Prisoner’s Dilemma Answers

I posted previously that Freakonomics was hosting a Prisoner’s Dilemma contest.  About a week ago they selected the top five answers and had a quick voting contest (comment democracy with 48 hours to decide the winner).  Since I am both currently attending one of the EITM summer programs and exercising my current mathematical knowledge by attempting to run a maximum likelihood estimation of a generalized Prisoner’s Dilemma model with a normally distributed cost function to the players for cooperation; it seemed like a good time to return to the post and evaluate the answers provided.

Adding a pre-game to the Prisoner’s Dilemma ought not to change the strategy of either player.  In theory, if you are asking your potential opponent/partner a question, you want to select someone who is going to play sub-optimally by either their own ignorance or your ability to convey to them that you are willing to cooperate (but will not anyways).  A rational interviewee will see this, and will either defect no matter what to dissuade you from picking them or attempt to coax the main player into cooperation only willing to defect later.  When evaluating any question you are asking another person a question in a non-cooperative framework, you must ascribe the same level of rationality that they will have in playing the game.  That is, if you believe people to remain rational actors, then talk prior to the game can remain cheap as a single question may not return an honest answer.

After the jump I discuss the five questions and the usefulness of each:

John List picked the top five responses:

1. “How old are you?”

2. “What is the number of ethics courses you’ve taken, minus the number of economics courses you’ve taken?”

3. “Given that you are in a bar, would you prefer to pursue the most attractive person in the bar, or would your efforts focus on someone less attractive?”

4. “What is the name and address of your most cherished family member?”

5. “Have you read Freakonomics?”

Question One: 1. “How old are you?”

This is potentially a very useful question as it is a way to elicit someone’s irrationality or inexperience.  I know of at least one experimental, working paper on how learning can promote rationality and early plays at a game may lead to seemingly irrational moves.  A player who does not fully ascertain a game and understand the proper moves will likely make mistakes.  Thus, if we see a younger opponent as being inexperienced at PD type games, then it might be possible they will play poorly and cooperate.  Additionally, if the old adage that suggests the young are liberal idealists while older individuals are conservative pragmatists is true, the age question may allow you to select an opponent based on probabilistic naivety.

The incentive to lie may still exist, but it is harder to accomplish this with visual confirmation of someone’s age.  While misleading someone by up to a decade is certainly possible, the difference in strategy may not matter – especially if there are stark contrasts between potential opponents.

Question Two: “What is the number of ethics courses you’ve taken, minus the number of economics courses you’ve taken?”

While interesting, I think the number of ethics courses are irrelevant to the equation – courses on ethics can produce a variety of people despite any theory that suggests otherwise.  Self-serving nihilists may take as many ethics courses as a "golden-rule abiding" Kantians and both of those pre-dispositions may have been formed prior to taking a class, not result because of it.  A useful question, in my opinion, would be the number of economics courses purely to see if they understand the generation, strategy, and outcome of similar games to prisoner’s dilemma.  This is especially helpful since PD is a very basic game.  Thus, a number “1” to my adaptation to the question is more useful than “-1” for the original question as the -1 could have a variety of interpretations.

Question Three: “Given that you are in a bar, would you prefer to pursue the most attractive person in the bar, or would your efforts focus on someone less attractive?”

I understand the motivation of the question and the blog lays it out, but I am not convinced this is useful information. List points out why this is a bad example in the movie A Beautiful Mind as Nash focused on non-cooperative game theory.  It fails here as PD is a non-cooperative game as well and provides different incentives.

Question Four:  “What is the name and address of your most cherished family member?”

The interviewee should lie.  There is no advantage to give out this information and allows the interviewer to exploit the situation by adding negative, external costs to the game.  In fact, an interviewee can gain further if they listed the name of an enemy and then proceeded to defect to get some external benefit as they placed their enemy at risk for retribution.

Question Five: “Have you read Freakonomics?”

Given that this list is from a blog from the individuals who wrote the book, this looks like pandering…and mostly is in my opinion.  This becomes a double-edged sword of information that may lead the interviewer astray with bad information.  A “yes” could mean both that a person may believe in cooperation in a non-cooperative game (given the non-straight forward economic behavior of individuals in the book may encourage altruism in a Prisoner’s Dilemma) and/or may be learned enough to know the optimal strategy in this current situation.  A “no” answer could mean that the person is ignorant about general economic behavior and rationality, that they find such information contained within Freakonomics to be irrelevant, or at best, equilibria behavior not properly specified in the appropriate  literature and therefore, not a worthy read.  Finally, they could just judge the book by the cover by using strategic information short cuts and will likely play optimally against you.

Given the Five Questions, it is clear to me that number one is the best proxy for gaining useful information.  The problem with all of the questions is that they rely on the person to betray their own rational self-interest and expose their ignorance or proclivity to irrational decisions.