A Note on Discontinuous Value Functions and Strategies in Affine-Quadratic Differential Games
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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- 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.
- Robert J. Barro & David B. Gordon, 1981. "A Positive Theory of Monetary Policy in a Natural-Rate Model," NBER Working Papers 0807, National Bureau of Economic Research, Inc.
- 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.