Game Theory Flashcards
What are the 8 Elements of a Game
Players Actions Order of Play Information Strategies Payoffs Outcome Equilibrium
What is the Equilibrium of a Game?
Strategy profile w/ Best Strategies for each player in a game
What does Complete Info mean?
Each Player knows all payoffs for all players
What is a Dominant Strategy?
Strategy where payoff for each decision are preferable to other strategy Regardless of Other Players decision
How does Iterated Elimination of Strictly Dominated Strategies Solve games?
Eliminates Strategies a Rational Player would NEVER play
What is the problem with IEoSDS?
Imprecise prediction about play of the Game
- i.e. If there is NO Strictly Dominated Strategy
Define Nash Equilibrium
Each players Predicted Strategy must be their Best Response to Predicted Strategy of Other Players
–> No Player wants to Deviate from Predicted Strategy
Why is NE a Stronger Solution concept than IEoSDS?
Strategies in NE ALWAYS survive IEoSDS
- Reverse NOT true
What does it mean if there are No Unique Solutions?
There are Multiple NE
What is the Cournot Duopoly Model?
2 Firms- Choose Output Quantity Simultaneously
What is NE for Cournot Model?
NE => q1* = q2*
If a firm picks higher output- Lower price- Loss Making
If a firm picks lower Output- Higher price- Other firm steals Market share
What happens to Equilibrium in Cournot?
Firms have Same Output
Same Market Price
Same Profits
Aggregate Output = 2 x qi
What is Bertrand Duopoly Model?
Firms choose Prices instead of Quantities- still use NE
How do firms choose Price in Bertrand?
Anticipate Price set by Other firm
- Each price must be Profit max. choice- given other firm’s decision
What is NE of Bertrand Model?
p = MC
Why is NE of Bertrand where p = MC?
p < MC : Make Loss on each unit sold- Increase Profit by Decreasing Output - (Increase MR)
p > MC : Either firm can undercut other by arbitrarily small amount, ⍷ > 0 - charge p - ⍷ - Steal all customers
Only Eq. is Competitive Eq. - Zero Profit (Bertrand Paradox)
How do you find NE for Differentiated Products?
Find Firm i’s Best Response to Firm j’s Eq. Price, pj*
Sub. one BR function into other firms BR function
What are the Slopes of BR functions in Cournot?
Negative Slope - ∂qi / ∂qj = –1/2 < 0
If one firm Increases Output- Optimal for other firm to Decrease Output
-Strategic Substitutes
What are the Slopes of BR functions in Bertrand?
Positive Slope
∂pi / ∂pj = b/2 > 0
If one Firm Increases Price- Optimal for other to Increase Price
-Strategic Complements
