1. Nash Equilibrium
A strategy combination (a,b) is a Nash equilibrium for two players if neither player would unilaterally deviate if he expected the other player to choose according to (a,b).
A strategy combination (a,b,c,…) is a Nash equilibrium for N players if no player would unilaterally deviate if he expected the other (N-1) players to choose according to (a,b,c,…).

2. The Ranked Coordination Game
BRYDOX
Large
Small
1,1
-1,-1
Large
APEX
Small
-1,-1
2,2

3. The Battle of the Sexes WOMAN Ballet Fight 10,20 -10,-10 Ballet MAN
20,10