Nash Equilibrium and the Prisoners' Dilemma

• John Vandivier

This article will introduce Nash Equilibrium and the Prisoners' Dilemma. I will argue that prima facie these provide proof that empathetic markets can produce Nash-Superior equilibria.

Let me start off by saying Khan Academy is super awesome. See their short introductory video on Nash Equilibrium and the Prisoners' Dilemma:

https://www.youtube.com/watch?v=UkXI-zPcDIM#t=272

First thoughts:

  • The PD does not show market failure or rational acceptance of sub-optimal outcomes because it presumes a non-free market. Rational choice models use a free market, so to say that there was a rational choice for sub-optimal outcomes is misleading. The truth is that there was an ignorant choice for sub-optimal outcomes, which is a rather obvious feature.
  • A free market would have a large number of entrants. The large number of entrants would guarantee a diversity in preferences. Some entrants would be high risk takers and some would be rationally empathetic. Some of the risk takers and all of the rationally empathetic actors would achieve the globally optimal outcome which would be a Nash-Superior equilibrium.
  • A free market would have a free flow of information. The dilemma presumes that the prisoners do not know what the other would do, but this assumption is false in a free market.
  • In a truly free market with a free flow of information the only way that the Nash Equilibrium would occur is due to lack of trust, deception or greed. This shows that free flow of information is different from free flow of accurate information, which would eliminate the possibility of deception. Lack of trust and greed are both personal preferences, which shows that some personal preferences are inefficient.
  • It is not clear that inefficient personal preferences are considered irrational under current rational actor, behavioral or other theories, but under a good theory these personal preferences would be deemed inferior.
  • At first glance these facts seem to imply that a moral, empathetic and free market will consistently produce results superior to Nash Equilibria. Furthermore, there seems to be some reason to think that moral markets, empathetic markets and free markets in the strict sense are possibly equivalent, or different ways of looking at the same thing.