. We want to have a positive balance at the end of the game.
2. We want to make more money than the other team.

At this point, I raised the issue that I had a very specific interest in remaining honest. To illustrate my point, I suggested that on week 11 we tell the other team to be open week 12. I had forgotten that the losses would quadruple, for my intent was to prevent anyone from cheating on week 12 (when there would be a strong desire to cheat). This idea did not go over well ("You're willing to loose money to be honest!?"). I tried to backtrack. Okay, but now—it's only week 8—why should we screw them now? Let's continue to abide by our agreement. They've been abiding by the agreement so far—let's just keep going—we're making money, people!

Honesty or Profits #

Someone calculated that if we screwed them now (week 8), and subsequently stayed open the remaining weeks (since we assume that they would stay open as well), we would still be in the black at the end of week 12, while the other team would be in the red.

We had been summoned to send a representative out for week 8 (our team was consistently late in sending someone out as our deliberations slowed us down). At this point our debate reached a fever pitch. Bob of the "I-want-to-win" camp asked for a vote; should we choose honesty or profits (his words).

So I asked each person: "Honesty or profits?"

Profits. Profits. Profits. Profits. Profits. Profits. Honesty. Profits. Honesty. Profits. Profits.

My vote was well known at this point, so I didn't even bother announcing my position. Moments later, one of the votes for "honesty" changed her mind and agreed that week 8 was an opportune time to screw the other team.

I decided that since Bob was so in favor of screwing the team "at some point, and it might as well be now" he should be the representative to go and announce that we were open. As he was walking out the door, I said "This is a stupid move; you're firing nukes on Russia—how do you think this is going to end?" My other classmates asked me "But what if they're open?" "If they're open," I replied, "then I'm an idiot and I was wrong. But watch, they are going to abide by the agreement, and from now on, it will just be us nuking each other." (I choose the Cold War analogy because we had all watched Thirteen Days as part of a previous assignment.)

The other team was closed and they were upset. Since negotiations had to occur, Bob tried to present the situation as "nothing personal"; that our group was "chaotic" and that it was "impossible to say how things would proceed".

On Week 9, both teams came out "Open", although the other team's sign also depicted a middle finger. Both representatives made it clear that they would remain open the remaining weeks, so the professor aborted the game and we convened for a post-session discussion.

Post-mortem #

During the discussion, it became clear that the other team had plans to screw us on Week 11 (on the assumption that we would screw them on Week 12). Unlike our team, they had chosen to make liberal use of the blackboard (we used the computer screen). Their board clearly showed their train of thought: "Ethics", "Honesty Is the Best Policy" were followed up by a large "SCREW THEM!" It was pointed out that despite being told "it's just business, nothing personal" every single person on their team took it very personally.

I raised the issue of how quickly people choose "profits" over "honesty", but my fellow teammates objected on the grounds that "they were operating within the game." My professor tried to make the point that "in real-life" people tend to weigh in the consequences more and that they might be less likely to defect.

Needless to say, I did not find this reassuring.

Final Score #

Despite my feeling that we had "lost" as we broke our agreement (and, in retrospect, we lost $140k in potential profits), we did satisfy the two criteria pinpointed by the group: we were in the black, and we made more money than the other team. Here is the final score:

See Also #

• Prisoner's Dilemma at Wikipedia

• Pareto Efficiency for the game-theoretic concept of optimizing gains.