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selfless person approaches jones and smith 100 bill and offers sell it highest bidder winn 0

A selfless person approaches Jones and Smith with a $100 bill and offers to sell it to the highest bidder, but the winning and losing bidders must pay her their bids. So if Jones bid $2 and Smith bids $1 they pay a total of $3, but Jones gets the money, leaving him with a net gain of $98 and Smith with -$1. If both bid the same amount, the $100is split evenly between them. Assume that each of them has only tow $1 bills on hand, leaving three possible bids: $0, $1 or $2. Write out the payoff matrix for this game and then find its Nash equilibrium.

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