A further problem with this mechanism: since the potential profit isn’t actually used up before the bet is resolved (i.e., each player still has the money they didn’t put on the table), the players can always make another bet with each other using their remaining money. But this knowledge changes the players’ incentives when they’re choosing the probabilities to output.
I’m guessing that in order to design a mechanism that is actually strategy proof, we’d need to make the cost more explicit, for example by having a third party collect some sort of fee based on the expressed probabilities.
I thought the rapidity with which the third person was described to have taken the funds in escrow and declared, “You wait” indicated that she (and you) had seen the problem pointed out by Wei_Dai and moved to block it. (Silly me?)
I wasn’t trying to indicate anything with the third person. Sorry for the confusion. I just thought that it would be hard to end the story without describing where the money goes, since the prediction I was referencing was not going to be answered for a year.
Yes. That is correct. It is only strategy proof if the max bet amount is fixed.
As for the used up potential, that is common in mechanism design. It is very common to have to choose between Pareto optimality and strategy proof.
A further problem with this mechanism: since the potential profit isn’t actually used up before the bet is resolved (i.e., each player still has the money they didn’t put on the table), the players can always make another bet with each other using their remaining money. But this knowledge changes the players’ incentives when they’re choosing the probabilities to output.
I’m guessing that in order to design a mechanism that is actually strategy proof, we’d need to make the cost more explicit, for example by having a third party collect some sort of fee based on the expressed probabilities.
From the OP:
The players had money left over. They only put in 16 of 50 dollars.
I thought the rapidity with which the third person was described to have taken the funds in escrow and declared, “You wait” indicated that she (and you) had seen the problem pointed out by Wei_Dai and moved to block it. (Silly me?)
Here I thought it was just a joke about someone stealing the stakes.
I wasn’t trying to indicate anything with the third person. Sorry for the confusion. I just thought that it would be hard to end the story without describing where the money goes, since the prediction I was referencing was not going to be answered for a year.