Competitive dynamics and the introduction of new products: The motion picture timing game

The extremely short life cycle and the rapid decay in revenues after opening coupled with the rapid and frequent introduction of new competitive products makes the timing of new product introductions in the motion picture industry critical, particularly during the high-revenue Christmas and summer seasons. Each studio wants to capture as much of the season as possible by opening early in the season. At the same time, each wants to avoid head-to-head competition. The authors model competition between two motion pictures in a share attraction framework and conduct an equilibrium analysis of the product introduction timing game in a finite season. The following three different equilibrium configurations emerge: (1) a single equilibrium with both movies opening simultaneously at the beginning of the season, (2) a single equilibrium with one movie opening at the beginning of the season and one delaying, and (3) dual equilibria, with either movie delaying opening. A key factor is the product life cycle, which can be captured well with a two-parameter exponential decline. The authors relate the life-cycle parameters to these possibilities with the general result that the weaker movie may be forced to delay opening. These results are related to case studies of the opening of recently released movies. A statistical analysis of the 1990 summer season in North America provides support for the conclusions and suggests that current release timing decisions can be improved; The authors discuss the rationale of "avoiding the competition" in the general context of product introduction timing

Spatial competition and bounded rationality: Retailing at the edge of chaos

The spatial dimension of competition among retail outlets is well researched and typically captured with spatial interaction models. A stream of theoretical research has studied the consequences of incorporating various types of dynamics into these models. We build on this research by incorporating a behavioral decision process based on bounded rationality, and by allowing for unexpected adversity in the environment in the form of exogenous shocks. Given these characteristics-spatial competition, boundedly rational decision making, and environmental adversity-we study the long-run dynamics of a model retail industry. The model reaches a stochastic steady state which is `'poised,'' in the sense that a shock may-or may not-trigger a wave of innovation which sweeps the entire system. Detailed investigation of this steady state shows that it has the characteristics of a general type of organization, known as self-organized criticality, that has been described in both theoretical biology and statistical physics

Finite mixtures of generalized linear regression models

Finite mixture models have now been used for more than hundred years (Newcomb (1886), Pearson (1894)). They are a very popular statistical modeling technique given that they constitute a flexible and-easily extensible model class for (1) approximating general distribution functions in a semi-parametric way and (2) accounting for unobserved heterogeneity. The number of applications has tremendously increased in the last decades as model estimation in a frequentist as well as a Bayesian framework has become feasible with the nowadays easily available computing power. The simplest finite mixture models are finite mixtures of distributions which are used for model-based clustering. In this case the model is given by a convex combination of a finite number of different distributions where each of the distributions is referred to as component. More complicated mixtures have been developed by inserting different kinds of models for each component. An obvious extension is to estimate a generalized linear model (McCullagh and Nelder (1989)) for each component. Finite mixtures of GLMs allow to relax the assumption that the regression coefficients and dispersion parameters are the same for all observations. In contrast to mixed effects models, where it is assumed that the distribution of the parameters over the observations is known, finite mixture models do not require to specify this distribution a-priori but allow to approximate it in a data-driven way. In a regression setting unobserved heterogeneity for example occurs if important covariates have been omitted in the data collection and hence their influence is not accounted for in the data analysis. In addition in some areas of application the modeling aim is to find groups of observations with similar regression coefficients. In market segmentation (Wedel and Kamakura (2001)) one kind of application among others of finite mixtures of GLMs aims for example at determining groups of consumers with similar price elasticities in order to develop an optimal pricing policy for a market segment

Evolutionary dynamics of rDNA clusters on chromosomes of moths and butterflies (Lepidoptera)

We examined chromosomal distribution of major ribosomal DNAs (rDNAs), clustered in the nucleolar organizer regions (NORs), in 18 species of moths and butterflies using fluorescence in situ hybridization (FISH) with a codling moth (Cydia pomonella) 18S rDNA probe. Most species showed one or two rDNA clusters in their haploid karyotype but exceptions with four to eleven clusters also occurred. Our results in a compilation with previous data revealed dynamic evolution of rDNA distribution in Lepidoptera except Noctuoidea, which showed a highly uniform rDNA pattern. In karyotypes with one NOR, interstitial location of rDNA prevailed, whereas two-NOR karyotypes showed mostly terminally located rDNA clusters. A possible origin of the single interstitial NOR by fusion between two NOR-chromosomes with terminal rDNA clusters lacks support in available data. In some species, spreading of rDNA to new, mostly terminal chromosome regions was found. The multiplication of rDNA clusters without alteration of chromosome numbers rules out chromosome fissions as a major mechanism of rDNA expansion. Based on rDNA dynamics in Lepidoptera and considering the role of ordered nuclear architecture in karyotype evolution, we propose ectopic recombination, i.e. homologous recombination between repetitive sequences of non-homologous chromosomes, as a primary motive force in rDNA repatterning