Age of Empires II (2013) + Age of Empires II: Definitive Edition - Multiplayer

Hello, everyone!

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I am trying to find a game that I like to play with my friends on steam. We meet everynight on discord and it is very fun!

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So they all have Age of Empires II (2013), which costs 20€ on steam. However, there is Age of Empires II: Definitive Edition, which costs 10€. Can I buy this one and play with them? Or is that impossible?

Thank you in advance!