You can battle other players, however at this time there aren’t many benefits to it. There are achievements that you can earn coins for completing: Win 1 Duel – ???, Win 10 Duels – 500 coins, Win 100 Duels – 3000 coins.
To duel another player: stand near them, tap on their character, select “Offer duel to the player”. That player gets sent a duel request and if they accept you have 60 seconds to battle it out.