Iterated games

I’ve been teaching game theory as part of my Analytic Methods for Lawyers class.  Yesterday, we finished up the problem set early in the class (as I’d kind of expected), so I decided to be bold and ask the class to consider iterated games.  I’d done some work on it a few years back and produced a Demonstration. But I’d done so before Mathematica had added better support for graphs and discrete Markov processes.  I wondered whether that additional functionality might simplify some of the exposition and analysis.  Turns out, as shown below, it does.

If you want to skip to the bottom line, here’s what I found:

  1. It is fairly easy to visualize and understand simle iterated games with Mathematica. The new Graph functionality and support for discrete Markov processes makes the matter somewhat easier.
  2. There are lots of weak Nash equilibria to simple iterated games. And many let one escape a prisoners dilemma. That’s very important because an awful lot of legal situations have an iterated prisoners dilemma as a sensible metaphor.
  3. Game theory starts out simple. Understanding the idea of a strategic form game is not that hard. Likewise, it isn’ t too bad understanding the concept of a Nash equilibrium (once John Nash helped find it in the first place). But the peculiar thing about game theory is how incredibly difficult it can get once one interjects just a tiny bit of complexity. This blog entry begins, I think, to explore that transition from simplicity to complexity.

[WolframCDF source=”http://mathlaw.org/wp-content/uploads/2013/04/iterated-games-v3.cdf” CDFwidth=”802″ CDFheight=”7400″ altimage=””]

 

Note: On April 11th, minor changes were made to the CDF file that had prevented the Manipulate from working properly and that corrected a typo.

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