Friday, July 13, 2012

What would game theory say about LIBOR?

On days like to day, I wish I were a game theorist.  The I could figure out what a Nash game would predict about LIBOR reporting, and how that would vary from honest reporting.

The rules of the game are well set out and mostly symmetric, although it is the mostly part that creates a problem.  Suppose there are N reporters and the LIBOR that is produced is based on the interquartile mean of what is reported.  Each bank is then seeking to maximize some objective function that depends on that interquartile mean, over which it has some influence.  If all banks have the same objective function, then symmetry will mean they all choose the same rate, which is not particularly interesting.

But each individual bank is gets some draw from a distribution, that it turn determines its optimal play.  This will produce heterogeneity in rates chosen.  Alas, I am not good enough at math to go any further than that...

[update: found a paper that does the exercise here.]