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There is a rising trend in supplying chain management to employ simultaneous cooperation and competition (coopetition) among supply chain partners as an efficient strategy to create value. There exist, however, few models which analyze coopetitive situations mathematically. Cooperative game theory is the common tool in analyzing cooperative situations. However, the term “cooperative” in “cooperative game theory” is absolutely misleading since it ultimately leads to competition analysis and ignores the internal structure of the cooperation. Coopetition, however, results in structural transformations in players. Therefore, we require a mathematical modeling approach which takes into account the internal structural changes due to cooperation among competitors. In so doing, in this paper we propose, we assume that those parameters of each firm’s profit function are subject to transformation by cooperation as a function of cooperation level so as to determine the right level of cooperation and production of firms while considering technical cooperation between them. Furthermore, we demonstrate the results of applying the idea to a supply chain situation where two similar suppliers participate. We conclude that under intuitive conditions coopetition strategy is superior to the pure competitive relationship between the suppliers in terms of profitability which validates the previous empirical results mathematically.

Recent global economic recession seems to have led surviving supply chains to employ strategies and tools that enhance the creation of value at less cost than ever before among which the emerging role of collaboration in improving supply chain value creation system is highly intensified both by academia and practitioners. For instance, Walker [

Traditionally, however, collaboration forms among partners with fully convergent goals so that cooperating competitors are unimaginable at the first thought. Cooperation among competitors or simply coopetition (Brandenburger and Nalebuff [

Despite the significance of coopetition in reshaping the value net of a supply chain and its emerging practice in real-life cases, the amount of academic research in this arena is still quite limited (Dagnino and Rocco [

The evolution of coopetition literature during 2000–2014.

Authors | Year | Research Area | Methodology |
---|---|---|---|

Bengtsson and Kock [ |
2000 | Business networks | Empirical |

Carayannis and Alexander [ |
2001 | Satellite industry | Empirical |

De Vlaam and De Jong [ |
2002 | Infrastructure sector | Empirical |

Levy et al. [ |
2003 | Knowledge sharing management | Empirical |

Soekijad and Andriessen [ |
2003 | Knowledge sharing management | Empirical |

Song [ |
2003 | Port management | Empirical |

Luo [ |
2004 | Multinational corporations | Conceptual |

Cheng [ |
2005 | ICT industry | Empirical |

Luo [ |
2005 | Multinational corporations | Conceptual |

Gnyawali et al. [ |
2006 | Competitive behavior | Empirical |

Luo et al. [ |
2006 | Cross-functional relationships | Empirical |

Reaidy et al. [ |
2006 | Manufacturing control systems | Analytical |

Luo [ |
2007 | Global competition | Conceptual |

Brandes et al. [ |
2007 | Automotive industry | Conceptual |

Gurnani et al. [ |
2007 | Supply chain management | Analytical |

López-Gómez and Molina-Meyer [ |
2007 | Dynamical systems | Analytical |

Barretta [ |
2008 | Health-care sector management | Empirical |

Bojar and Drelichowski [ |
2008 | Agriculture sector management | Empirical |

Chin et al. [ |
2008 | Manufacturing strategy management | Empirical |

Eriksson [ |
2008 | Buyer-supplier relationships | Empirical |

Min et al. [ |
2008 | Cluster supply chains | Analytical |

Wang and Krakover [ |
2008 | Tourism industry | Empirical |

Bakshi and Kleindorfer [ |
2009 | Supply chain management | Analytical |

Baumard [ |
2009 | SME innovation strategies | Conceptual |

Brolø [ |
2009 | Financial sector | Empirical |

Cassiman et al. [ |
2009 | Research and development | Empirical |

Czakon [ |
2009 | SME relationships | Empirical |

Gnyawali and Park [ |
2009 | SME technological innovations | Conceptual |

Gueguen [ |
2009 | Information technology sector | Empirical |

Mione [ |
2009 | Institutional standards development | Empirical |

Nadin [ |
2009 | Automotive industry | Empirical |

Ritala and Hurmelinna-aukkanen [ |
2009 | Research and development | Conceptual |

Robert et al. [ |
2009 | SME relationships | Empirical |

Tidström [ |
2009 | Business networks | Empirical |

Watanabe et al. [ |
2009 | Research and development | Empirical |

Wu et al. [ |
2009 | Supply chain management | Empirical |

Kovács and Spens [ |
2010 | Relief supply chain management | Conceptual |

Wilhelm [ |
2011 | Supply chain relations | Empirical |

Akdoğan and Cingšz [ |
2012 | Small and medium sized businesses | Empirical |

Dahl [ |
2013 | Industrial marketing | Empirical |

Tidström [ |
2013 | Industrial marketing | Empirical |

Achcaoucaou et al. [ |
2014 | Knowledge sharing | Empirical |

Karhu et al. [ |
2014 | Mobile ecosystems | Empirical |

Consequently, the main issue we address in this paper is proposing a modeling approach to examine deeper levels of coopetition mathematically. Cooperative game theory is the common tool to analyze cooperative settings (Nagarajan and Sošić [

Therefore, our main contribution in this paper is a mathematical procedure to model coopetition which can pave the way for future research in the analysis of coopetitive situations. The remainder of this paper is as follows. In Section

“Coopetition” is a business strategy in which firms simultaneously cooperate and compete with each other, which are traditionally regarded as two opposite sides of the same coin. The term coopetition is originally attributed to Ray Noorda, the first CEO of Novell Software company who applied it in early 1990’s to express his business philosophy of “partner with anybody and everybody that made sense” (Lipnack and Stamps [

