Basically, you'd like to reward everyone according to the amount of information they contribute. The game isn't constant sum overall since the amount of information people bring to the market can vary. Ideally, you'd still like the total subsidy to be bounded so there's no chance for infinite liability.
Depending on how the market is structured, if someone thinks another person has strictly more information than them, they should disclose that fact and receive no payout (at least in expectation). Hanson's market scoring rules reward everyone according to how much they improve on the last person's prediction. If Bob participates in the market before you, you should just match his prediction. If you participate before him, you can give what information you do have and then he'll add his unique information later.
Many thanks for the pointer to LMSR! That seems to answer all my questions.
(Why aren't scoring rules mentioned in the Wikipedia article on prediction markets? I had a vague idea of what prediction parkets were, but it turns out I missed the most important part, and asked a whole bunch of ignorant questions... Anyway, it's a relief to finally understand this stuff.)
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.