Acceptable points in antagonistic games with ordered outcomes

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.