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Managerial Delegation in a Dynamic Renewable Resource Oligopoly

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Dynamic Perspectives on Managerial Decision Making

Part of the book series: Dynamic Modeling and Econometrics in Economics and Finance ((DMEF,volume 22))

Abstract

I propose a differential oligopoly game of resource extraction under linear and nonlinear feedback strategies, where firms are managerial and delegation contract are based on output levels. The model shows that delegation expands the set of stable nonlinear feedback equilibria as well as the residual steady state resource stock. Additionally, the separation between ownership and control mitigates the voracity effect associated with high values of the reproduction rate of the resource.

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Notes

  1. 1.

    See the seminal contributions by Gordon (1954) and Hardin (1968). The subsequent literature includes, among many others, Levhari and Mirman (1980), Clemhout and Wan (1985), Clark (1990), Benhabib and Radner (1992), Dockner and Sorger (1996), Dawid and Kopel (1997), Sorger (1998), and Benchekroun and Long (2002), among many others. Advanced overviews of the early stages of this debate are in Dasgupta and Heal (1979) and Clark (1990). A recent survey of differential games of resource extraction is in Lambertini (2013, Chap. 9).

  2. 2.

    This idea is pervasive in the literature treating differential oligopoly games with quantity competition (Driskill and McCafferty 1989); capacity accumulation (Reynolds 1987, 1991); sticky prices (Fershtman and Kamien 1987; Cellini and Lambertini 2004).

  3. 3.

    Under monopoly the delegation to managers would not be operated by stockholders, so I’m assuming this case away.

  4. 4.

    As in Benchekroun and Long (2002), Fujiwara (2008) and Tornell and Velasco (1992), among several others.

  5. 5.

    This contract is equivalent to that considered in Fershtman and Judd (1987), where the maximand is a weighted average of profits and revenues, \(M_{i} =\alpha \pi _{i} + \left (1-\alpha \right )R_{i},\) R i  = pq i . A proof of the equivalence is in Lambertini and Trombetta (2002).

  6. 6.

    The analysis of this specific aspect in the corresponding model without any form of delegation can be found in Lambertini and Mantovani (2014, pp. 119–21).

  7. 7.

    That is, here the open-loop solution is a degenerate feedback one. For more on games with this feature, see Fershtman (1987), Mehlmann (1988, Chap. 4), Dockner et al. (2000, Chap. 7), and Cellini et al. (2005), inter alia.

  8. 8.

    Nonlinear feedback solutions have been investigated in oligopoly theory, environmental and resource economics and other fields. See Tsutsui and Mino (1990), Shimomura (1991), Dockner and Sorger (1996), Itaya and Shimomura (2001), Rubio and Casino (2002), and Colombo and Labrecciosa (2015), inter alia.

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Acknowledgements

I would like to thank Herbert Dawid, Arsen Palestini and two anonymous reviewers for precious comments and suggestions. The usual disclaimer applies.

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Authors and Affiliations

  1. Department of Economics, University of Bologna, Strada Maggiore 45, 40125, Bologna, Italy

    Luca Lambertini

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  1. Luca Lambertini
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Correspondence to Luca Lambertini .

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Editors and Affiliations

  1. Department of Business Administration and Economics and Center for Mathematical Economics, Bielefeld University, Bielefeld, Germany

    Herbert Dawid

  2. Department of Business Administration, University of Vienna, Vienna, Wien, Austria

    Karl F. Doerner

  3. Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Wien, Austria

    Gustav Feichtinger

  4. Department of Econometrics and Operations Research & CentER, Tilburg University, Tilburg, The Netherlands

    Peter M. Kort

  5. Department of Business Administration, University of Vienna, Vienna, Wien, Austria

    Andrea Seidl

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Lambertini, L. (2016). Managerial Delegation in a Dynamic Renewable Resource Oligopoly. In: Dawid, H., Doerner, K., Feichtinger, G., Kort, P., Seidl, A. (eds) Dynamic Perspectives on Managerial Decision Making. Dynamic Modeling and Econometrics in Economics and Finance, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-39120-5_6

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