Wednesday, May 29, 2013

Austrians and Game Theory

My favorite area of economics and mathematics is Game Theory.  It is a fascinating subject with a wide variety of applications.  As someone who used to consider myself an adherent of the Austrian school of economics I know it deals with some of the issues Austrian Economists have with normal General Equilibrium methods of economics. Also, it just so happened to be "co-founded" by an Austrian economist, Oskar Morgenstern.  I knew Mises was not a fan of game theory, however, I was interested to see what current Austrian economists think of it and that is what motivated this post.  Needless to say there is a lack of understanding.

I went searching on to find as many articles I could, this first led me to the blog.  People there had varying opinions of game theory but the overwhelming understanding of game theory was completely mistaken.  One person mentioned how game theory is largely based off the prisoners dilemma and therefore is a useless thing to study.  This is very frustrating because game theory has roots all the way back to Emile Borel and other mathematicians, it's most influential work was published in 1944, and the prisoner's dilemma as we know it is credited to Luce and Raiffa in 1957!  This, amongst other fallacious arguments, were very common in these blog discussions.

Okay, so people writing on the blogs misunderstand game theory, but the trained economists couldn't be so drastically mistaken could they?  In an article entitled "The Games Economists Play" by Robert Murphy he attacks the conclusions of game theory in a clearly misinformed fashion.  He analyzes the aforementioned prisoner's dilemma and uses it to claim that because of this we should not accept game theory in general.

In the prisoners dilemma, two players are accused of committing crimes, one minor crime in which their guilt can be proven with out a confession, and major crime for which they cannot be convicted unless at least one confesses.  The confessor will go free but the other will go to jail for 6 years.  If neither confess, they will go to jail for only 1 year.  If they both confess they will go to jail for 5 years.  In this game without communication, the Nash Equilibrium is for each player to confess and hence go to jail for 5 years.  This, to Robert Murphy, is the downfall of game theory because each person could increase their non-jail time time by not confessing.

What Dr. Murphy does not understand is that Nash Equilibrium does not tell you the outcome will be optimal, only the strategies that rational players will make.  The reason the prisoner's dilemma is so famous is because it was the first example of an inefficient Nash Equilibrium (at least that I have found in my research)  Furthermore, he says

"Even here, the game theorists orthodox analysis is not entirely appealing: real world players often do cooperate even in a one-shot prisoner's dilemma"

This made me wonder if he is completely unaware of the study of games with communication?  Or even the study of cooperative game theory.  In the situation described above it is assumed that the prisoner's cannot communicate and have zero way of knowing what the other will do.  Hence, it certainly becomes much more plausible to confess (I have watched enough First 48 on A&E to see that people often do confess).  Also, if we analyze the game properly the outcome makes complete sense.  Since the criminals are not cooperating or communicating in any way, as soon as criminal A thinks criminal B will not confess, criminal A has all the incentive to confess.  His choice becomes either go to prison for one year or zero years.  Likewise for the other criminal.  Now one could argue that many criminals would rather go to jail than be a "rat".  This is where I would like to point out that the focal point effect already deals with this objection.  

Now, if we look at this game through a cooperative game theory lens, the outcome changes entirely.  Through this lens, we can consider any way in which the criminals will cooperate.  Consider the possibility that there is a contract signed before hand in which the criminals agree to not confess otherwise face a punishment worse than prison.  In this game, the person does not have any incentive to cheat because the time he spends free will be worse than time in prison due to the punishment.  Hence, the equilibrium now becomes both criminals not confessing.  

Two more points to consider: first, he mentions people using the prisoner's dilemma to argue for government intervention.  Again, these people do not understand the fact that the criminals have no way to communicate or cooperate.  Hence, their argument is invalid.  Further, the fact that Robert Murphy would actually use this argument to argue against game theory is intellectually dishonest.  He is misrepresenting something he should have studied while getting his PhD.  Any game theorist knows the prisoner dilemma can actually be used to argue for LESS government.

Finally, he gives a formidable representation of "backward-substitution".  Again, I am wondering if he is unaware of the vast literature on the subject of repeated games.  In 1982 Kreps, Milgrom, Roberts and Wilson constructed a way to show that "non-confession" strategy will be employed given an initial certain doubt and actions during the game.  The explanation gets very technical with a lot of game theoretical terms so I will not go into it here, but it is discussed in full detail in "Game Theory: Analysis of Conflict" by Roger B. Myerson in section 7.6.  Also, there are game theorists who study forward induction as well.

In conclusion, it is clear to see Robert Murphy builds up a straw man representation of game theory in order to tear it down.  No where does he address any of the advancements of game theory in the last 20-30 years.  He does not address perfect equilibrium, proper equilibrium, sequential equilibrium, subgame perfect equilibrium, trembling hand perfect equilibrium, the focal point effect, repeated games and the list could go on.  He does however, address Nash equilibrium and the prisoners dilemma, two aspects of game theory developed in the 1950's.  Both of which have been greatly advanced.

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