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Differentiable game complete analysis for tourism firm decisions

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  • Carfì, David

Abstract

In this paper we apply the complete analysis of a differentiable game (recently introduced by the author) to determine possible suitable behaviors (actions) of tourism firms during strategic interactions with other tourism firms, from both non-cooperative and cooperative point of view. To associate with a real strategic interaction among tourism firms a differentiable game any player’s strategy-set must, for instance, be a part of a topological vector space, closure of an open subset of the space. The most frequent case is that in which the strategy-sets are compact intervals of the real line. On the other hand, very often, the actions at disposal of a player can form a finite set, and in this case a natural manner to construct a game representing the economic situation is the von Neumann convexification (also known as canonical extension) that leads to a differentiable game with probabilistic scenarios, and thus even more suitable for the purpose of represent real interactions. For what concerns the complete analysis of a differentiable game, its first goal is the precise knowledge of the Pareto boundaries (maximal and minimal) of the payoff space, this knowledge will allow us to evaluate the quality of the different Nash equilibria (by the distances from the Nash equilibria themselves to Pareto boundaries, with respect to appropriate metrics), in order to determine some “focal” equilibrium points collectively more satisfactory than each other. Moreover, the complete knowledge of the payoff-space will allow to develop explicitly the cooperative phase of the game and the various bargaining problems rising from the strategic interaction of the tourist firms (Nash bargaining problem, Kalai-Smorodinski bargaining problem and so on). In the paper we shall deal with some practical study cases.

Suggested Citation

  • Carfì, David, 2009. "Differentiable game complete analysis for tourism firm decisions," MPRA Paper 29193, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:29193
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    File URL: https://mpra.ub.uni-muenchen.de/29193/1/MPRA_paper_29193.pdf
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    References listed on IDEAS

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    1. Carfì, David, 2008. "Optimal boundaries for decisions," MPRA Paper 29243, University Library of Munich, Germany.
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    Cited by:

    1. David Carfì & Emanuele Perrone, 2013. "Asymmetric Cournot Duopoly: A Game Complete Analysis," Journal of Reviews on Global Economics, Lifescience Global, vol. 2, pages 194-202.
    2. Carfì, David & Perrone, Emanuele, 2011. "Asymmetric Bertrand duopoly: game complete analysis by algebra system Maxima," MPRA Paper 35417, University Library of Munich, Germany.
    3. Carfì, David & Musolino, Francesco, 2012. "A coopetitive approach to financial markets stabilization and risk management," MPRA Paper 37098, University Library of Munich, Germany.
    4. David CARFÌ & Emanuele PERRONE, 2011. "Game Complete Analysis Of Bertrand Duopoly," Theoretical and Practical Research in the Economic Fields, ASERS Publishing, vol. 2(1), pages 4-21.
    5. Carfì, David & Musolino, Francesco, 2012. "Game theory model for European government bonds market stabilization: a saving-State proposal," MPRA Paper 39742, University Library of Munich, Germany.
    6. Carfì, David & Perrone, Emanuele, 2012. "Game complete analysis of symmetric Cournot duopoly," MPRA Paper 35930, University Library of Munich, Germany.
    7. Musolino, Francesco & Carfì, David, 2012. "A game theory model for currency markets stabilization," MPRA Paper 39240, University Library of Munich, Germany.
    8. 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.
    9. Carfì, David & Musolino, Francesco, 2012. "Game theory and speculation on government bonds," Economic Modelling, Elsevier, vol. 29(6), pages 2417-2426.
    10. Carfì, David & Ricciardello, Angela & Agreste, Santa, 2011. "An Algorithm for payoff space in C1 parametric games," MPRA Paper 32099, University Library of Munich, Germany.

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    More about this item

    Keywords

    Tourism fir; differentiable game; strategic interaction; non-cooperative behaviour; cooperative behavior; Pareto efficiency.;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • 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
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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