Monotonic -equilibria in strongly symmetric games

-equilibrium allows for worse actions to be played with higher probability than better actions. I introduce a refinement that addresses this shortcoming: an -equilibrium is monotonic if each player assigns (weakly) higher probabilities to better actions. This concept is logically independent of strong -equilibrium. I study these refinements of -equilibrium in games with countably many players and finitely many pure strategies, and prove the existence of monotonic -equilibrium in a special class of such games—strongly symmetric games. The proof is constructive and it implies, in particular, the existence of symmetric -equilibrium in strongly symmetric games. This result fails to hold in the larger class of weakly symmetric games.