How does a Sequential game work?
Players do NOT choose Simultaneously - Player 2 can Observe Player 1s move Payoffs = u1(a1,a2) and u2(a1,a2) - Payoffs are Common Knowledge Dynamic games w/ Complete + Perfect Info
What is the main Issue with Dynamic Games?
Credibility
Why is Credibility an issue for Dynamic Games?
Player 2s Best Response may offer no incentive for Player 1 to adopt different Strategy
How do you find the Solution to a Sequential game?
Backwards Induction
- Work from End Result to first decision
- How does Stage n-1 react to Solution…
How does Stage 1 react to best decision in Stage 2
What is a Stackelberg Model of Duopoly?
Dominant Firm moves first- chooses Output
Follower firm moves second- chooses Output based on q1
How would Stackelberg be solved?
Backwards Induction
1 . Solve max π2 = q2 (a - q1 - q2 - c) Using Product Rule
=> Gives Firm 2 Reaction Function - q2* = (a - q1 - c)/2
2 . Sub. q2* into max π1 = q1 (a - q1 - q2* - c)
- Solves for q1*
3 . Sub. q1* into q2* => Outcome is q1* and q2*
What 3 things are always True for Stackelberg?
- Aggregate Quantities of Stackelberg > Aggregate Quantities in NE of Cournot
- Market Price in Stackelberg < Market Price in Cournot
- Firm 1 better off in Stackelberg than Cournot
- Firm 2 worse off than in Cournot
What can Sequential Games with Simultaneous Moves cause?
Subgame Perfect Equilibrium
What is Subgame Perfect Equilibrium (SPE)?
List of Strategies for each player, which yield a NE in every Subgame of the game
If Players 1 + 2 make decision- then Players 3 + 4 Observe then make decision- how is SPE found?
Backwards Induction
1. Stage 2: Solve Simultaneous game between 3 + 4
2. Stage 1: Players 1 + 2 anticipate Stage 2 Solution + Simultaneously make decision based off Stage 2 result
SPE = decisions made by each player
When is a NE Subgame Perfect?
If Players Strategies constitute NE in every Subgame
