Bargaining power in bilateral monopoly and cooperative choice of corporate social responsibility

ABSTRACT

We analyse the cooperative choice of corporate social responsibility when a manufacturer and a retailer in a bilateral monopoly may hold different bargaining powers. We find that an increase in the bargaining power of one of the firms leads to an increase in the degree of social concern of the other firm in the bilateral monopoly and a reduction in its own degree of social concern. It also leads to an increase in the firm´s own profits and a reduction in the other firm’s profits, but it has no effect on the quantity sold, its price, total profits, consumer surplus or social surplus. Just as in the symmetric case, both the manufacturer and the retailer cooperatively choose higher degrees of social concern than under a non-cooperative framework and these choices completely solve the double-marginalization problem.

KEYWORDS:

• Bilateral monopoly
• corporate social responsibility
• double marginalization problem
• supply chain
• generalized Nash bargaining

JEL CLASSIFICATION:

• D21
• L12
• L22
• M14

Acknowledgement

The author thanks an anonymous referee for valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ Studies of CSR with competition among firms include Kopel and Brand (2012), Lambertini and Tampieri (2015), Fanti and Buccella (2017a, 2017b) and Planer-Friedrich and Sahm (2020). Bénabou and Tirole (2010) provide a general overview of CSR.

² Also related are García, Leal, and Lee (2018) and Li and Zhou (2019).

³ Binmore, Rubinstein, and Wolinsky (1986).

⁴ Other examples include Baron, Berman, and Wu (2016) and Sheu and Gao (2014). See Nagarajan and Sošić (2008) for an early survey of cooperative game theory, including Nash bargaining, to supply chain management.

⁵ See Brand and Grothe (2015, 279–280).

⁶ They also examine the cases where i) the retailer (manufacturer) acts as the leader (follower) and ii) firms’ choices are simultaneous. In both cases firms pursue simple profit maximization.

⁷ See Brand and Grothe (2015, 282).

⁸ See Nash (1950).

⁹ The Generalized Nash Bargaining Solution.

¹⁰ The second-order condition is also satisfied.

¹¹ The superscript G denotes the GNBS.:

¹² See also Anbarci and Sun (2013) and Britz, Herings, and Predtetchinski (2010).

¹³ For cases in the supply chain management literature see for example p. 117 in Clark and Pereau (2021) and pp. 229–230 in Matsui (2020).

¹⁴ It is worth noting the difference in the number of employees of both companies, 5 for Verner Frang and 28,000 for B&Q, (Kogg 2003a).

¹⁵ These examples are based on Kogg (2003a, 2003b), Murphy and Bendell (1998) and Humphrey (1998).

¹⁶ Kogg (2003b, 61).

¹⁷ Note however that, as Humphrey (1998) points out, B&Q had an extensive environmental policy that went beyond the timber policy examined in this example.

¹⁸ See also Oczkowski (1999).