Quantitative treatment of decision-making can often be handled by optimization of a mathematical model.
Common examples are refinery scheduling, distribution networks, inventory control, etc. Some of these require allowance for uncertainties such as costs, product yields, or raw material availability and quality. Nevertheless, the model can still be optimized (with some additional effort), after introducing statistical distribution functions for the uncertain quantities. However, some problems involve a few major competitors with diametrically opposed objectives. Significant shifts, from past behavior, by one competitor may then result in unpredictable reactions from others. We describe some game theory models which focus clearly on the interactions among competitors.
Le problème de la décision peut souvent être traité quantitativement par optimisation d'un modèle mathé- matique. Le planning dans une raffinerie, les réseaux de distribution, les controles d'inventaire sont des examples communs. I1 est parfois nécessaire de tenir compte d'incertitudes telles que: coûts, rendements, ou disponibilité et qualité de la matière première. Le problème peut toutefois être encore optimisé (moyennant un effort supplémentaire) par l'introduction de fonctions de distribution représentant les incertitudes.
Cependant dans certaines situations on considère une compétition entre éléments à objectifs diamètralement opposés. Un changement de comportement de l'un d'entre eux peut entraîner des réactions imprévisibles des autres. Nous décrivons quelques modèles de la théorie des jeux centrés sur les interactions entre ces eléments compétitifs.
In this paper we describe our initial efforts to develop methods for quantitative treatment of decision-making in complex competitive situations. Like others in the oil industry, we had acquired a certain facility with mathematical modeling of very complex situations, such as refinery operations and transportation networks. We were familiar with the elements of stochastic simulation which led to the decision theory of Chernoff and others, the industrial dynamics of Forrester5 and his co-workers, the venture analysis of Andersen, l and the risk analysis described by Hertz.7 Moreover, we had learned to optimize both linear and non-linear problems6*8* l43l8 and even to develop the principles behind optimization of stochastic situations. But none of these really tackled the fundamental competitive situation. The best approach for this seemed to be game theory. After the fundamental work by von Neumann and Morgenstern,20 and their successors,9 this has grown more and more mathematical in nature, and is by R. R. HUGHES and J. C. ORNEA Shell Development Company Emeryville, California getting further and further removed from practical applications in industry. Nevertheless, there have been some attempts to
