(8.3) Dynamic (sequential) games

Question 1

3

What are other names for sequential games?

Answer 1

• dynamic
• extensive form
• game tree

Question 2

What is the key difference between simultaneous and sequential games

Answer 2

in sequential games, players can observe other players’ actions before making their own decisions

Question 3

Define ‘nodes’

Answer 3

decision points

Question 4

Define ‘branches’

Answer 4

available actions

Question 5

Define ‘terminal nodes’

Answer 5

final payoffs

Question 6

1

Which player’s payoff is represented by the 1st number?

Answer 6

Player that moves first

Question 7

photo

Map this out in a game tree where the column player moves first

Answer 7

Question 8

1

What method do we use to solve sequential games?

Answer 8

backward induction

Question 9

What does SPE stand for?

Answer 9

subgame prime equilibrium

Question 10

4

Describe the process to find SPE by backward induction

Answer 10

1. Start at the final decision nodes
2. Determine optimal actions for each player at each node
3. Work backwards through the tree
4. Apply rational choice at each decision point

Question 11

2

What is an SPE?

Answer 11

• Set of strategies which constitutes an NE in every subgame, found by backward induction
• Represents optimal strategy for each player at every possible node, including those that may never be reached

Question 12

2

Here is a game tree. Find the SPE

Answer 12

• Player 1: enter (best responds in both subgames)
• Player 2: quit if player 1 enters, stay if player 1 exits (optimal if player 1 threat credible)

Question 13

1

What is necessary to solve an SPE?

Answer 13

Must specify credible strategies at every possible point in the game

key to state when solving problems

Question 14

5

Look at this game tree. There is a NE at (stay and fight, don’t enter). What is the problem with this NE? Use this to explain the prediction of how the game will be played out.

Answer 14

• Credibility problem
• NE relies on row player’s ‘threat to fight’ if column player enters
• If column player actually enters, row player faces a choice between fighting (payoff = -1) or quitting (payoff= 0)
• rationally, row player would choose to quit
• knowing this, column player should enter

Question 15

2

If a player has a strictly dominant strategy, which threat is credible?

Answer 15

• The strictly dominant strat is always credible
• The promise to play other strat is never credible

Question 16

3

If a player has a weakly dominant strategy, is the threat to play it always credible?

Answer 16

• Not always
• For some nodes, may be indifferent
• So can deviate without reducing payoff