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Question 2 Consider the following two-player coordination game in extensive form. Both players want to coordinate on choosing the same action. However, player 1 has a preference for both players choosing a, while player 2 has a preference for both players choosing b. Before taking their simultaneous actions, player 1 can \"posture\" by either acting happy (h) or by complaining (c), which player 2 can observe. If player 1 complains, it reduces his own payoff by 2. The payoffs are depicted in the following game tree. Player 1 h c Player 2 a b Player 1 a b 4,1 0,0 0,0 1,4 Player 1 a b Player 2 a b 2,1 -2,0 -2,0 -1,4 1. Determine all subgame perfect equilibria in pure strategies. 2. Determine all strictly dominated strategies in the game. 3. Consider the reduced extensive game obtained by removing all strategies that are strictly dominated. Find all subgame perfect equilibria in pure strategies of this reduced game. 4. Explain why in the reduced game, there is no SPE in which both players choose b, even though there exists such an equilibrium in the original game. What effect has the removal of strictly dominated strategies from the game?

          Question 2 Consider the following two-player coordination game in extensive form. Both
players want to coordinate on choosing the same action. However, player 1 has a preference
for both players choosing a, while player 2 has a preference for both players choosing b. Before
taking their simultaneous actions, player 1 can \"posture\" by either acting happy (h) or by
complaining (c), which player 2 can observe. If player 1 complains, it reduces his own payoff
by 2. The payoffs are depicted in the following game tree.
Player 1
h
c
Player 2
a
b
Player 1
a
b
4,1	0,0
0,0	1,4
Player 1
a
b
Player 2
a	b
2,1	-2,0
-2,0	-1,4
1. Determine all subgame perfect equilibria in pure strategies.
2. Determine all strictly dominated strategies in the game.
3. Consider the reduced extensive game obtained by removing all strategies that are
strictly dominated. Find all subgame perfect equilibria in pure strategies of this reduced
game.
4. Explain why in the reduced game, there is no SPE in which both players choose b,
even though there exists such an equilibrium in the original game. What effect has the
removal of strictly dominated strategies from the game?

Question 2 Consider the following two-player coordination game in extensive form. Both
players want to coordinate on choosing the same action. However, player 1 has a preference
for both players choosing a, while player 2 has a preference for both players choosing b. Before
taking their simultaneous actions, player 1 can p̈ostureb̈y either acting happy (h) or by
complaining (c), which player 2 can observe. If player 1 complains, it reduces his own payoff
by 2. The payoffs are depicted in the following game tree.
Player 1
h
c
Player 2
a
b
Player 1
a
b
4,1 0,0
0,0 1,4
Player 1
a
b
Player 2
a b
2,1 -2,0
-2,0 -1,4
1. Determine all subgame perfect equilibria in pure strategies.
2. Determine all strictly dominated strategies in the game.
3. Consider the reduced extensive game obtained by removing all strategies that are
strictly dominated. Find all subgame perfect equilibria in pure strategies of this reduced
game.
4. Explain why in the reduced game, there is no SPE in which both players choose b,
even though there exists such an equilibrium in the original game. What effect has the
removal of strictly dominated strategies from the game?

Added by Susan C.

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