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A note on discontinuous value functions and strategies in affine-quadratic differential games

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  • Jensen, Henrik
  • Lockwood, Ben

Abstract

We present an economic example of an affine-quadratic differential game where in Markov-perfect Nash equilibrium, the value function of a player is discontinuous in the model's parameters, implying that the strategy of that player is also discontinuous, even though the data of the game (state equation and pay-offs) are continuous in the parameters. Sufficient conditions ruling out such discontinuities are presented for the general scalar case.
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Suggested Citation

  • Jensen, Henrik & Lockwood, Ben, 1998. "A note on discontinuous value functions and strategies in affine-quadratic differential games," Economics Letters, Elsevier, vol. 61(3), pages 301-306, December.
    • Handle: RePEc:eee:ecolet:v:61:y:1998:i:3:p:301-306
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    References listed on IDEAS

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    1. Barro, Robert J & Gordon, David B, 1983. "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 589-610, August.
    2. Lockwood, Ben, 1996. "Uniqueness of Markov-perfect equilibrium in infinite-time affine-quadratic differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 20(5), pages 751-765, May.
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    Cited by:

    1. Gianluigi Vernasca, 2003. "Dynamic Price Competition with Price Adjustment Costs and Product Differentiation," Working Papers 2003.120, Fondazione Eni Enrico Mattei.
    2. AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," LIDAM Discussion Papers CORE 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Thomas Aronsson & Kenneth Backlund & Karl-Gustav Löfgren, 2001. "International Cooperation over Green Taxes: On the Impossibility of Achieving a Probability-One Gain," CESifo Working Paper Series 567, CESifo.
    4. repec:bla:econom:v:65:y:1998:i:259:p:327-45 is not listed on IDEAS
    5. Vernasca, Gianluigi, 2003. "Dynamic Price Competition With Price Adjustment Costs And Product Differentiation," The Warwick Economics Research Paper Series (TWERPS) 681, University of Warwick, Department of Economics.

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    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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