Please answer this game theory question that I made up myself, for me. I actually don't know the right answer, even though I made up the question. It hurts my head. Thanks. 2 People (Person A and Person B) are at a very special auction for a very special thing. The item in question is a Marble Chess Set worth $25. Inside the Chess set there is a random amount of money between $1 and $800 cash. Both People have 1 Bid, and 1 bid only, and Person A bids first. Person B can choose not to bid, or can bid $1 higher than Person A and win the Chess Set. Person A is given information that the case's cash money amount that is hidden in the case is exactly $700, making the case worth $725 total. Person B is given the information that Person A knows how much money is in the case, but doesn't know how much it is himself. What is the optimal starting bid for Person A? Should Person B bid?

@speedcolaa

7 жыл бұрын

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@mesplin3

7 жыл бұрын

EricSmyth14 My guess would be that A would bid $724. If B bids, then he gets what he paid for. Else A receives $1 of utility.

@EricSmyth4Christ

7 жыл бұрын

I figured it out originally when I told my dad about it, even as he claimed to not know. Since then, I forgot, so I got to figure it out again, lol. Here is what I think/thought it was Person B should Bid because person A has to set a value for the case that is lower than what is in there to stop himself from being reverse freerolled. Person A, even knowing person B should bid, cannot do anything about it, and has to set the value of the box at $724 like you said, but really, any value 724 or less. What I think would make it better as a question is if Person A picked an amount that was more than the case was worth and person B didn't bid, then person B would have to pay person A the difference, and person A would get the box for free. What is the answer then?

@joshuapowles6910

7 жыл бұрын

I computed the QRE with the software Gambit for the chess set worth between $1 and $5 and A able to bid between $0 and $6 in whole dollars. I found that A always bids $1 less than the value of the chess set, while B employs a mixture, choosing not to bid with probability 1/(2^n) where n = the maximum possible value - A's bid. If this holds for your example, then a plausible NE will be when A bids $724 and B bids with probability 1 - 1/(2^101), and doesn't bid with probability 1/(2^101) or around one in 2.5 nonillion. Perhaps B does not prefer to always bid because if that were the case then A would have no incentive to bid in any predictable manner, since A will always get nothing. Why shouldn't A bid higher than the actual value, the theory says, as long as it is low enough that B doesn't know the difference and is sure to bid regardless.

@joshuapowles6910

7 жыл бұрын

Hi, to address your last paragraph I modified my smaller-scale game accordingly, and found that for A bidding higher strictly dominated bidding lower. If A bids off to infinity, or to the very maximum, what can B do about it? B has to pay A the difference to avoid having to pay the difference plus $1.

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