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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