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Showing posts from November, 2009

Randomization of threats and promises

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An extract from T. C. Schelling Economics Division, The RAND Corporation, P-1716 June 5, 1959 [Preventing deduction and anticipation in a zero-sum game] In the theory of games of pure conflict ("zero-sum" games) randomized strategies play a central role. It may be no exaggeration to say that the potentialities of randomized behavior account for most of the interest in game theory during the past decade and half (*). The essence of randomization in a two-person zero-sum game is to preclude the adversary's gaining intelligence about one's own mode of play -- to prevent his deductive anticipation of how one may make up one's own mind, and to protect oneself from tell-tale regularities of behavior that an adversary might anticipate. In the game that mix conflict with common interest, however, randomization plays no such principal role, and the role it does play is rather different. [Giving fractional/sampled information to avoid total war situations in a general game...

Robust Optimization

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Decision under uncertainty with imperfect probabilistic description of reality The field of decision-making under uncertainty was pioneered in the 1950s by Dantzig [6] and Charnes and Cooper [5], who set the foundation for, respectively, stochastic programming and optimization under probabilistic constraints. While these classes of problems require very different models and solution techniques, they share the same assumption that the probability distributions of the random variables are known exactly, and despite Scarf's [10] early observation that we may have reason to suspect that the future demand will come from a distribution that differs from that governing past history in an unpredictable way," the majority of the research efforts in decision-making under uncertainty over the past decades have relied on the precise knowledge of the underlying probabilities . Even under this simplifying assumption, a number of computational issues arises, e.g., the need for multi-variate ...