Love for Emilia
When Arcite and Palamon first see Emilia wandering in the garden beneath their prison cell, they both immediately fall in love with her and decide to become enemies as they compete for her affections. Ironically, however, for the majority of the play, Emilia has no idea who either man is, let alone how they feel about her.
Arcite in Disguise
After Theseus frees Arcite from prison, he banishes him and tells him never to return to Athens again. Arcite disobeys and remains in Athens in disguise, deciding to participate in the May Day games as a means to getting closer to Emilia. His plan works, and Theseus awards Arcite (whom he believes to be an unknown competitor) with the position of Emilia's servant.
Fair Combat
When Palamon and Arcite cross paths after Palamon is freed from prison, they decide that their only option is to engage in single combat with one another. However, Palamon is weak from his time in prison and Arcite agrees to let him recuperate to ensure a fair fight. During this time, Arcite cares for Palamon by bringing him food and drinks, ironically reflecting the love they formerly had for one another.
Arcite's Victory
Before the battle, Arcite prays to Mars for victory. Palamon, however, prays to Venus for love. The audience therefore likely knows what will happen to the characters before they themselves do (Arcite wins, ensuring his victory, but dies, allowing Palamon to pursue his love for Emilia).