A stack of n one thousand rupee notes lies on a table. Two Players labeled A and B take turns taking money from the stack, one or two notes per turn. The game ends when the stack runs out or one of the players takes two notes (whichever comes first). Both players keep what they have taken to that point.
a) Draw the game tree when the initial stack consists of n=5 thousand rupee notes.
b) Solve the game by backwards induction.
c) The first node can be represented as (5,A); this means that there are 4 notes on the table and it is A's turn to move. Using this notation, count the number of decision nodes for A: these are the positions at which A must make a choice. List all the strategies for A, and also list all the strategies for B. Make a table which lists strategies of A in the rows and strategies of B in the columns and lists payoffs to A and B as (a,b) in the table.