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# pure strategy Nash equilibrium

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You have been offered the chance to participate in a Treasure Hunt game whose rules are as follows. THere are three coloured boxes: red, green and yellow. The game show host must hide a \$100 bill in a box of his choice. You have the option of opening one and only one box/ If the money was hidden in that box, you win it. Otherwise, it returns to the host. Each box has a fee which you must pay to the host if you choose to open that box. The fees are \$50 for the red box, \$20 for the green box, and \$0 for the yellow box. Assume that both you and the show host want to maximize expected earnings.

a) Write down the normal form (payoff matrix) of this game.
b) Find the Nash equilibrium.

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#### Solution Preview

See attached.

If you see carefully what I said was that you cannot find a pure strategy Nash equilibrium and I am certain that you cannot find one. What you can do is start generating your own beliefs and then come up with a Bayesian Nash equilibrium or go for a mixed strategy Nash equilibrium. For that we ...

#### Solution Summary

A pure strategy Nash equilibrium is considered.

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