Question: 1. Two players play a game to split $4. Each player will simultaneously write down an amount (in whole dollars) between $0 and $4. If the sum of the two amounts is more than $4, each player gets $0. If the sum of the two amounts is less than or equal to $4, each player gets the amount that he or she wrote.
(a) Draw the game in strategic form.
(b) Does either player have a dominant strategy If so, what is it?
(c) Find all of the Nash equilibria for this game, considering only pure strategies.
Now change the game so that if the sum of the amounts is less than or equal to $4, each player gets the amount that the other player wrote.
(d) Does either player have a dominant strategy in this new game? If so, what is it?
(e) Find all of the Nash equilibria for this new game, again considering only pure stratgies.