Game Theory

Question 1

What is Game Theory?

Answer 1

Study of how People Behave in Strategic Situations

Question 2

What is a Strategic Situation?

Answer 2

Where each Decision-maker must Consider how others will respond to its actions

Question 3

What are the 5 components of a Game?

Answer 3

Players
Strategies
Payoffs
Timing
An Equilibrium concept

Question 4

What are the Players?

Answer 4

Parties who make Decisions

Question 5

What are Strategies?

Answer 5

Range of decisions the Players can Make

Question 6

What are Payoffs?

Answer 6

Each Player is Motivated by what they will Gain from the Outcome

Question 7

What is Timing?

Answer 7

Who can do what, when?

Question 8

What is an Equilibrium Concept?

Answer 8

What kind of Outcome will be looked for

Question 9

What is a Nash Equilibrium?

Answer 9

Where no Player can change their Equilibrium Strategy + Receive a Higher Payoff

• No force acting for change- No Player wants to Deviate from their Equilibrium
• No Player regrets Strategy Decision

Question 10

Under a Nash equilibrium, where can there ALWAYS be Equilibrium?

Answer 10

Dominant Strategies Equilibrium

Question 11

What are the 3 main reasons we Observe Cooperation?

Answer 11

1. Different Games
2. Repeat Play of Games
3. Lack of Information

Question 12

Why might Different Games lead to Cooperation?

Answer 12

Game may not be a Prisoner’s Dilemma style

Question 13

How can Repeat Play of Games lead to Cooperation?

Answer 13

More games allows Players to learn about each other + develop Trust
-Allows to threaten punishment for cheating

Question 14

How can Lack of Information lead to Cooperation?

Answer 14

Players may not know Numbers in Payoff Matrix

–> More Inclined to Cooperate

Question 15

What does Cournot Quantity Competition model?

Answer 15

Models Strategic Interactions between few firms using Rev./Cost/Demand Curves

Question 16

What are the Total Costs of Firms?

Answer 16

TCi = cqi
i = different firms

Question 17

What are the Marginal Costs of each firm?

Answer 17

MC1 = MC2 = c

Question 18

What are the 3 assumptions of firms?

Answer 18

Each produce Homogenous Goods
Produce quantities qi
Firms are Symmetrical

Question 19

if there are 2 firms, what is the Profit Function of firm 1?

Answer 19

Prof. 1 = P(Q)q1 - cq1

Question 20

Derive the FOC of the Profit Function. given that Market Demand = a - bQ

Answer 20

Q = q1 + q2 ==> P = a - b(q1 + q2)
Prof. 1 = P(Q)q1 - cq1
==> [a - b(q1 + q2)]q1 - cq1
FOC (dProf/dq1): a - b(q1 + q2) - b(1 + dq2/dq1)q1 - c = 0

Question 21

What doe dq2/dq1 show?

Answer 21

How Firm 1 thinks Firm 2’s choice of q2 will respond to Firm 1’s choice of q1

Question 22

What is the Cournot Conjecture + what is it assumed to be + what does it mean?

Answer 22

dq2/dq1 = 0
Firm 1 assumes Firm 2 will NOT adjust q2 in response to Firm 1’s choice of q1
–> Each firm chooses Output assuming others will NOT change their Output

Question 23

Derive Firm 1’s Reaction Function from the FOC, given Cournot’s Conjecture

Answer 23

FOC: a - b(q1 + q2) - bq1 - c = 0

q1 = (a - bq2 - c)/2b ==> (a-c)/2b - q2/2

Question 24

What does the Reaction Function show?

Answer 24

Shows Best Value of q1 in response to a given q2

Question 25

If a Increases, what happens to q1?

Answer 25

Increased a = Increased Demand | q1 Increases

Question 26

If c Increases, what happens to q1?

Answer 26

Increased c = Increased MC | q1 Decreases

Question 27

If q2 Increases, what happens to q1?

Answer 27

Q = q1 + q2 | q1 Decreases to keep Price high

Question 28

If b Increases, what happens to q1?

