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An Algorithm for payoff space in C1 parametric games

Author

Listed:
  • Carfì, David
  • Ricciardello, Angela
  • Agreste, Santa

Abstract

We present a novel algorithm to determine the payoff-space of certain normal-form C1 parametric games, and - more generally - of continuous families of normal-form C1 games. The algorithm has been implemented by using MATLAB, and it has been applied to several examples. The implementation of the algorithm gives the parametric expressions of the critical zone of any game in the family under consideration both in the bistrategy space and in the payoff space and the graphical representations of the disjoint union (with respect to the parameter set of the parametric game) of the family of all payoff spaces. We have so the parametric representation of the union of all the critical zones. One of the main motivations of our paper is that, in the applications, many normal-form games appear naturally in a parametric fashion; moreover, some efficient models of coopetition are parametric games of the considered type. Specifically, we have realized an algorithm that provides the parametric and graphical representation of the payoff space and of the critical zone of a parametric game in normal-form, supported by a finite family of compact intervals of the real line. Our final goal is to provide a valuable tool to study simply (but completely) normal-form C1-parametric games in two dimensions.

Suggested Citation

  • Carfì, David & Ricciardello, Angela & Agreste, Santa, 2011. "An Algorithm for payoff space in C1 parametric games," MPRA Paper 32099, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:32099
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    File URL: https://mpra.ub.uni-muenchen.de/32099/1/MPRA_paper_32099.pdf
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    References listed on IDEAS

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    1. Carfì, David, 2009. "Differentiable game complete analysis for tourism firm decisions," MPRA Paper 29193, University Library of Munich, Germany.
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    Citations

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    Cited by:

    1. Carfì, David, 2011. "Financial Lie groups," MPRA Paper 31303, University Library of Munich, Germany.
    2. Carfì, David, 2010. "A model for coopetitive games," MPRA Paper 59633, University Library of Munich, Germany.
    3. David CARFI & Caterina FICI, 2012. "The Government-Taxpayer Game," Theoretical and Practical Research in the Economic Fields, ASERS Publishing, vol. 3(1), pages 13-25.
    4. David carf'i, 2011. "Financial Lie groups," Papers 1106.0562, arXiv.org.
    5. Carfí, David & Musolino, Francesco, 2014. "Speculative and hedging interaction model in oil and U.S. dollar markets with financial transaction taxes," Economic Modelling, Elsevier, vol. 37(C), pages 306-319.

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    More about this item

    Keywords

    two player normal form games; bargaining problems; cooperative games; competitive games; complete study of a normal-form game;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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