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Cournot Competition and Static Games by Windy Natriavi S. (0806350770)

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Page 1: Ppt Oi Final

Cournot Competition and

Static Gamesby Windy Natriavi S.

(0806350770)

Page 2: Ppt Oi Final

Agenda PresentationWhy do we need game theory?

Types of Games (Cooperative Vs. Non-cooperative)

Nash Equilibrium

How does it apply in real life?

Oligopoly Markets

Cournot Oligopoly

Cournot Oligopoly Theory

Cournot Oligopoly Theory with Many Firms

Cournot Oligopoly Theory with Different Costs

What determines a firm’s operating profit margin?

Its Concentration Index

Profitability

Conclusion

Page 3: Ppt Oi Final

Why do we need game theory?

๏ Existence of economic profit drives firms to enter the market

๏ Lower barrier cost (can be seen through AFTA, improved technology, and faster application time to establish a business in Indonesia in only 60 days)

๏ More anti-trust laws are approved to protect the consumers and ensure healthy competitiveness in the market

‣ As a result, in an industry there are usually many firms and competitor (s) in the market.

Page 4: Ppt Oi Final

Why do we need game theory?

• Because more firms enter the market, competitiveness gets tighter.

‣ The decision of each firm in the market is interdependent, meaning that in order to make decisions, a firm has to also consider other firm’s actions.

➡ So game theory is...concerned with situations in which decision-makers interact with one another, and in which the happiness of each participant with the outcome depends not just on his or her own decisions but on the decisions made by everyone

Page 5: Ppt Oi Final

Types of Game Theory

• differs in how companies formalize their interdependence and the timing

Cooperative Game Theory

Non-Cooperative Game Theory

described as all the outcomes available to the firms in the game as combinations of

actions

described as all the moves/ strategies available to the firms (players) in the

game

firms can interact with each other and cooperative solution concepts

firms interact with one another to maximize their own goals

Example: a seller (player 1) has two potential buyers (player 2 and player 3) and a

production cost of $4. Player two is willing to pay maximum $11 for a unit and player 3 is

willing to pay maximum $9. In these interactions between player 1 and player 2/3,

it is called a cooperative game

Example: two market players (Pond’s and Olay) are both competing in facial care

toward the anti-aging community. In this case, the players are playing a

noncooperative game where both players are competing toward obtaining the

largest market share.

Page 6: Ppt Oi Final

Nash Equilibrium

• ..is the condition when no firm wants to change its current strategy given that no other firm changes its current strategy

• the dominated strategy is the strategy that always gives the least pay-off to a firm no matter what the other player strategy is. In this case, Giant would never choose premium because it always gives the least pay-off to the firm no matter what Carrefour does.

• the dominating strategy is the strategy that always gives the highest pay-off to a firm no matter what the other player strategy is. In this cae, Giant would choose standard pricing strategy because it gives higher pay off no matter what Carrefour does. Using rationale, this strategy will be chosen.

Page 7: Ppt Oi Final

Oligopoly Market Theory

• oligopoly market is a market form in which a market or industry is dominated by a small number of producers

• ...has several forms which are differentiated by its emphasis:

★Cournot Oligopoly Theory with Two Firms

★Cournot Oligopoly Theory with Many Firms

★Cournot Oligopoly Theory with Different Costs

Page 8: Ppt Oi Final

Cournot Oligopoly Theory with Two Firms

• assumes that there are two big market players in the industry that

dominates the other firms (ex: Coke and Pepsi)

• firms compete on the basis of quantity rather than price (Coke & Pepsi’s price is less or more the same which is SGD$3.3 for a 1.5 Liter bottle)

• each firm makes a decision assuming that the other firm’s behaviour is constant (fixed) in the short term.

• the market demand curve is supposed to be linear and marginal cost is constant (that’s why in the short term the other firm’s behaviour is thought to be constant)

➡ To find the Nash Equilibrium in the market, we have to consider on how each firm reacts to a change in the output of the other firm. Nash equilibrium is reached when neither Coke nor Pepsi changes its strategy regardless of how it thinks the other firm is going to act.

Page 9: Ppt Oi Final

Cournot Oligopoly Theory with Two Firms

Example

• Suppose that Coke & Pepsi are two big players in the carbonated soft drink industry

• Coke’s demand function would be P = (a + bQ) and in which the oligopoly case it will be P = a + b(Q1 + Q2)

• Coke’s demand function is noted as below P = (60-Q2) - Q1 where Q2 is the quantity produced by Pepsi and Q1 is the quantity produced by Coke.

• Marginal cost is constant at 12 dollars per unit.

• How does Coke maximize its production function? In other words, how does Coke optimize its quantity and price?

