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Acceptable points in antagonistic games with ordered outcomes
Contributions to game theory and management, Tome 12 (2019), pp. 282-294.

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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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Victor V. Rozen. Acceptable points in antagonistic games with ordered outcomes. Contributions to game theory and management, Tome 12 (2019), pp. 282-294. http://geodesic.mathdoc.fr/item/CGTM_2019_12_a16/

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[3] Rozen V. V., Decision making under qualitative criteria. Mathematical models, Palmarium Academic Publishing, Saarbrucken, Deutschland, 2013 (in Russian)

[4] Rozen V. V., “Acceptable Points in Games with Preference Relations”, Collected papers presented on the Eleventh International Conference Game Theory and Management, Contributions to game theory and management, XI, eds. Petrosyan L. A., Zenkevich N. A., Graduate School of Management SPbU, SPb., 2018, 196–206 | MR