Acceptability prioritized preferences and equilibrium existence

Economic agents may sometimes find themselves in circumstances in which they are effectively endowed with preferences that place a priority on first meeting specific "acceptability standards" before attention can be placed on optimizing their "aspirational objective." We introduce the notion of acceptability prioritized preferences to model such situations and show that not only are these preferences generally discontinuous, but they can also fail to be characterizable by utility functions of any kind. Despite this fact, we establish a pure strategy Nash equilibrium existence result for interactive environments whose populations include agents endowed with acceptability prioritized preferences.