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Margiocco, M.; Patrone, F.; Pusillo, L.

On the Tikhonov well-posedness of concave games and Cournot oligopoly games. (English) Zbl 1011.91004

J. Optimization Theory Appl. 112, No. 2, 361-379 (2002).
The authors study a very essential problem concerning \(n\)-person noncooperative games. They analyse, under what assumption the game is Tikhonov well-posed (T-wp), that is, when the game has a Nash equilibrium (NE) satisfying the two conditions: (1) NE is unique, and (2) NE is a limit of every sequence of \(\varepsilon\)-Nash equilibria as \(\varepsilon \rightarrow 0\). Several sufficient conditions for games to have the T-wp property are given. Also one can find many interesting examples. The obtained results are applied to show that a Carnot oligopoly game has the T-wp property.
Reviewer: Tadeusz Radzik (Jelenia, Gora)

Cited in 21 Documents

MSC:

91A10 Noncooperative games
91A06 \(n\)-person games, \(n>2\)

Keywords:

well posedness; Nash equilibrium; noncooperative games; concave games; Carnot oligopoly games
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\textit{M. Margiocco} et al., J. Optim. Theory Appl. 112, No. 2, 361--379 (2002; Zbl 1011.91004)
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