Abstract
In this paper, we consider oligopolistic firms with supply chain networks who are involved in the production, storage, and distribution of a homogeneous product to demand markets and explore what has become known in the literature as the “merger paradox.” We present the oligopolistic supply chain network equilibrium model associated with the competing firms before the horizontal mergers and also develop the supply chain network optimization model post the complete merger. In addition, we develop the model in which only a subset of the firms in the industry merge. The governing concept of the competing firms is that of Cournot–Nash equilibrium. We utilize finite-dimensional variational inequality theory for the formulation, analysis, and solution of both the pre and the post-merger supply chain network problems. We provide numerical examples for which we compute the total costs, the total revenues, as well as the profits obtained for the firms pre and post the mergers for a variety of distinct oligopoly problems. The generality of the network models and the flexibility of the computational approach, which yields closed form expressions for the product flows at each iteration, allows us to obtain deeper insights into the merger paradox.
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Bazaraa MS, Sherali HD, Shetty CM (1993) Nonlinear programming: theory and algorithms. Wiley, New York
Beverage World (2007) Molson Coors Brewing Co. http://www.beverageworld.com/content/view/33296/
Brown G, Keegan J, Vigus B, Wood K (2001) The Kellogg company optimizes production, inventory and distribution. Interfaces 31: 1–15
CNNMoney.com (1999) Exxon-Mobil merger done. November 30
Cournot AA (1838) Researches into the mathematical principles of the theory of wealth, English translation, MacMillan, London, England, 1897
Creane A, Davidson C (2004) Multidivisional firms, internal competition and the merger paradox. Can J Econ 37: 951–977
Dafermos S, Nagurney A (1987) Oligopolistic and competitive behavior of spatially separated markets. Reg Sci Urban Econ 17: 245–254
Dafermos S, Sparrow FT (1969) The traffic assignment problem for a general network. J Res Natl Bureau Stand 73: 91–118
Dupuis P, Nagurney A (1993) Dynamical systems and variational inequalities. Ann Oper Res 44: 9–42
Farrell J, Shapiro C (1990) Horizontal mergers: an equilibrium analysis. Am Econ Rev 80: 107–126
Flam SP, Ben-Israel A (1990) A continuous approach to oligopolistic market equilibrium. Oper Res 38: 1045–1051
Friedman J (1982) Oligopoly theory. In: Arrow KJ, Intriligator MD (eds) Handbook of mathematical economics vol II. North Holland, Amsterdam, pp 490–534
Gabay D, Moulin H (1980) On the uniqueness and stability of Nash equilibria in noncooperative games. In: Bensoussan A, Kleindorfer P, Tapiero CS (eds) Applied stochastic control of econometrics and management science. North-Holland, Amsterdam, pp 271–294
Ghosal V, Stennek J (eds) (2007) The political economy of antitrust. Elsevier, Amsterdam
Global News Wire (2008) Delta and Northwest merge, creating premier global airline. Press release, October 29
Gupta D, Gerchak Y (2002) Quantifying operational synergies in a merger and acquisition. Manage Sci 48: 517–534
Hakkinen L, Norrman A, Hilmola O-P, Ojala L (2004) Logistics integration in horizontal mergers and acquisitions. Int J Logist Manag 15: 27–42
Herd T, Saksena AK, Steger TW (2005) Delivering merger synergy: a supply chain perspective on achieving high performance. Outlook—point of view, Accenture, May
Kusstatscher V, Cooper CL (2005) Managing emotions in mergers and acquisitions. Edward Elgar Publishing, Cheltenham
Langabeer J, Seifert D (2003) Supply chain integration: the key to merger success (synergy). Supply Chain Manag Rev 7: 58–64
Meschi M (1997) Analytical perspectives on mergers and acquisitions. A survey. Paper Number 5-97, ISSN number 1366-6290, Centre for International Business Studies, South Bank University, London
Min H, Zhou G (2002) Supply chain modeling: past, present, future. Comput Ind Eng 43: 231–249
Murphy FH, Sherali HD, Soyster AL (1982) A mathematical programming approach for determining oligopolistic market equilibrium. Math Program 24: 92–106
Nagurney A (1993) Network economics: a variational inequality approach. Kluwer Academic Publishers, Dordrecht
Nagurney A (2006a) On the relationship between supply chain and transportation network equilibria: a supernetwork equivalence with computations. Transp Res E 42: 293–316
Nagurney A (2006b) Supply chain network economics: dynamics of prices, flows and profits. Edward Elgar Publishing, Cheltenham
Nagurney A (2009) A system-optimization perspective for supply chain network integration: the horizontal merger case. Transp Res E 45: 1–15
Nagurney A, Zhang D (1996a) Stability of spatial price equilibrium modeled as a projected dynamical system. J Econ Dyn Control 20: 43–63
Nagurney A, Zhang D (1996b) Projected dynamical systems and variational inequalities with applications. Kluwer Academic Publishers, Boston
Nagurney A, Dupuis P, Zhang D (1994) A dynamical systems approach for network oligopolies and variational inequalities. Ann Oper Res 28: 263–293
Nagurney A, Takayama T, Zhang D (1995) Massively parallel computation of spatial price equilibrium problems as dynamical systems. J Econ Dyn Control 18: 3–37
Nagurney A, Dong J, Zhang D (2002) A supply chain network equilibrium model. Transp Res E 38: 281–303
Nash JF (1950) Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, USA 36: 48–49
Nash JF (1951) Noncooperative games. Ann Math 54: 286–298
Pepall L, Richards D, Norman G (1999) Industrial organization: contemporary theory and practice. South-Western College Publishing, Cleveland
Perry MK, Porter RH (1985) Oligopoly and the incentive for horizontal merger. Am Econ Rev 75: 219–227
Phoenix Business Journal (2009) Wells Fargo, Wachovia complete merger. January 2
Salant S, Switzer S, Reynolds R (1983) Losses due to merger: the effects of an exogenous change in industry structure on Cournot-Nash equilibrium. Q J Econ 48: 185–200
Sandholm WH, Dokumaci E, Lahkar R (2008) The projection dynamic and the replicator dynamic. Games Econ Behav 64: 666–683
Soylu A, Oruc C, Turkay M, Fujita K, Asakura T (2006) Synergy analysis of collaborative supply chain management in energy systems using multi-period MILP. Eur J Oper Res 174: 387–403
Tirole J (1988) The theory of industrial organization. MIT Press, Cambridge
TradingMarkets.com (2008) Anheuser-Busch shareholders okays InBev merger. November 12
Xu S (2007) Supply chain synergy in mergers and acquisitions: strategies, models and key factors, PhD dissertation. University of Massachusetts, Amherst
Zhang D (2006) A network economic model for supply chain vs. supply chain competition. Omega 34: 283–295
Zhang D, Nagurney A (1997) Formulation, stability, and computation of traffic network equilibria as projected dynamical systems. J Optim Theory Appl 93: 417–444
Zhang D, Dong J, Nagurney A (2003) A supply chain network economy: modeling and qualitative analysis. In: Nagurney A (eds) Innovations in financial and economic networks. Edward Elgar Publishing, Cheltenham, pp 197–213
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This paper may be viewed as a contribution to the marriage of frameworks in operations research/management science and computational economics.
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Nagurney, A. Formulation and analysis of horizontal mergers among oligopolistic firms with insights into the merger paradox: a supply chain network perspective. Comput Manag Sci 7, 377–406 (2010). https://doi.org/10.1007/s10287-009-0095-6
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DOI: https://doi.org/10.1007/s10287-009-0095-6