I will run an ultimatum game (1000 mana) among two randomly selected manifolders who participated in this market.
Market resolves to Yes if the responder accepts the proposal.
Market resolves to No if the responder rejects the proposal.
Description of the ultimatum game:
One player, the proposer, is endowed with 1000mana. The proposer is tasked with splitting it with another player, the responder. Once the proposer communicates his decision, the responder may accept it or reject it. If the responder accepts, the money is split per the proposal; if the responder rejects, both players receive nothing.
More details about the ultimatum game on Wikipedia: https://en.wikipedia.org/wiki/Ultimatum_game
How the proposer and responder is selected:
At market closes, I will use #FairlyRandom to draw a random number to select the proposer, and ask the proposer to propose how to split the mana (in the comments section). Then I will randomly draw a responder, and ask the responder to decide whether to accept the proposal (in the comments section). *I will restrict the proposer and responder sample to those will less than 200 shares in the market, so that the ultimatum game incentives are not distorted by too much.
If the randomly drawn proposer or responder did not make their choice in the comments section within 24 hours, I will randomly select another manifolder to replace them.
The prize mana of the ultimatum game will be sent to the proposer and responder through manalink.
@dominic For what it's worth, I probably would have taken most amounts of mana >100 offered to me. I don't have a lot of mana, and this provides a nice boost. Lots of discussion about precommitment and stuff below, but to me, the decision is fairly clear, especially because it's very unlikely that this is going to be a repeated game.
Now that market is closed and Users tab is settled, I'll use FairlyRandom to randomly select the proposer. (starting from top left, excluding the users with over 200 shares)
I’ve read planecrash so if I won I’d offer Ṁ500 and probabilistically reject unfair splits such that the EV of offering them is less than Ṁ500.
Does the proposer know who the responder is when they propose?
Can proposer and responder be the same person?
What if there are fewer than 2 traders with less than 200 shares?
3'. What if there are more than 2 traders with less than 200 mana, but they don't respond within 24 hours?
Reply to 1: The proposer do not know who the responder is when they propose, since the responder will be randomly chosen after the proposer propose
Reply to 2: The proposer and responder will not be the same person (I will redraw if they happened to be the same
Reply to 3: I think there will be more than 2 traders with less than 200 shares by the time the market closes. I will probably find a proposer and responder outside of this market if that end up happening.
If I am chosen as the responder, I precommit to reject any offer that is less than 75% of the sum of mana to be split.
(Unless I'm offered some external incentive to accept it, as in Yev's comment below.)
If I'm chosen as the proposer, I precommit to not offer more than 50% to the responder (with a similar caveat about external incentives). Sorry, Isaac, I guess you'll never accept my offer.
@Yev It's possible that I may take the "do nothing" route unintentionally, by not being active on Manifold at the time. But I'd ask that Ammon treat that as a rejection, since that's what I intend to do if I check the market in time. My choice under the given circumstances has already been made, and it's "reject".
@Boklam If I'm chosen as the responder and the offerer offers me 50%, I will decline*, and they get nothing. If they offer me 75%, I will accept, and they get 25%. 25% is more than 0%, so their best choice in the moment is to make me that offer.
(*Still subject to the same caveats about external offers.)
Oh I actually didn't see Yev's above comment that said the same thing. I said that completely independently, which I guess is good evidence about the likely success of Isaac's strategy :)
@IsaacKing I already had this type of pre-commitment in mind as a general principle guided by general game-theoretic principles, I just hadn't stated it for this particular market. When you made your precommitment, it was already too late for you (if in fact we get paired up)!
Additionally, my commitment serves to dissuade others from making an attempt like yours. So I believe it would be a good game theoretic move even if I hadn't already thought about this sort of thing.
@jack I am confused by this notion of precommitment.
There's a different notion of "commitment" which I understand. It is the making legible of future incentives to oneself that will cause the behavior to which one desires to commit. But if such incentives do not exist, and you do not have the means to create them, then you cannot "commit" in this sense.
Isaac, what exactly do you lose by violating your precommitment?
(Otherwise, here is how I play this game: the offerer has first-move advantage, but the responder has the option to reject the deal on principle. Therefore the offerer expects to get more than 50%, but if the offerer demands too much more, the offer might be rejected.)
Feel free to create a market on whether I'll follow through on my committment. :)
@IsaacKing But whoever is chosen as the proposer wouldn't know you are the responder until after they have already made their proposal. Even if I was willing to give in to your ultimatum, I wouldn't have any way to do so when chosen as the proposer. Are you suggesting that the best strategy for the proposer is to give the responder a 75% split, just in case you end up being the responder?