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

Question

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 $1 they pay a total of $3, but Jones get 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,$2. Write out the payoff matrix for this game, and then find its Nash equilibrium.

Explanation / Answer

Jones
          $0    $1    $2.
          $0    0, 0          99,0    98,0

Smith $1         0,99         49,49            98,-1

         $2               0,98 -1,98             48,48 ----- Nash Equilibrium

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