A game-theoretic interpretation of Sun Tzu's The Art of War

Abstract

Over 25 hundred years ago the Chinese scholar Sun Tzu, in The Art of War, attempted to codify the general strategic character of conflict and, in the process, offer practical advice about how to win military conflicts. His advice is credited with having greatly influenced both Japanese military and business practices, as well as Mao Tse-Tung's approach to conflict and revolution. The question, however, is whether or to what extent Sun Tzu anticipated the implications of the contemporary theory of conflict--game theory. The thesis of this essay is that he can be credited with having anticipated the concepts of dominant, minmax, and mixed strategies, but that he failed to intuit the full implications of the notion of equilibrium strategies. Thus, while he offers a partial resolution of 'he-thinks-that-I-think' regresses, his advice remains vulnerable to a more complete strategic analysis. In judging Sun Tzu's contribution to our understanding of strategy, however, we should keep in mind that resolving circular reasoning in some circumstances requires the use of advanced principles of probability theory and mathematics, and so we should not be surprised to learn that Sun Tzu's treatment of information is incomplete. Indeed, we should marvel at the fact that he understood intuitively as much as he did.

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