Don't know what make and model but the majority of pedals have cup and cone bearings within. The "bolt" in the centre you referred to is probably the cap, and you should find an axle with bearings inside, it sounds like the locknut and therefore cone within is loose.
This is likely to be a somewhat relevant guide although your pedals are not the same. Essential health warning is that pedals are often fiddly to work with and in many cases require unusual and special tools to do it properly. So if they are cheap replacement should be considered.
Before Mickle jumping in reminding us scatterbrains the wonders of warranty
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you could try asking the seller to deal with it if they were only lightly used and/or still within warranty period.