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Payoff space in \(C^1\)-games. (English) Zbl 1185.91018
Summary: In this paper we give a general method to determine the payoff space, and consequently, in some particular cases, the Pareto boundaries, of certain type of normal form game with \(n\)-persons having payoff functions of class \(C^1\). Specifically, we consider n-person games in which the strategy set of any player is a compact interval of the real line, and in which the payoff functions are \(C^1\), in the sense that they are restrictions of \(C^1\) functions defined in open neighborhoods of the strategy profile space of the game. We face the problem of determining the payoff space and its Pareto optimal boundaries and, finally, of finding some classical compromise solutions.

MSC:
91A05 2-person games
91A06 \(n\)-person games, \(n>2\)
91A10 Noncooperative games
91A12 Cooperative games
91A44 Games involving topology, set theory, or logic
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