Answer 28

Increased b = Demand becomes Steeper- Increased P from Lower q1 q1 Decreases

Question 29

What would Firm 2's Reaction Function be and why?

Answer 29

q2 = (a - bq1 - c)/2b | Due to Symmetry

Question 30

Where would the Nash equilibrium be for the 2 firms?

Answer 30

Where the 2 firms' Reaction Functions Intersect

Question 31

How do you solve for the Cournot Nash equilibrium?

Answer 31

Solve Simultaneous Equations of Reaction Functions solve by Symmetry or substitution q1nc = q2nc

Question 32

Given the firms' Reaction Function to be (a - bq - c)/2b, what would be q1nc and q2nc- the Cournot Nash equilibrium?

Answer 32

q1nc = (a - bq2 - c)/2b = (a - bq1 - c)/2b = q2nc | ==> q1nc = (a-c)/3b = q2nc by Symmetry

Question 33

How would an Increase in Demand (a) affect the Reaction Functions?

Answer 33

Both Reaction Functions would shift to the Right by Increase in a Increased Demand--> Output more Profitable--> Increased Output

Question 34

How would a Decrease in Firm 1's MC (c) affect the Reaction Functions?

Answer 34

Firm 1's Reaction Function shifts to the Right by Decrease in c Firm 1 now more Cost Competitive than Firm 2--> Gains larger Market Share

Question 35

For N Symmetric firms, what is the Profit Function and its FOC?

Answer 35

Profit i = P(Q)qi - cqi | FOC: P + qi(dP/dQ)(dQ/dqi) - c = 0

Question 36

For N Symmetric firms, what is MR and MC?

Answer 36

``` MR = P + qi(dP/dQ)(dQ/dqi) MC = cqi ```

Question 37

For N Symmetric firms, what is the Cournot Conjecture?

Answer 37

dQ/dqi = 1

Question 38

By Symmetry, for N Symmetric firms, what is qi?

Answer 38

qi = Q/N

Question 39

For N Symmetric firms, using the Cournot Conjecture + qi, what is the equation for MR = MC?

Answer 39

P + (Q/N)(dP/dQ) = c ==> P [1 + (1/N) (Q/P) (dP/dQ)] = c => P [1 + (1/Ne)] = c e = PeD

Question 40

Given P [1 + (1/Ne)] = c, what happens to the Outcome as N tends to 1?

Answer 40

Monopoly Outcome- P > c

Question 41

Given P [1 + (1/Ne)] = c, what happens to the Outcome as N tends to Infinity?

Answer 41

Perfectly Competitive Outcome- P = c

Question 42

Given P [1 + (1/Ne)] = c, what happens to the Outcome as e tends to Infinity?

Answer 42

Perfectly Competitive Outcome- P = c

Question 43

Given P [1 + (1/Ne)] = c, what happens to the Outcome as N Increases or e Decreases (towards Negative Infinity)?

Answer 43

P tends to c

Question 44

What is Stackelberg Quantity Leadership?

Answer 44

One Firm sets Output before others + can stick to it - Firm can Increase Profits as it can Influence Follower's Output Decision - -> Leader can always choose Cournot NE if it wanted to

Question 45

What is Bertrand Price competition?

Answer 45

Firms Simultaneously choose PRICE not Output | - Firms can now Lose ALL Market Share- even if only 2 firms

Question 46

Explain Bertrand Price competition

Answer 46

Assume Duopoly: Homogenous Output, MC1 = MC2 = c, No Fixed Costs If Firm 1 chooses P1 > c => Firm 2 can choose P2 where c < P2 < P1 - Firm 2 gains All Market Share + Profit

Question 47

In Bertrand Price competition, why can't P2, where c < P2 < P1, be a Nash equilibrium?

Answer 47

Firm 1 would want to Deviate + set Price where c < P1 < P2

Question 48

Where is the only Nash equilibrium under Bertrand Price competition?

Answer 48

c = P1BN = P2BN | Outcome is Efficient- same as Perfectly Competitive outcome