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A robust route to randomness in a simple Cournot duopoly game where ambiguity aversion meets constant expectations

Author

Listed:
  • D. Radi

    (Catholic University of the Sacred Heart
    Technical University of Ostrava)

  • L. Gardini

    (University of Urbino Carlo Bo)

  • D. Goldbaum

    (University of Technology Sydney)

Abstract

In this paper we investigate the dynamics of a duopoly game with ambiguity aversion regarding uncertainty in demand and constant expectations concerning competitor production. The focus is on an asymmetric Cournot game where players engage in robust optimization and have different beliefs about the possible realizations of the random parameters of the price function. The players’ ambiguity aversion introduces multiple equilibria and instability that otherwise would not be present. The investigation of the global dynamics of the game reveals the emergence, through border-collision bifurcations, of periodic and chaotic dynamics.

Suggested Citation

  • D. Radi & L. Gardini & D. Goldbaum, 2024. "A robust route to randomness in a simple Cournot duopoly game where ambiguity aversion meets constant expectations," Annals of Operations Research, Springer, vol. 337(3), pages 769-807, June.
  • Handle: RePEc:spr:annopr:v:337:y:2024:i:3:d:10.1007_s10479-023-05686-8
    DOI: 10.1007/s10479-023-05686-8
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    1. Diego A. Comin & Thomas Philippon, 2006. "The Rise in Firm-Level Volatility: Causes and Consequences," NBER Chapters, in: NBER Macroeconomics Annual 2005, Volume 20, pages 167-228, National Bureau of Economic Research, Inc.
    2. Dirk Czarnitzki & Andrew A. Toole, 2011. "Patent Protection, Market Uncertainty, and R&D Investment," The Review of Economics and Statistics, MIT Press, vol. 93(1), pages 147-159, February.
    3. John D. Hey & Gianna Lotito, 2018. "Naive, resolute or sophisticated? A study of dynamic decision making," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 11, pages 275-299, World Scientific Publishing Co. Pte. Ltd..
    4. Caballero, Ricardo J, 1991. "On the Sign of the Investment-Uncertainty Relationship," American Economic Review, American Economic Association, vol. 81(1), pages 279-288, March.
    5. Huang, Weihong, 2008. "The long-run benefits of chaos to oligopolistic firms," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1332-1355, April.
    6. Nocetti, Diego & Smith, William T., 2011. "Price uncertainty, saving, and welfare," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1139-1149, July.
    7. Alan Carruth & Andy Dickerson & Andrew Henley, 2000. "What do We Know About Investment Under Uncertainty?," Journal of Economic Surveys, Wiley Blackwell, vol. 14(2), pages 119-154, April.
    8. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    9. Crespi, Giovanni P. & Kuroiwa, Daishi & Rocca, Matteo, 2018. "Robust optimization: Sensitivity to uncertainty in scalar and vector cases, with applications," Operations Research Perspectives, Elsevier, vol. 5(C), pages 113-119.
    10. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-924, July.
    11. Comin, Diego & Mulani, Sunil, 2009. "A theory of growth and volatility at the aggregate and firm level," Journal of Monetary Economics, Elsevier, vol. 56(8), pages 1023-1042, November.
    12. Sakai, Yasuhiro, 1985. "The value of information in a simple duopoly model," Journal of Economic Theory, Elsevier, vol. 36(1), pages 36-54, June.
    13. David A. Maleug & Shunichi O. Tsutsui, 1998. "Oligopoly Information Exchange when Non‐negative Price and Output Constraints may Bind," Australian Economic Papers, Wiley Blackwell, vol. 37(4), pages 363-371, December.
    14. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    15. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 1999. "Learning in Cournot Oligopoly--An Experiment," Economic Journal, Royal Economic Society, vol. 109(454), pages 80-95, March.
    16. Malueg, David A. & Tsutsui, Shunichi O., 1996. "Duopoly information exchange: The case of unknown slope," International Journal of Industrial Organization, Elsevier, vol. 14(1), pages 119-136.
    17. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    18. repec:bla:ausecp:v:37:y:1998:i:4:p:363-71 is not listed on IDEAS
    19. Lepore, Jason J., 2012. "Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 177-186.
    20. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    21. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    22. 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.
    23. Peter J. Hammond, 1976. "Changing Tastes and Coherent Dynamic Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(1), pages 159-173.
    24. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
    25. repec:bla:jecsur:v:14:y:2000:i:2:p:119-53 is not listed on IDEAS
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