Browning et al. [

The metamorphosis of coopetition literature from 1995 to 2014 is reviewed in Table

Coopetition research quantity during 1995–2014 in

In coopetition, competitors cooperate with each other, the success of which depends on many factors. For example, Wang et al. [

Coopetition, however, leads to structural transformations in players (see e.g., [

Consider the function

The set of all noncooperative games is denoted by

The game

The main idea behind the above modeling approach is to reflect the impact of cooperation on cooperating competing firms in mathematical models by assuming that the main parameters are themselves a function of the level of effort contributed by each player to the cooperation. For example, if the purpose of firms is to cooperate so as to reduce unit production cost

In order to show the applicability of the idea, we apply it in a classic Cournot duopoly game [

Although Cournot games are explored well both theoretically and computationally (see e.g., Han and Liu [

Consider the vector of variables

In order to show the structural impacts of cooperation based on this approach, we next provide scenarios to determine the right level of cooperation.

In the first scenario, we assume that firms take a competitive approach to the issue. Therefore, they do not share their basic information to set the level of production as well as the level of cooperation (see Ahmadi-Javid and Hoseinpour [

For notational simplicity, we define the following parameter:

It is clear that the extent of effectiveness of cooperation in terms of cost reduction is limited and does not pass a certain limit in real world improvement projects. We formally define this intuitive idea by demanding that the coopetition index

If the total market demand is sufficiently large but not unlimited and the coopetition index is significant, there exists a unique feasible Nash equilibrium in which

In order to find production and cooperation levels in Nash equilibrium, we form the best response functions and solve the simultaneous equations. Replacing (

Since the total market demand is sufficiently large but not unlimited and the coopetition index is significant, the following conditions also hold:

If the total market demand is sufficiently large but not unlimited and the coopetition index is significant, there exists a unique feasible Nash equilibrium in which coopetitive Cournot duopoly is preferred over the classic Cournot duopoly unless the cooperation cost is considerably unaffordable.

In a classic Cournot duopoly model (Cournot [

Figure

In the scenario where the cooperation level is set competitively, for different values of

In the scenario where the cooperation level is set competitively, for different values of

In the scenario where the cooperation level is set competitively, for different values of

If the total market demand is sufficiently large but not unlimited, the coopetition index is significant, and cooperation cost is considerably unaffordable, there exists a unique feasible Nash equilibrium in which the production level of coopetitive Cournot duopoly is equal to the classic Cournot duopoly and the cooperation level vanishes.

These properties can be proven easily by analyzing the solutions obtained for the Nash equilibria in Proposition

In the second scenario, we assume that competing firms share the information in setting both the production level and cooperation level. Therefore, the sum of profit of both parties is maximized here (see Ahmadi-Javid and Hoseinpour [

It is clear that the extent of effectiveness of cooperation in terms of cost reduction is limited and does not pass a certain limit in the real world improvement projects. In this scenario, we formally define this intuitive idea by demanding that the coopetition index

If the total market demand is sufficiently large but not unlimited and the coopetition index is significant, there exists a unique feasible Pareto equilibrium in which

In order to find production and cooperation levels in Pareto equilibrium, we form the best response functions and solve the simultaneous equations. Taking derivatives of profit function

Since the total market demand is sufficiently large but not unlimited and the coopetition index is significant, the following conditions also hold:

If the total market demand is sufficiently large but not unlimited and the coopetition index is significant, there exists a unique feasible Pareto equilibrium in which coopetitive Cournot duopoly is always preferred over the classic Cournot duopoly.

In a classic Cournot duopoly model (Cournot [

Figure

In the scenario where the cooperation level is set cooperatively, for different values of

In the scenario where the cooperation level is set cooperatively, for different values of

In the scenario where the cooperation level is set cooperatively, for different values of

If the total market demand is sufficiently large but not unlimited, the coopetition index is significant and cooperation cost is considerably unaffordable; there exists a unique feasible Pareto equilibrium in which the production level of coopetitive Cournot duopoly is less than the classic Cournot duopoly and the cooperation level vanishes.

These properties can be proven easily by analyzing the solutions obtained for the Pareto equilibria in Proposition

The lower level of production in the case of cooperation as indicated by Property

In the previous section, we analyzed two scenarios of coopetition between two similar suppliers where we analytically proved the superiority of coopetitive relationship over the classic pure competition. We now provide our main result in Proposition

If the total market demand is sufficiently large but not unlimited and the coopetition index is significant in the sense of Nash scenario, for each

This proposition can be proven easily by analyzing the solutions obtained for the Nash and Pareto equilibria in Propositions

As it can be inferred from Figure

The total market demand is sufficiently large but not unlimited and the coopetition index is significant in the sense of Nash scenario, where

In this paper, we proposed, we consider that those parameters of the situation under study are affected as a result of coopetition, as a function of level of cooperation contributed by each firm. We conclude based on our mathematical analysis that coopetition is preferred over pure competition in terms of profitability which validates the existing empirical literature on the advantages of coopetition. As the strategy is expected to be used in more real life situations, we propose our paper to apply our modeling approach to analyze future situations where coopetition is under evaluation to be chosen as the firm’s strategy. Therefore, we expect future research models particularly in the area of supply chain management to apply such approaches to embed the concept of coopetition within the model, the importance of which lies in determining the right level of cooperation so as to guarantee the strategy success.

The authors declare that there is no conflict of interests regarding the publication of this paper.