Author: haroonkhan

In this section we consider Nash equilibrium for the case in which a continuum of infinite actions is available to each player. To be specific, we analyze the behavior of two firms competing with each other in terms of quantities produced. Both firms would like to maximize their profit, but they influence each other since…

The concepts that we have used so far make sense, but they are a bit too restrictive and limit the set of games for which we may make reasonable predictions. A better approach, in a sense that we should clarify, is Nash equilibrium. Before formalizing the concept, imagine a game in which there is one…

Sometimes, it is fairly easy to argue which outcome is to be expected. If we consider the strategies for firm A in Table 14.1, we see that: So, whatever firm B plays, firm A is better off by playing low. The symmetry of the game implies that the same consideration applies to firm B, which will also…

The standard example to illustrate the normal form representation of a simple game is the prisoner’s dilemma, which is arguably the prototypical example of a two-player game. The prisoner’s dilemma has been phrased in many different ways;12 in the next example we use what is closest to a business management setting. Example 14.4 (Prisoner’s dilemma) Consider two…

In the previous section we have considered a case in which two stakeholders, a producer and a distributor, make their decisions in a specific order. The producer (leader) determines product quality, as well as the probability distribution of demand as a consequence; the distributor (follower) chooses the order quantity. In other cases, however, decisions are…

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…