Sunday, July 18, 2010

David Blackwell (1919 - 2010) -- and Game Theory

     David Blackwell, the first black scholar to be admitted to the National Academy of Sciences, a probabilist and statistician, died early this month. His NY Times and Washington Post obituaries tell of his many contributions. Blackwell's career connects to poetry through his interest in the Theory of Games.  He was co-author with Meyer Girshick of Theory of Games and Statistical Decisions, 1954, one of the early treatises on game theory.  

     A recent witty and lucid introduction to game theory is offered by Alexander Mehlmann in The Game's Afoot!  Game Theory in Myth and Paradox (volume 5 of the AMS Student Mathematical Library and translated by David  Kramer). Mehlmann, a professor at Vienna University of Technology, is also a poet and translator--and The Game's Afoot  is peppered with literary epigraphs which include the following:

     From time to time we take our pen in hand
     And scribble symbols on a blank white sheet.
     Their meaning is at everyone's command.
     It is a game whose rules are nice and neat.

This quatrain is from Herman Hesse's The Glass Bead Game (translation by Richard and Clara Winston);  Hesse's novel was published in 1943 -- almost coincident with the 1944 publication by John Von Neumann and Oskar Morgenstern of Theory of Games and Economic Behavior, a volume that marked, for all practical purposes, the birth of game theory.  

In Game Theory as in other mathematical ventures it is a useful habit of thought not to rule out the impossible; in time, it will exclude itself.  The following sentiment about decisions that go against the course of events is one of the stanzas offered by mathematician-writer Lewis Carroll's Mad Gardener in Sylvie and Bruno.

     He thought he saw an Argument
        That proved he was the Pope:
     He looked again, and found it was
       A Bar of Mottled Soap.
     "A fact so dread," he faintly said,
       "Extinguishes all hope."

Mehlmann concludes The Game's Afoot!  with his own lightly mocking "Postlude in Rhyme" called "The Mad Reviewer's Song" which follows the style of Carroll; here are two of his stanzas:

     He thought he saw a Strategy
        Undominated, Strict:
     He looked again, and found it was
        Quite Easy to Depict.
     "I'll never play a game," he said,
        "So simple to predict!"

     He thought he saw a Nash Profile
        Remaining unrefined:
     He looked again, and found it was
        Induction from Behind.
     "Before more doubts arise," he said,
        "Apply it!  Never mind!"

Long live the theory of games!!

1 comment:

  1. In the MAA death notices ( I found information about the passing (in June) of another game theorist--William F Lucas, who specialized in fair-division and voting systems.