HADAMARD AND TYKHONOV WELL-POSEDNESS IN TWO PLAYER GAMES

Graziano Pieri () and Anna Torre ()
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Graziano Pieri: Dipartimento di Scienze per l'Architettura, Universita' di Genova, stradone S. Agostino 37, 16123 Genova, Italy
Anna Torre: Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy

International Game Theory Review (IGTR), 2003, vol. 05, issue 04, 375-384

Abstract: We give a suitable definition of Hadamard well-posedness for Nash equilibria of a game, that is, the stability of Nash equilibrium point with respect to perturbations of payoff functions. Our definition generalizes the analogous notion for minimum problems. For a game with continuous payoff functions, we restrict ourselves to Hadamard well-posedness with respect to uniform convergence and compare this notion with Tykhonov well-posedness of the same game. The main results are: Hadamard implies Tykhonov well-posedness and the converse is true if the payoff functions are bounded. For a zero-sum game the two notions are equivalent.

Keywords: Two-player; zero-sum game; Tykhonov well-posedness; Hadamard well-posedness (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0219198903001124

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