A selfless person approaches Jones and Smith with a $100 bill and offers to sell it

to the highest bidder, but both the winning and losing bidders must pay her their

bids. So if Jones bids $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 $100 is split evenly between them. Assume that each of them

has only two $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