Dominant-strategy equilibrium ($s_i\in {\bigcap }_{s_{-i}}{\mathrm{BR}}_i(s_{-i})\forall i$)

A strategy profile in which each player uses a dominant strategy. Every such profile is a Nash equilibrium, since each prescribed choice is a best response to the actual opposing choices in particular. The converse fails: a Nash equilibrium only requires a best response to those actual choices. With the weak convention for dominant strategy, ties are allowed; a strictly dominant strategy requires strict improvement over every alternative against every opposing profile.