This could just be a personality trait that may not be all bad. People tend to think someone is a push over if they let things like this happen, when in reality they are probably the person that doesn't get stressed out over the small stuff, and last time I checked, generosity is a good thing. = )
All that being said, I think you may be jumping the gun a bit. He is only 1 and just may not care too much yet. When kids hit 2 or 3 they start laying more claim to their stuff. All 4 of my kids are totally different in this area and my first one certainly was more like what you are describing. As he got older, he began to protect his things yet always kept that sharing nature, which really worked out since he now has three younger siblings to exercise his patience with.
Just let your baby be, he doesn't care yet so you shouldn't either. He is who he is. Now, if he is older and starts getting bullied or something like that, you probably need to intervene, but for now, he is just a baby, enjoy.
Good luck.