Prisoners’ Dilemma Part 1– The Game

The other day I stumbled across an old game known as “Prisoners’ Dilemma”.  I believe the first time I learned of the game was a general psychology class.  For some reason, this time around the game really captured my interest.  The rules are extremely simple and straight forward, but actually playing it is anything but.

 

Prisoners’ Dilemma– The Game

A game of Prisoners’ Dilemma consists of two opponents and a neutral banker.  The two players each choose to play one of two possible cards: “Cooperate” or “Defect”.  Players each play their cards face down such that the other player (nor the banker for that matter) has no way of knowing which card was selected.  Once both players have made their choice and played a card, the banker reveals both cards and then pays out to the players as follows:

Both Cooperate $300 to each player
One Defect, one Cooperate
$500 to player playing Defect, MINUS $100 to player playing Cooperate.
Both Defect ZERO payout to either player

 

Iterative Rounds

Playing a single game of Prisoners’ Dilemma isn’t very interesting:  A purely rational player, carefully thinking through each possibility and weighing them in her mind will realize the following:  If her opponent other player plays “Cooperate”, the best card to play is “Defect”, scoring the $500 prize!  Incidentally, if the other player chooses “Defect”, “Defect” is still the best card to play, protecting one’s self from the $100 penalty.  So “Defect” is the only card that makes any sense to play.  Assuming that the other player is also rational, she will also reason out that “Defect” is the only reasonable card to play.  Thus, the single game is deterministic and extremely uninteresting.

If, however, one plays Prisoners’ Dilemma as an iterated series of games with neither player knowing when the game will end, the game loses it’s single outcome, deterministic nature.  Knowing that one will be interacting with one’s opponent for some time to come gives the rational player more space:  They may build trust and mutually prosper.  They may betray trust and reap the high-value payoff of doing so, or may suffer the indignities of betrayal at the hand of their opponent .  They may choose to immediately retaliate against such betrayals, or craftily lie in wait for a better opportunity to serve up revenge not only cold, but lucrative as well.

 

Two Mental Models

I think there are two very interesting ways to think about Prisoners’ Dilemma:  One is to treat the game as a study in psychology.  You take to the streets in the role of the banker, and ask strangers to play against each other.  You study not only what the individuals are choosing but why.  You look for patterns of behavior and perhaps correlate them with other ways of grouping individuals (age, gender, socioeconomic status, race, etc).  Your hope, and the question you are trying to answer, is something about the nature of the human condition.  Why do we make the decisions we do?  When do we prefer to cooperate with each other and when do we prefer to benefit ourselves at any cost?

The other interesting way to think about Prisoners’ Dilemma is to treat the game as a puzzle to be solved:  How exactly does it work?  What methods are available to use in playing the game and when should they be used to secure the largest possible win?  Are there robust strategies available which are relatively simple and yet (think: Tic-Tac-Toe) guarantee a win (or at least a tie) every time they are used?  Rather than using the game as a tool to understand something more about who we are, your goal, instead, is to try to understand the nature of the tool itself.

 

When do Cheaters Prosper?

To some, this latter way of thinking about the game may seem mundane, academic and lacking appeal.  Until such time as the multi-million dollar Prisoners’ Dilemma tournament is announced, knowing exactly how to win the game is unlikely to be of real benefit to anyone.  That is true enough, but  has nothing to do with my interest in truly understanding the game and how to win it.

Parallels for Prisoners’ Dilemma are extremely common, not only in “natural” systems (like animals sharing food, removing parasites, protecting each other’s young, neighbors helping each other) but also in things particularly human:  Economics, business, politics, foreign-policy, etc.

 

Can “Nice Guys” Finish First?  When and How?

Any situation in which individuals may benefit by cooperating is likely subject to many, if not all the same drivers within the Prisoners’ Dilemma Game.  In all these situations, there is a clear temptation to cheat– to find, for example, ourselves pressed into a “mandatory” fishing trip when our neighbors are moving their belongings out of their home and into the moving truck– but still avail ourselves of their assistance when we are the ones moving.

If we understand the forces that drive the game, we can look to find similar drivers in life.  If there are particularly robust strategies or patterns of behavior that are particularly influential on the outcome of the game, we should expect to find them extensively employed, or a reasons why not.

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