Category: Multiple Decision Makers, Subjective Probability, and Other Wild Beasts

The last point that we stressed in the previous section is the potential difficulty due to the interaction of multiple noncooperative, if not competitive, decision makers. The example we consider is a generalization of the newsvendor model:6 In order to be able to find analytical solutions, we depart from the usual assumption of normal demand,…

The last point that we stressed in the previous section is the potential difficulty due to the interaction of multiple noncooperative, if not competitive, decision makers. The example we consider is a generalization of the newsvendor model:6 In order to be able to find analytical solutions, we depart from the usual assumption of normal demand,…

The last point that we stressed in the previous section is the potential difficulty due to the interaction of multiple noncooperative, if not competitive, decision makers. The example we consider is a generalization of the newsvendor model:6 In order to be able to find analytical solutions, we depart from the usual assumption of normal demand,…

Consider the decision problem The objective function (14.1) can be interpreted in terms of a profit depending on two decision variables, x1 and x2, which must stay within feasible sets S1 and S2, respectively. Note that, even though the constraints on x1 and x2 are separable, we cannot decompose the overall problem, since the two decisions interact through the two profit functions π1(x1, x2) and π2(x1, x2). Nevertheless,…

The scenario tree of Fig. 14.1 may apply, e.g., to a two-stage stochastic programming problem. In a multistage stochastic programming model we have to make a sequence of decisions; a multistage scenario tree, like the one shown in Fig. 13.11, may be used to depict uncertainty. Even if we take for granted that sensible probabilities can be assigned…

The most troublesome case is when some scenarios are particularly dangerous, yet quite unlikely. How can we trust estimates of very low probabilities? To get the message, consider financial risk management. Here we need to work with extreme events (stock market crashes, defaults on sovereign debt, etc.), whose probabilities can be very low and very difficult to…

If we are about to launch a brand-new product, uncertainty about future sales is rather different from that in the previous case. Maybe, we know pretty well what may happen, so that the scenarios in Fig. 14.1 are known. However, it is quite hard to assess their probabilities. The following definitions, although not generally accepted, have been…

Let us compare two random experiments: fair coin flipping and the draw of a multidimensional random variable, with a possibly complicated joint probability density. The two cases may look quite different. The first one can be represented by a quite simple Bernoulli random variable, and calculating expected values of whatever function of the outcome is…

When we flip a fair coin, we are uncertain about the outcome. However, we are pretty sure about the rules of the game: The coin will either land head or tail, and to all practical purposes we assume that the two outcomes are equally likely. However, what about an alien who has never seen a…

The presented a rather standard view of quantitative modeling. When dealing with probabilities, we have often taken for granted a frequentist perspective; our approach to statistics, especially in terms of parameter estimation, has been an orthodox one. Actually, these are not the only possible viewpoints. In fact, probability and statistics are a branch of mathematics…