 Formalisms such as Coalition Logic are too weak to express Nash equilibria. However, they can express the fact that certain effectivity functions allow for the possibility of a Nash equilibrium. This is what in Hansen &amp; Pauly 2002 is called Nash-consistent Coalition Logic. Nash Equilibrium is in fact not definable in basic modal logic (Benthem et al. 2011), but it can be done with a modality that intersects both the preference and the choice relations (Benthem et al. 2011).