In the game of \Take-away coins", players 1 and 2 alternatively remove the coins
on a table. On each turn, a player must remove one, two or three coins. Passing
back any coin to the table is not allowed. Player 1 moves rst. The player who
removes the last coin on the table loses one dollar to the other player. Let r1; r2,
and r3 denote the removal of one, two or three coins respectively.
(a) Suppose that there are three coins on the table originally.
i. Give an extensive form representation of the game.
ii. How many strategies are there for player 1?
iii. How many strategies are there for player 2?
iv. What is the backwards induction outcome of the game?
v. Give a normal-form representation of the game.
vi. Find a pure-strategy subgame perfect Nash equilibrium of the game.
(b) Suppose that there are twelve coins on the table originally. Find a backwards
induction outcome of this game.