We report some new results on compromise solutions studied by Yu [Yu, P. L. 1973. A class of decisions for group decision problems. Management Sci. 19 (8, April) 936-946]. The following article focuses on the relation between the compromise solution and its parameter. In particular, we show that, under some nice conditions, the compromise solution is a continuous function of its parameter. A fundamental monotonicity result (Theorem 3.1) concerning compromise solutions is derived. The result enables us to generate the bounds of all compromise solutions. When n = 2, two monotonicity results are derived. These yield a good interpretation of the parameter p. When p is small the "group utility" is emphasized; and when p increases the individual regrets receive more weight. Finally we construct an example to illustrate that the monotonicity results for n = 2 are almost impossible to be generated for n > 2.
The analysis of stochastic models is often greatly complicated if there are censored observations of the random variables. This paper characterizes families of distributions which help keep tractable the analysis of such models. Our primary motivation is to provide guidance to practitioners in the selection of distributions: If a modeler feels that no member of the families we characterize is a reasonable approximation, then he will almost surely encounter serious analytic and computational problems if his data include censored observations. We characterize a family of distributions for which there exist fixed-dimensional sufficient statistics of purely censored observations. We also characterize an important subset of this family, appropriate for situations where data include both censored and exact observations. We derive the corresponding predictive distributions using arbitrary priors and present some general results relating stochastic dominance among predictive distributions to the parameters of the prior. We also analyze the cases of discrete and mixed random variables.informational dynamics, censored data, stochastic models, Newsboy problem, sufficient statistic
Rapid technological developments and deregulation of the telecommunications industry have changed the way in which content providers distribute and price their goods and services. Instead of selling a bundle of content and access through proprietary networks, these firms are shifting their distribution channels to the Internet. In this new setting, the content and Internet service providers find themselves in a relationship that is simultaneously cooperative and competitive. We find that proprietary content providers prefer the Internet channels to direct channels only if the access market is sufficiently competitive. Furthermore, maintaining a direct channel in addition to the Internet channels changes the equilibrium enough that the proprietary content providers prefer having the Internet channels, regardless of the level of competition in the access market. Telecommunications technology developments uniformly increase content providers' profit. On the other hand, the technology impact on Internet service provider profits is nonmonotonic: Their profits may increase or decrease as a result of lower telecommunication costs. While initially the ISP profit increases as more customers are drawn to the Internet, it eventually decreases as the spatial competition becomes more intense. We also show that proprietary content providers should benefit from having some free content available at the Internet service providers' sites to induce more customers to join the Internet.electronic commerce, electronic publishing, digital content, information goods, internet service providers (ISP), pricing content, industrial organization, spatial competition, industry structure
The question as to the optimality of advertising pulsing has attracted many researchers over the last half-century. In this paper we specify a market share model in which there are two advertising-setting firms as well as a no-purchase option. The framework is that of a first-order Markov process with three states. The objective of both firms is to maximize profits. We are able to demonstrate, for a diminishing returns advertising function, that the optimal advertising strategy is pulsing. The frequency of the advertising pulse is shown to depend on the magnitude of the market share retention rate (state dependence); the higher it is, the less frequent the advertising. We further find that the optimal advertising budgets do not remain the same when the frequency of pulsing changes. Finally, we show that it is optimal for both firms to advertise in phase.
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