# A Gang of One

Here’s a fun variant of the repeated prisoner’s dilemma game.

Picture a lecture audience. I announce that I’ll go along every row, starting at the front, and give each member a chance to say “cooperate” or “defect.” Each time someone says “cooperate” I’ll award ten cents to her and to everyone else in the audience. Each time someone says “defect” I’ll award a dollar only to her. And I ask that they play this game solely to maximize their individual total income, without worrying about friendship, politeness, the common good, etc. I say that I will stop at an unpredictable point after at least twenty players have played, at which time each member can collect her earnings.

You gotta love the instruction not to be “worrying about friendship, politeness, the common good, etc.” The game creates a group out of the audience with all the group dynamics in play particularly because there is no privacy. In the original prisoner’s dilemma that players are part of a gang, here we make the audience into a gang; while instructing them not to act like one.

That framing is from an interesting synopsis of a set of some ideas that apparently were first formalized by George Ainslie, e.g. that we all prefer short term pleasures and we tend to severely discount long term benefits as we make our choices in life. Given the choice between a chocolate bar right now and a chocolate cake tomorrow we tend to take the chocolate bar. This behavioral default is apparently well documented in man and other animals.

Formally we ought to discount future rewards by some reasonably uniform rate. So if we are offered a \$100 tomorrow and \$10 in an hour we ought to just compute the option value of each discounting by some interest rate based on the risk we percieve the future payoff to have. This kind of discounting is expediential; and it isn’t biased about things that are closer vs. farther away. It will cough up the same answer for 5 today vs. 10 tomorrow no matter what units (days, weeks, years) you use when you ask.

We animals don’t do that. Another way of saying that we like short-term benefits is that we discount things in small time units very sharply. A cookie in 30 seconds vs. a nice lunch in an hour? The cookie wins. It’s not rational but it’s how we are wired.

This leads to all kinds of common but irrational behaviors. Breaking the diet, staying up to late, having a few too many beers, failing to hold our tongue, etc. etc.

But most interestingly it puts us into a game just like the one above with ourselves. We are the audience. At each step in the game we have a choice to defect and take the dollar; but if we can manage not to defect then we can capture the long-term gains. We are caught in a gang of one our loyalty to our future selves continually tested against a hardwired setting that tempts us into short term defections.