Some Results on the Markov Equilibria of a Class of Homogeneous Differential Games
We consider the class of differential games with transition dynamics and constraints that are homogeneous of degree one. We show that if the integrand of the objective function is homogeneous of degree , then best replies to linear homogeneous Markov strategies are linear homogeneous, and the value function is homogeneous of degree . A parallel result holds when one applies logarithmic transformation to the integrand. Examples are provided.
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