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Characterizing the value functions of polynomial games. (English) Zbl 1525.91004

Summary: We provide a characterization of the set of real-valued functions that can be the value function of some polynomial game. Specifically, we prove that a function \(u : \mathbb{R} \to \mathbb{R}\) is the value function of some polynomial game if and only if \(u\) is a continuous piecewise rational function.

MSC:

91A10 Noncooperative games
91A06 \(n\)-person games, \(n>2\)
91A27 Games with incomplete information, Bayesian games
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