Thanks for letting me know.
As it happens, I think I just figured out the answer myself. What I need is an @ElementCollection of Basic types -- as in the second example on this page:
http://wiki.eclipse.org/EclipseLink/Examples/JPA/2.0/ElementCollections
Even though the player_ids in my example reference player objects in another Entity table, I only need to treat them as basic objects (ids) most of the time when being referenced from the Game entity objects.
So I can redefine the @ManyToMany relationship between the Game and Player objects as the Games having an @ElementCollection of player_ids. That will prevent JPA from loading all those Player objects just so I can get at the ids. It also makes it much easier to process the player_ids when they are not properties of a bean. When I do need more information about the player, I can easily access it using the player_id I already have.
I haven't tried this yet, but it looks reasonably certain that this is the answer I was looking for.
Note: this is a JPA 2.0 solution only.
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