P2 and P3 play with a penny. P1 picks between same (S) and different (D). After observing P1's choice, P2 and P3 get to picked Simultaneously independently either head (H) and tail (T). Then the coins are shown If P1 played S and P2 and P3 played the same (either played H or both played T) then P1 get both pennies. If P1 played D and P2 and P3 played differently (one played H and the other played T) then P1 again gets both pennies. Otherwise, P2 and P3 get one penny each and P1 gets nothing
(a) Please draw the extensive form
(b) What would be a strategy for P1 in this game?
(c) What would be the strategy space for P2?
(d) What is the pay of function?
(e) What would be a strategy problem?