28 June 2010

Simple rules, complex games

Bendor and Hammond rethink Graham Allison:
Several times in Essence of Decision, Allison uses the metaphor of chess when describing how leaders are constrained in their choice of options. This is odd, because chess is the paradigmatic example of a choice situation that involves only a handful of basic rules yet exhibits truly Byzantine strategic complexity. ... As is well known and as Allison himself noted, the number of possible sequences of play (i.e., behavhior) in chess is staggeringly large ... A common estimate is 10^120, a number so large as to be equivalent, for all practical purposes, to infinity. Human beings can never exhaust the richness of chess. This is pure combinatorial explosion: the rules are deterministic. Nor does the complexity depend upon stochastic inputs ... And the 'board' of any moderately large battle is more variegated than the (nontopographical) eight-by-eight chessboard. Therefore, chess, the paradigmatic choice environment of behavioral decision theory, provides a lower bound for the complexity of behavior one would expect to see in a clash between two governments.
This is simultaneously an exercise in brilliant rhetoric (and brings to mind how a fan of Uncle Duke in Doonesbury once congratulated the Hunter Thompson-esque writer for using words like they were blunt instruments) and also a little misleading. I am persuaded that Allison is wrong, but I am not persuaded that this is a good rebuttal to the argument. After all, there are practically infinitely many chess moves, but surely we can foreclose a great many of them after the first move or so (who plays 1. a4 h5, for instance?). More important, Allison and analysts more generally don't have to explain the entire game but merely how to analyze the situation at hand from the perspective of players whose interests are rational. And it is much easier to calculate how to improve one's position with a time horizon of four or five moves than it is to calculate more moves than there are atoms in the universe.

(Creative Commons photo by Ed Yourdon)
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