DYADIC THEORETICAL GAMES MODELS OF DECISION-MAKING FOR THE LEXICOGRAPHIC VECTOR PAYOFFS

Mindia E. Salukvadze (), Guram Beltadze () and Francisco Criado ()
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Mindia E. Salukvadze: Archil Eliashvili Institute of Control Systems, 34, K. Gamsakhurdia St., Tbilisi 380060, Georgia
Guram Beltadze: Department of Control Systems, Georgian Technical University, 77, M. Kostava St., Tbilisi 0175, Georgia
Francisco Criado: Department of Statistics and Operational Research Malaga University, Campus de Teatinos, Malaga 29071, Spain

International Journal of Information Technology & Decision Making (IJITDM), 2009, vol. 08, issue 02, 193-216

Abstract: This article is about the full analysis of one concrete class of general non-cooperative lexicographic games and its computer programming. In such game, the payoffs of players are lexicographic vector payoffs —mscalar criteria vectors. At the same time, these criteria are strictly ranked on the set of the situations with lexicographic preference. In some such kind of game a Nash's equilibrium may not exist. In the given article the full analysis of one class of dyadic lexicographic games is worked out. Such kind of class is the non-cooperative lexicographic games, where each player has got two pure strategies and the payoff of each player solely depends on the strategies of two players in each situation. Therefore, the player's payoffs are given by2 × 2matrices, the elements of which are lexicographic utilities.

Keywords: Game theory; non-cooperative lexicographical games; affine games; equalized situation; Nash's equilibrium (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1142/S0219622009003430

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