Abstract:
The acceptability concept is a naturally generalization of the
equilibrium concept. An outcome of a game is called an acceptable
one if no players which have an objection to it in the form their
strategies. Note that for the class of games with payoff function,
acceptability condition is equivalent to individual rationality
condition. This article is a continuation of the previous work of
the author (see Rozen, 2018). The aim of the article is a detection
of structure of the set of acceptable outcomes in antagonistic games
with ordered outcomes (all required definitions for antagonistic
games with ordered outcomes indicated in the introduction, see
section 1). In section 2 we offer some classification for outcomes
in antagonistic games. Using this classification, a localization of
acceptable outcomes is specified (see section 3). In section 4
certain sufficient conditions for non-emptiness and uniqueness of
acceptable outcomes are found. Some examples related to localization
of acceptable outcomes in antagonistic games with ordered outcomes
are given.
Keywords:antagonistic game with ordered outcomes, acceptable point, saddle point, centre of game, periphery of game.
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