Economic and Game Theory
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I was wondering if anyone could help me out with a game theory question:
My game involves two opposing players, M and W.
M’s objective is to pay the smallest amount. W’s objective is to gain the biggest amount.
M has to make a decision as to weather or not he should ask a fortune teller for advice, or take the advice of W.
W is right 90% of the time. The fortune teller is right 100% of the time.
If M asks the fortune teller, and the fortune teller and W say the same thing, it will cost M $15,000.
If the fortune teller and W do not say the same thing, it will cost W $15,000.
M has the option of exiting the game by paying W a fee.
The question is :
What price should W set so that M could exit the game?
Logically, I see this as $14,999. However that is not rational, as M’s benefit to W would not be tolerated for $1.
So I see the question as then becoming “what is a reasonable discount from $15,000” that M would consider to be a greater benefit to himself.
Instinctively I see this as 75% of $15k as I feel 50% would be a loss for W.
Can anyone direct me or advise me on the best logical approach to take on this?