The authors introduce the class of “personalized” Nash equilibria (P-NE) which provides a unified approach for various kind of approximate Nash equilibria solutions. This is done by introducing a personalized choice rule \(p\) for all the potential players and substituting a conveniently defined characterizations for one person rationality (OPR) by (P-OPR). It is also proved that (P-NE) contains all of the solutions characterized by consistency and converse consistency. See also the article by B. Peleg, J. Potters, and S. Tijs [Econ. Theory 7, 81–93 (1996; Zbl 0840.90138)].