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|کد مقاله||سال انتشار||تعداد صفحات مقاله انگلیسی||ترجمه فارسی|
|23605||2001||23 صفحه PDF||سفارش دهید|
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Physica A: Statistical Mechanics and its Applications, Volume 301, Issues 1–4, 1 December 2001, Pages 512–534
This paper analyzes a model for the competition dynamics of web sites in the Internet, based on the Lotka–Volterra competition equations. This model shows the well known appearance of a winner-take-all characteristic and is based in the nonvalidity of traditional offer and demand equilibrium theory of these kinds of markets. From the stability analysis of the model, we establish a series of rules which are useful for defining strategies in the Internet market. One of the most important results that emerge from this simple model is the appearance of some unexpected phenomena related to the collaboration and competition between sites.
One of the most important drawbacks when planning the development of web sites is the absence of realistic mathematical models of the Internet markets. In the same way in which we can find models for the different phenomena in the traditional economy (equilibrium models, offer and demand models, competition models, etc.), it could be useful to develop mathematical explanations for the Internet business. In the past few years, some models of the competition dynamics of the Internet, and other phenomena related to the World Wide Web, have emerged ,  and . Precisely, in Ref. , a model based on the Lotka–Volterra competition equations for n variables was first used considering complete symmetric conditions for the competition parameters. In this paper, we are using the same model for the case of three variables, since it is the simplest to account at the same time for collaboration and competition. The model does not consider any random effects, which could be desirable for a more real description. However, we want to point out that our main interest resides in the competitive dynamics of the model. Furthermore, we believe that this is a good starting point to gain a better understanding of the dynamics of the web sites. Seasonal effects, which might be modeled by external periodic perturbations or random perturbations, to take into account fluctuations on the system or the unpredictable behavior of the Internet users, could be useful in further developments. Stochastic effects for a generalized Lotka–Volterra model have been included in Ref. . One of the main objectives here is to show how unexpected behaviors of these markets are predicted by simple models. Results from our analysis make it possible to obtain some rules, which can be useful to understand the competitive dynamics between the different web sites. As a matter of fact, one of the conclusions of our work is that very new and interesting phenomena emerge from the models when cooperation between sites is considered. In the same way in which some kind of ants and mushrooms cooperate in particular ecosystems complementing its capabilities and surviving like a single being, little web sites can collaborate with each other to avoid being destroyed by powerful Internet corporations. Even more interesting is the fact that the cooperation between sites drives to better economic results in terms of investment revenues. Numerical simulations show that the investment necessary for new companies to get into a particular Internet market segment is higher when one tries to accomplish it by developing a large single site. The cost can be extremely reduced by introducing little cooperating sites that complement its contents and services. The organization of this paper is as follows: First, we describe the mathematical model and compute the fixed points and its stability. These results are used later to perform an analysis of the different kinds of markets. This previous analysis is used to define strategies for the web sites. Finally, a critical review of the model is performed and the conclusions are presented.
نتیجه گیری انگلیسی
We have seen that a very simple model predicts the main characteristics of the Internet markets and can be useful to define strategies, although the results should not be taken literally. There are a lot of different effects that the model does not contemplate. In particular, as we have mentioned in the paper, we are not considering random forces into the model. We have chosen the three-variable system, to show one of the most important aspects of our work, which is the nonlinear effects on the competition between web sites. Moreover, the model should also be able to evolve allowing sites to change their strategy dynamically. Nowadays, the parameters involved in the strategy, the competition rates essentially, are taken as constant values that do not change with time. It would be interesting to add the possibility of modifying these parameters depending on the market evolution; in this way, sites could change their strategies adapting them to the particular conditions of the market. Another drawback of the model is that the parameters remain too abstract: we are talking about the competition rates, the growth rates, the initial conditions and the evolution in time, but it is not really clear how these parameters can be interpreted in a real situation. An economist or a company leader would like to calculate the α and the γ of a particular web site. Although we know that their values are related to real characteristics of the sites like the interest of its contents and its similarity with other sites, this is not enough when we are trying to predict the evolution of a market segment through the model. Moreover, the time unit also remains too ambiguous; the model can predict an increase in traffic in, say, two units of time, but in order to deploy a realistic strategy it would be necessary to know if these two units mean 2 months or 2 years. Most of these indefinite items could be solved comparing the model results with traffic analysis statistics or real web sites. If we could find a market segment where the hypothesis of the model could be matched, assuming it is possible to estimate the value of the different parameters, we could easily decide what the appropriate unit of time is by simply comparing the predictions of the model with the real data. Unfortunately, Internet traffic statistics are not easy to obtain. Another possible improvement of the model is related to adding noise and seasonal effects to the model. This could take account of changes in the parameters due to external events. Internet users are less interested when they are on vacation than when they are at work, so the parameter α can be expressed as the sum of periodical forces modeling the seasonal, weekly and daily behaviors of the customers. Our first developments show that these effects can modify the predictions of the model and thus can induce modifications in the strategies. More advanced models should take account of complex phenomena like cross marketing (when a site has links to other sites), reinvestments of the profit, the presence of external investments, etc. In spite of these imperfections, we believe that the model is a good starting point and an interesting tool to gain insight into the mechanism that govern the competition dynamics of the Internet markets. It shows that unlike the traditional material goods-based markets, the Internet is not driven by offer and demand principles, because the production cost of electronic goods does not depend on the number of replications. This makes that, once a site controls a market segment, the most powerful one, the rest of the competitors have little chance of finding a place in the segment, because the main one is able to fulfil all the market demand. It is also because of that, that a winner-take-all characteristic appears under strong competition conditions. Furthermore, the model gives a very important role to the alliances in the Internet. Until today, alliances of web sites have taken place in the form of one company absorbing another, but the electronic contents of two allied sites usually are far from being complementary. The model predicts that specializing the contents of allied web sites, dividing the contents according to the customers tastes, may give much better results than maintaining huge sites dealing with almost all possible themes a person can be interested in. One could criticize that there is no solid evidence for the validity of the model. It is true that it would be necessary to perform an exhaustive analysis of real traffic statistics to verify it, but there are indications that prove that some of the behaviors predicted by the model are true . On the other hand, the results obtained from the model seem to be in the same line than the conclusions obtained by analysts in the past few years, who predict the crisis of generic portals and propose thematic sites as the alternative for the Internet future. As a summary, in this paper we have shown that the Lotka–Volterra competition equations can be an adequate model to describe the competitive dynamics of the Internet markets. We have seen how different sites may plan different strategies depending on the conditions of the particular market segment they are in: strong sites may look for high competition conditions, weak sites may look for noncompetitive markets or may ally with other sites if the markets are highly competitive. We also have seen how the traditional equilibrium theory is not applicable any more in this kind of markets. More complex models of the Internet dynamics, taking account of a larger number of phenomena, should be developed in order to create a more complete theory describing virtual markets.