Consider the following game, called ‘Picking stones’. There are three players, A, B and C, who...
Consider the following game, called ‘Picking stones’. There are three players, A, B and C, who have four stones set in front of them. The rules of the game are as follows. A moves first and takes one or two stones. B moves next and takes one or two stones. Then, if there are any stones left, C moves and takes one or two stones. Finally, A picks up the last stone, if there is one left. Whoever picks up the last (fourth) stone wins.
a) Draw the extensive form of the game.
(b) Is it ever possible for A to win this game? Explain your answer.
(c) Derive all the subgame perfect equilibria of this game.
Homework Answers
Answer :
a) The extensive tree amd possible outcomes are:
1)
>A(1)>>B(1)>>C(1)>>A(1). ==> A will win.
2)
A(2)>>B(1)>>C(1). ==> C will win.
3)
A(1)>>B(2)>>C(1). ==> C will win.
4)
A(1)>>B(1)>>C(2). ==> C will win.
5)
A(2)>>B(2)>>C(0). ==> B will win.
b) A can win the game only in 1st condition only. But that will not happen, because all the players know the rules to win. So B or C will pic the last stone. This is my explanation.
Thank you .
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