Differentiable game complete analysis for tourism firm decisions

Carfì, David (2009): Differentiable game complete analysis for tourism firm decisions. Published in: Proceedings of THE 2009 INTERNATIONAL CONFERENCE ON TOURISM and WORKSHOP on Sustainable tourism within High Risk areas of environmental crisis (2009): pp. 1-10.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Tourism fir; differentiable game; strategic interaction; non-cooperative behaviour; cooperative behavior; Pareto efficiency.
• Subjects: D - Microeconomics > D2 - Production and Organizations > D21 - Firm Behavior: Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance

References

[1] M. Thea Sinclair - Mike Stabler, The economics of tourism, Routledge 1997

[2] D. Carfì, Topics in Game Theory, Il Gabbiano 2009

[3] Jean Pierre Aubin, Mathematical methods of game and economic theory, (Revised Edition) North-Holland.

[4] Jean Pierre Aubin, Optima and equilibria, Springer Verlag.

[5] David Carfì, Optimal boundaries for decisions, Atti dell'Accademia Peloritana dei Pericolanti - Classe di Scienze Fisiche, Matematiche e Naturali Vol. LXXXVI, (2008)

[6] David Carfì, Payoff space and Pareto boundaries of C1 Games, APPS vol. 2009