The short answer to this is no. Online multiplayer on the PlayStation 4 is not free. You must own a PS Plus subscription in order to play online games on the PS4. Here is why.
While multiplayer was free on the PS3, it was often the cases where an online pass was used as a means for developers and Sony to get back some losses made on the network. Running a large gaming network like this is incredibly expensive. Making it free meant the quality suffered. To maintain quality and to get rid of the online pass system that was unfair and people generally hated, Sony decided to charge for the use of the PlayStation network.
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