We provide existence results for equilibria of games where players employ abstract (non binary) choice rules. Such results are shown to encompass as a relevant instance that of games where players have (non-transitive) SSB (Skew-Symmetric Bilinear) preferences, as will as other well-known transitive (e. g. Nash´s) and non-transitive (e. g. Shafer and Sonnenschein´s) models in the literature. Further, our general model contains games where players display procedural rationality.
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