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Advances on Stackelberg open‐loop and feedback strategies

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  • Koji Shimomura
  • Danyang Xie

Abstract

In this paper, we study a familiar type of dynamic games called “common‐property resource games” to establish the following results. First, the Stackelberg equilibrium may not exist in some cases, with open‐loop strategies as well as with feedback strategies. Second, an explicit example is given to show that under feedback strategies, the best linear strategy on the part of the leader is inferior to a nonlinear strategy so that it is dangerous to confine our search to the Stackelberg equilibrium in the space of linear functions. Most importantly, we establish an “Implementation Lemma”, which allows us to develop one methodology to obtain the Stackelberg equilibrium with feedback strategies when the equilibrium is assumed to exist.

Suggested Citation

  • Koji Shimomura & Danyang Xie, 2008. "Advances on Stackelberg open‐loop and feedback strategies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(1), pages 115-133, March.
    • Handle: RePEc:bla:ijethy:v:4:y:2008:i:1:p:115-133
    DOI: 10.1111/j.1742-7363.2007.00071.x
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    Cited by:

    1. Kenji Fujiwara & Ngo Long, 2011. "Welfare Implications of Leadership in a Resource Market under Bilateral Monopoly," Dynamic Games and Applications, Springer, vol. 1(4), pages 479-497, December.
    2. Ngo Long & Gerhard Sorger, 2010. "A dynamic principal-agent problem as a feedback Stackelberg differential game," 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. 18(4), pages 491-509, December.
    3. Michael Caputo & Chen Ling, 2015. "Intrinsic Comparative Dynamics of Locally Differentiable Feedback Stackelberg Equilibria," Dynamic Games and Applications, Springer, vol. 5(1), pages 1-25, March.
    4. Ngo Long, 2011. "Dynamic Games in the Economics of Natural Resources: A Survey," Dynamic Games and Applications, Springer, vol. 1(1), pages 115-148, March.
    5. Van Gorder, Robert A. & Caputo, Michael R., 2010. "Envelope theorems for locally differentiable open-loop Stackelberg equilibria of finite horizon differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1123-1139, June.
    6. Antoniadou, Elena & Koulovatianos, Christos & Mirman, Leonard J., 2013. "Strategic exploitation of a common-property resource under uncertainty," Journal of Environmental Economics and Management, Elsevier, vol. 65(1), pages 28-39.

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