[*Probably not -- as with chess, fresh variants on poker are rare]
I've been thinking that some of our recent threads come down to how information flows or fails to flow through a system and sometimes when trying to find a new way of thinking about a problem, I find it useful to find an analogous situation in a game, or, failing that, to tweak a game to get an appropriate analogy out of it.
Here's what I came up with. I'm not sure it's all that playable (and I'm open to improvements), but it does raise some of the right questions.
This is a variant of seven card stud with one major addition.
Start by dealing the cards, three up, four down. Players check their cards then complete a normal round of betting.
Starting with the player to the left of the dealer, the bidding round starts. The bidder indicates another player and offers a certain amount to see a certain card* (for example "five dollars for the second hole card from the left"). If the offer is accepted, the card is shown to the bidder. A bid can be extended even if the other player has folded. Each accepted offer starts another round of betting. Additional bidding rounds continue until there is a round with no offers accepted.
Would this work? I'm not sure, but it does give one a chance to think through different situations involving the exchange of information in a zero sum game. For example, the information of what's in your hand is almost certainly worth more than what you'd be offered if you intended to play out the hand but is of almost no value (other than giving some insight to your playing style) if you intend to fold. I believe that bids should run the highest with seven players, a large pot and a small number of folds.
I believe there are other games with negotiated exchanges of information but I'm drawing blank on what they are.
*Unlike roll-your-own games where the player chooses which card to reveal.