# 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, l

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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