Game Theory III – Sequential
Games
Managerial Economics
Kyle Anderson
Sequential Games
• Does the outcome of a game change if one
player chooses first?
• Sequential games:
– Multiple players
– Perfect information
– Sequential moves
• The second player gets to observe the first
player’s move prior to making a decision.
Kyle J. Anderson
Simultaneous move game
Stay
Don’t stay
Hotel – decent
quality
Hotel – low
quality
5, 5
0, -5
-10, 10
0, 0
• How would this game be different if one player
moved first?
Sequential move games
Stay
5, 5
Don’t
-5, 0
Traveler
High Quality
Stay
Hotel
Low Quality
10, -10
Traveler
Don’t
0, 0
Solve by Backward Induction – Last stage first
What outcome do we expect?
*Payoffs for Hotel are listed first
Sequential move games
High Q
5, 5
Hotel
Low Q
Stay
High Q
Traveler
Don’t Stay
-10, 10
0, -5
Hotel
Low Q
0, 0
Solve by Backward Induction – Last stage first
What outcome do we expect?
*Payoffs for Hotel are listed first
Three stage military game
Defend
Attack
1
Fight
-5, -10
Retreat
-1, 9
1
2
Surrender 10, -5
Don’t
0, 10
What outcome do we expect?
Three stage military game
Defend
Attack
1
Fight
-5, -10
Retreat
-1, 9
1
2
Surrender 10, -5
Don’t
0, 10
What if player 1 says it will never retreat?
Credible Commitment – Visible and Irrevocable
Market Entry Game
Enter
-5, -5
Firm 2
Don’t
10, 0
Enter
Firm 1
Don’t
Enter
0, 10
Firm 2
Don’t
0, 0
First mover advantage – whichever firm commits to
open first will be the one to earn positive profits.
How do firms use strategic
commitment?
• Committing to enter a market:
– Committing to land/building
– Union contracts
– Development spending
• Committing to increase production:
– Expand capacity
Big Finish
• Sequential Games can lead to different outcomes.
• To solve a sequential game, look at the last decision(s)
first.
• Credible commitment can lead to higher payouts if they
deter rivals.