Question: Three people simultaneously choose an integer between 0 and 9 (i.e. 0,1,2,3. . .). If they all three choose the same, then each person receives

Three people simultaneously choose an integer between 0 and 9 (i.e. 0,1,2,3. . .). If they all three choose the same, then each person receives a number of dollars equal to the integer chose. If any are different then they must pay a number of dollars equal to the integer they chose.

a. What are the pure strategy NE of this game?

b. Now let them choose real numbers between 0 and 9 (i.e. 0,0.1,0.2,. . .1,1.1. . .) . Now a player is paid their choice if it is equal to 1/2 of the average choice made by the other players. If they do not choose 1/2 of the average, then they pay an amount equal to their choice. What are the pure strategy NE of this game?

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