I think this is a case where you need to clarify what your point was. You never said why ownership was a contrived concept, making it fairly easy for someone without telepathic powers to miss that point. It’s also not clear how this is gamifying the notion of ownership, which biases it perpetuates, or why.
You say here that it’s a self serving bias, but it’s not clear what “it” is. Is “it” the thing that is hypothetically owned, or the concept of ownership itself? Ownership could lead to self-serving bias, certainly. I might think my car is the best car, because it’s mine (I don’t. My car is actually pretty shitty, because I can’t afford to get it fixed properly). However, L_Mariachi’s point still works. I own money. It’d be silly to think that my money spends better than anyone else’s money, but it’s important to understand that it’s my money. Otherwise, someone else could use my money in exchange for goods and services. This would be non-optimal, because I contribute to society in exchange for that money, so I can get the goods and services. Should someone else use my money, and should I be able to use someone else’s money, because there is no ownership, I have little reason to contribute to society. More directly, I could take goods, if not services and bypass the money part altogether. With the concept of ownership being meaningless, I have little incentives to offer in exchange for the services of others. Hypothetically I could offer to trade my services in exchange for theirs. This isn’t workable though, because while I believe the services I am able to provide are important, they are only important to a select few people, and those people are not the same people as those I would need services from.
So, if I understand you correctly, we could do away with the concept of ownership and reduce our biases, but we would also have to start growing our own food and making our own clothes. This may seem extreme, but when it comes down to it, ownership and currency are contrived social constructs. This does not mean they weren’t contrived for a reason, however, in much the same way as traffic lights are a contrived construct, but still far better than the simpler alternative of road anarchy.