The arsonist set 13 bins and a sofa alight at Frydenbølien, Danmarksplass, Nedre Korskirkeallmenning and Michael Krohns Gate in the city centre between 11pm on Wednesday night and 5am on Thursday morning.
All the fires were extinguished before causing serious damage or threat to life.
By Thursday morning, police had still received no witness reports which might help identify the perpetrator.
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"We want tips from the public in the case, said Preben Wallestad from the Bergen police told NTB.