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Corporate social responsibility and endogenous competition structure in an industry composed of firms with biased managers

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Abstract

In this study, we revisit the endogenous choice between price and quantity contracts in a duopoly composed of asymmetric firms engaged in corporate social responsibility (CSR) with possibly biased managers. We find that Cournot competition can change to an equilibrium competition structure regardless of the degree of homogeneity between the goods produced by them and the degree of importance of their CSR. Furthermore, we show that Bertrand competition, in addition to Cournot competition, can be observed in equilibrium when the degrees of importance of CSR between firm owners are sufficiently asymmetric with each other. This result is supported by the manipulation of the types of managers with respect to the biased scale of the demand size in the market by their owners when the degree of importance of their CSR changes.

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Notes

  1. See Tremblay and Xiao (2019) for achievements in the field of cognitive biases in the last few decades.

  2. Subsequent works include Reisinger and Ressner (2009), Matsumura and Ogawa (2012), Chirco and Scrimitore (2013), Scrimitore (2013),Tremblay et al. (2013), and Pal (2015) on this latter topic.

  3. Hino and Zennyo (2017) analyzed a managerial delegation game relevant to the degree of importance of a firm’s CSR where its owner provides to the manager a contract composed of its profit and consumer surplus or social welfare. On the other hand, in the context of the impact of CSR activities on the environment, Lambertini and Tampieri (2015) explored the effect of a CSR firm’s socially responsible behavior on its profits and social welfare when production entails an environmental externality and Lambertini et al. (2016) investigated a linear state differential game describing an asymmetric Cournot duopoly with capacity accumulation à la Ramsey and a negative environmental externality (pollution) in an asymmetric duopoly composed of a CSR firm with the environmental effects of production in its objective function and a PM firm. Most recently, Fukuda and Ouchida (2020) developed a CSR activity under a time-consistent emission tax in a monopoly and analyzed the effects of CSR behavior on economic welfare and the environment.

  4. In other words, \(\theta _i\) means “the degree of importance of SW” within firm i.

  5. As indicated in Englmaier and Reisinger (2014) and Meccheri (2021), the type of manager in firm i, \(k_i\), can also be regarded as a lottery over different levels of the market size parameter in the inverse demand. Since an overconfident (underconfident) manager overestimates (underestimates) the probability of high (low) market size realizations, they consider a higher (lower) expected market size. Owing to risk neutrality in this case, the probabilistic notation can be neglected; hence, we can focus on expected values only.

  6. The second-order condition for the manager of firm i is satisfied.

  7. The second-order condition for the owner of firm i is satisfied.

  8. In the p–p game, we generally describe the payoffs for the owners of firms i and j in each game.

  9. The second-order condition for the manager of firm i is satisfied.

  10. The second-order condition for the owners of firms i is satisfied.

  11. In the q–p game, we generally describe the payoffs for the owners of firms i and j in each game.

  12. The second-order conditions for the managers of firms i and j are satisfied.

  13. The second-order conditions for the owners of firms i and j are satisfied.

  14. In the p–q and q–p games, we generally describe the payoffs for the owners of firms i and j in each game.

  15. In particular, Nakamura (2021b) also employed a similar approach.

  16. Here, from the symmetry between firms i and j, we focus on the situation in which \(\theta _i\) is sufficiently high and \(\theta _j\) is sufficiently low.

  17. This result is similar to those obtained in Nakamura (2021a) and Nakamura (2022) that considered industries composed of managerial CSR firms FJSV delegation.

  18. We discuss the situation such that the stage where each firm’s owner simultaneously selects the degree of her CSR (for example, “stage 0”) is added before she endogenously and simultaneously determines her strategy with each other, in all the four games, i.e., the p–p game, the p–q game, the q–p game, and the q–q game. From analytical calculations, we obtain the results that \(\partial V^{lm}_i / \partial \theta _i > 0\) for any \(\theta _j\) in the cases of \(\delta \) = 0.2, 0.4, 0.6, and 0.8 (\(l, m = p, q\) and \(i, j = 1, 2\); \(i \ne j\)). Thus, the degree of importance of CSR within each firm is 1 in equilibrium in the cases of \(\delta \) = 0.2, 0.4, 0.6, and 0.8, leading to the result that the first best solution from the viewpoint of social welfare is obtained in equilibrium. As as consequence, if the stage where each firm’s owner simultaneously selects the degree of her CSR is added to the game as stage 0, all the four games, i.e., the p–p game, the p–q game, the q–p game, and the q–q game, can be observed in equilibrium in the cases of \(\delta \) = 0.2, 0.4, 0.6, and 0.8 (\(V^{pp}_i (\theta _i = 1, \theta _j = 1)\) = \(V^{pq}_i (\theta _i = 1, \theta _j = 1)\) = \(V^{qp}_i (\theta _i = 1, \theta _j = 1)\) = \(V^{qq}_i (\theta _i = 1, \theta _j = 1)\)).

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  1. College of Economics, Nihon University, 1-3-2 Misaki-cho, Chiyoda-ku, Tokyo, 101-8360, Japan

    Yasuhiko Nakamura

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Correspondence to Yasuhiko Nakamura.

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We are grateful to the anonymous referee for their helpful comments and suggestions. We are grateful for the financial support of KAKENHI (21K01491). This research was also supported by a grant-in-aid from the Zengin Foundation for Studies on Economics and Finance. Any remaining errors are our own.

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Nakamura, Y. Corporate social responsibility and endogenous competition structure in an industry composed of firms with biased managers. Int Rev Econ 69, 301–321 (2022). https://doi.org/10.1007/s12232-022-00393-5

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