Three players independently and simultaneously choose integer numbers between (and including) 10 and 100. Players are paid the lower of the three numbers, and, in addition, an amount R = 4 is transferred from the player with the higher number to the player with the lower number. If the three numbers are equal, no transfer is made. If two players choose the same number and this number is the highest, each one transfers 2 to the player with the lower number (that receives 4). If two players choose the same number and this number is the lowest, each one receives 2 from the player with the higher number (that pays 4).

a. Find the best response of Player 1 to player 2 choosing 20 and player 3 choosing 30.

b. Find all Nash equilibria in pure strategies