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 How would this game be different if one player moved first? Hotel – decent quality Hotel – low quality Stay 5, 5 -10, 10 Don’t stay 0, -5 0, 0

Sequential move games Stay 5, 5 Don’t -5, 0 High Quality Stay 10, -10 Traveler Don’t -5, 0 High Quality Stay 10, -10 Hotel Traveler Low Quality 0, 0 Don’t 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 Low Q -10, 10 Stay High Q 0, -5 Hotel Low Q -10, 10 Stay High Q 0, -5 Traveler Hotel Don’t Stay 0, 0 Low Q Solve by Backward Induction – Last stage first What outcome do we expect? *Payoffs for Hotel are listed first

Three stage military game Fight -5, -10 Defend 1 2 Attack -1, 9 Retreat 1 Surrender 10, -5 Don’t 0, 10 What outcome do we expect?

Three stage military game Fight -5, -10 Defend 1 2 Attack -1, 9 Retreat 1 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 Don’t 10, 0 Enter Enter 0, 10 Don’t Firm 2 Don’t 10, 0 Enter Enter 0, 10 Don’t Firm 1 Firm 2 0, 0 Don’t 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.