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Journal of Applied Mathematics
Volume 2014, Article ID 952046, 11 pages
Research Article

A Dynamic Model of the Tragedy of the Commons in Marketing-Intensive Industries

School of Management, Kyung Hee University, 26, Kyungheedae-ro, Dongdaemun-gu, Seoul 130-701, Republic of Korea

Received 18 January 2014; Revised 17 March 2014; Accepted 18 March 2014; Published 27 April 2014

Academic Editor: Nachamada Blamah

Copyright © 2014 Dohoon Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study provides a dynamic model and analyzes its process that may plunge the business ecosystem into ToC (the Tragedy of the Commons). When developing the model, we have in mind some industries where the marketing competition to secure a large installed base is intense. The social commerce industry is a representative example of this type of industries, but the scope of this study is not limited to the industry. We first introduce a previous study focusing on the static Nash equilibrium, and then present an extended version of the basic model in a dynamic perspective. According to our analyses on the dynamic equilibria together with their stability, there may be a unique interior equilibrium, but it is highly likely unstable. In addition, possible (near) boundary equilibria are also unstable for a wide range of parameter values. We also conduct some numerical experiments and discover cycles as solutions to some particular instances. Since those cycles contain the ToC traps, a policy measure or regulation may need to be employed. Our approach and results will help to figure out a clue to escape from the ToC trap, thereby shedding new light on the sustainable growth of the business ecosystem, which is prone to excessive marketing competition.