If such transfer of resources is allowed, your share of negentropy must depend only on your contribution, the total contribution and the number of players. If we further assume that zero contribution implies zero share, it's straightforward to prove (by division in half, etc.) that proportional allocation is the only possible scheme.

This still isn't very satisfying. John Nash would have advised us to model the situation with free transfer as a game within some larger class of games and apply some general concept like the Shapley value to make the answer pop out. But I'm not yet sure how to do that.