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Hadamard And Tykhonov Well-Posedness In Two Player Games

Author

Listed:
  • 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)

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.

Suggested Citation

  • Graziano Pieri & Anna Torre, 2003. "Hadamard And Tykhonov Well-Posedness In Two Player Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 375-384.
    • Handle: RePEc:wsi:igtrxx:v:05:y:2003:i:04:n:s0219198903001124
    DOI: 10.1142/S0219198903001124
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    Keywords

    Two-player; zero-sum game; Tykhonov well-posedness; Hadamard well-posedness;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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