You could try signalling that unless they trade with you you’ll put them at a disadvantage. Consider—“Player 1, both you and Player 2 want this property. This property for one of your properties is a fair swap that benefits both of us, but if you turn me down I’ll trade it to Player 2 for their best offer, which benefits Player 2 a lot and me only a little. Player 2, if you don’t give me even the small amount I ask for, I’ll randomly give it to some other player.” If you signal credibly (ie you actually do it if someone calls your bluff) then Player 1 should make the trade provided he values your property more than you knocking yourself out of the game (ie the trade really DOES have to be a fair deal—you can’t just use this to up your bargaining ante).
Part of your argument could be the (truthful) observation that the losers in a trade aren’t the people who made the less valuable trade, but the people who didn’t trade at all—if you play at a very conservative table it might be in your interest to trade at a disadvantage and exploit the increased variance a monopoly gives you.
The major downside here is that many people don’t play Monopoly to win, and strategies that optimise for winning using game theory and the like are seen as ‘unsporting’. Sometimes you just need to accept that to keep your family happy you have to play Monopoly and get bored.
While on the one hand I completely agree with you given your starting premises, I don’t necessarily think we’re in quite the zero information situation you describe. For example, it is pretty well accepted (even amongst people who don’t think cryo will work) that simply freezing yourself without cryopreservant lowers your chance of revivification. This is a pretty important consensus since cryopreservant is highly toxic, but we extrapolate from current trends and conclude, “Curing poisoning is probably an easier task than reconstructing information destroyed by entropy, so I should adopt the ‘cryopreservant’ branch of strategy-space”. This indicates we don’t really have no information about the correct cryo strategy; though I totally accept your weaker claim that I seem to demand much MORE information than we can reasonably be expected to possess.
I think we’re in a situation more like a friend ringing up and says, “We’re going to play Ticket to Ride tonight; it’s like Monopoly only better”. We don’t have enough information to decide whether we want to be the top hat or the battleship (which is a meaningless question anyway since the answer is always ‘top hat’), but we might have enough information to begin to say, “On my first turn I will study the layout of the board carefully (rather than act quickly)” and “I will attempt to remain on good terms with the other players insofar as they can hurt me and I cannot overwhelmingly hurt them” or even “It is unlikely this game will involve serious roleplay. I will not put on my robe and wizard hat”. None of these are enough to guarentee a win, but neither are they trivial realisations; I think it is reasonable to believe probability theory, human nature and my own utility function will not change dramatically in the time it takes me to be revivified, so basing strategy on these characteristics seems worthwhile.