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 the 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 swame amount , the $100 is split evenly between them. assume that each of them has only two $1 bills on hand, leaving possible bids, $0, $1, or $2. what is the pay off matrix for this game, and the 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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