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Stochastic programming: potential hazards when random variables reflect market interaction. (English) Zbl 1101.90047
Summary: There are two types of random phenomena modeled in stochastic programs. One type is what we may term “external” or “natural” random variables, such as temperature or the roll of a dice. But in many other cases, random variables are used to reflect the behavior of other market participants. This is the case for such as price and demand of a product. Using simple game theoretic models, we demonstrate that stochastic programming may not be appropriate in these cases, as there may be no feasible way to replace the decisions of others by a random variable, and arrive at the correct decision. Hence, this simple note is a warning against certain types of stochastic programming models. Stochastic programming is unproblematic in pure forms of monopoly and perfect competition, and also with respect to external random phenomena. But if market power is involved, such as in oligopolies, the modeling may not be appropriate.

90C15 Stochastic programming
91B26 Auctions, bargaining, bidding and selling, and other market models
91A15 Stochastic games, stochastic differential games
Full Text: DOI
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