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

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 — m scalar 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 by 2 × 2 matrices, the elements of which are lexicographic utilities.