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On a class of state-redundant differential games

Author

Listed:
  • Luca Lambertini

    (University of Bologna)

  • Arsen Palestini

    (Sapienza University of Rome)

Abstract

This paper identifies a class of state-redundant games whose open-loop solution is a degenerate feedback one. The structure of the game features an instantaneous payoff which is at least cubic, and state equations linear in states and controls. The model can be used to illustrate games in the field of industrial organization and management, involving advertising campaigns under product differentiation and either quantity or price competition.

Suggested Citation

  • Luca Lambertini & Arsen Palestini, 2025. "On a class of state-redundant differential games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 33(2), pages 375-389, June.
    • Handle: RePEc:spr:cejnor:v:33:y:2025:i:2:d:10.1007_s10100-025-00965-0
    DOI: 10.1007/s10100-025-00965-0
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    References listed on IDEAS

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    1. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    2. Giulio Ecchia & Luca Lambertini, 1997. "Minimum Quality Standards and Collusion," Journal of Industrial Economics, Wiley Blackwell, vol. 45(1), pages 101-113, March.
    3. repec:bla:econom:v:51:y:1984:i:23:p:271-81 is not listed on IDEAS
    4. Crampes, Claude & Hollander, Abraham, 1995. "Duopoly and quality standards," European Economic Review, Elsevier, vol. 39(1), pages 71-82, January.
    5. Lambertini, Luca, 1996. "Choosing Roles in a Duopoly for Endogenously Differentiated Products," Australian Economic Papers, Wiley Blackwell, vol. 35(67), pages 205-224, December.
    6. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    7. Benchekroun, Hassan & van Long, Ngo, 1998. "Efficiency inducing taxation for polluting oligopolists," Journal of Public Economics, Elsevier, vol. 70(2), pages 325-342, November.
    8. Lambertini,Luca, 2018. "Differential Games in Industrial Economics," Cambridge Books, Cambridge University Press, number 9781316616499, September.
    9. Cremer, Helmuth & Thisse, Jacques-Francois, 1991. "Location Models of Horizontal Differentiation: A Special Case of Vertical Differentiation Models," Journal of Industrial Economics, Wiley Blackwell, vol. 39(4), pages 383-390, June.
    10. Lambertini, Luca & Zaccour, Georges, 2015. "Inverted-U aggregate investment curves in a dynamic game of advertising," Economics Letters, Elsevier, vol. 132(C), pages 34-38.
    11. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, Enero-Abr.
    12. Luca Lambertini, 2006. "The Economics of Vertically Differentiated Markets," Books, Edward Elgar Publishing, number 4224.
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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