Page 10: Ppt Oi Final

Cournot Oligopoly Theory with Two Firms

Example

• Coke’s total revenue function would be = P x Q which in this case is Q[(60-Q2) - Q1] = 60Q1- Q1Q2 - Q1

2

• The marginal revenue function would then be = 60 - Q2 - 2Q1

• 60 - Q2 - 2Q1 = 12

2Q1 = 48 - Q2

• This also goes on for Pepsi, so in the end we will get the following equations:

To find optimal solution, MR = MCTo find optimal solution, MR = MC

Q1 = 24 - 0.5Q2 [1.1] – Coke’s perspectiveQ2 = 24 - 0.5Q1 [1.2] – Pepsi’s perspective

Page 11: Ppt Oi Final

Cournot Oligopoly Theory with Two Firms

Example

•Equilibrium is achieved by solving the equations simultaneously and is located at the intersection of the two reaction functions

Page 12: Ppt Oi Final

Cournot Oligopoly Theory with Two Firms

Example

• As noted before, Q1 = 24 – 0.5 Q2 and Q2 = 24 – 0.5 Q1

• If we solve the equation, we will have the answer that each firm produces 16 units of output.

• P will then be written as (60 – Q1 – Q2) which is 60 – 32 = 28

As we can see, competition between the two firms causes them to overproduce, thereby making the price lower than it would have been in the case of monopoly price at (A-c)/2B. Output is also less than the competitive output (A-c) / B where price is equal to marginal cost.

Page 13: Ppt Oi Final

Cournot Oligopoly Theory with Many

Firms• There are cases where more

than just two firms producing the same product, where Q = q1 + q2 + … + qN Ex: Telkomsel, Indosat, XL, 3, etc.

• Demand can then be written as P = A - BQ = A - B(q1 + q2 + … + qN).

• If we look at the perspective of Firm 1, its output would be P = A - B(q2 + … + qN) - Bq1

• Q-1 = q2 + q3 + … + qN.

• Therefore, the demand for firm 1 is

• P = (A - BQ-1) - Bq1.

Page 14: Ppt Oi Final

Cournot Oligopoly Theory with Many

Firms

• MR1 = (A - BQ-1) - 2Bq1

• We will solve the quantity of output for Firm 1 as Q1 = (A - c)/2B - Q-1/2

• Because the firms are identical, then we will have Q-1 = (N-1)Q1

• Q1 = (A - c)/2B - (N - 1)Q1/2

• Q1 = (A - c)/(N + 1)B

• The total number of outputs in the market will be summed up as Q= N(A - c)/(N + 1)B

• The equilibrium price in the firm will be written as P= A - BQ = (A + Nc)/(N + 1)

• Profit of firm 1 is P1 = (P* - c)Q1

To find optimal solution, MR = MCTo find optimal solution, MR = MC

As the number of As the number of firms increases, firms increases, the number of the number of

outputs produced outputs produced by a firm is by a firm is

reduced, although reduced, although the total the total

aggregate number aggregate number of outputs of outputs increases.increases.

Page 15: Ppt Oi Final

Cournot Oligopoly Theory with Many

Firms• We can also see that as the number

of firms increases, the price tends to be closer to the marginal cost

Therefore, because of the larger aggregate output

and the lower price which can be given to each firm, profit per firm will fall.

Page 16: Ppt Oi Final

Cournot Oligopoly Theory with Different

Costs• Take for example McDonald’s and Burger King where they both have different costs in producing a burger. For McDonald’s the marginal cost is MD and for Burger King the marginal cost is MB.

• demand for the whole market can be written down as

• P = A - B.Q = A - B(Q1 + Q2)

• To maximize profit,

• MR1 = MC1 and MR2 = MC2.

• If we see from the perspective of McDonald’s, which is firm 1, this will bring us to another equation of (A - Bq2) - 2Bq1 = c1

• the number of outputs produced by McDonald’s as Q1 = (A - c1)/2B - q2/2 and the number of outputs produced by Burger King as Q2= (A - c1)/2B – q1/2

• the final output for McDonald’s would be Q1 = (A - 2c1 + c2)/3B and the final output for Burger King would be Q2 = (A - 2c2 + c1)/3B

Page 17: Ppt Oi Final

Cournot Oligopoly Theory with Different

Costs• What would happen if in this case Firm 2 has a lower marginal cost?

• Its reaction curve will shift upward to the right

• Burger King) will have bigger capacity to produce than Firm 1, making the number of outputs that it produces compared to Firm 1 is higher. As a result, the number of outputs that are produced by Firm 2 increases and the number of outputs that are produced by Firm 1 decreases.

• In equilibrium, McDonald’s would produce QC

1 = (A - 2c1 + c2)/3B

• and Burger King would produce QC2 = (A

- 2c2 + c1)/3B

• Total output therefore would be: Q = (2A - c1 - c2)/3B

Page 18: Ppt Oi Final

Cournot Oligopoly Theory with Different

Costs• demand is written as P = A - B.Q.

• price at P= A - (2A - c1 - c2)/3 = (A + c1 +c2)/3.

• measure the profit for McDonald’s as (P*- c1)QC1 = (A - 2c1 + c2)2/9 and Burger

King’s profit as (P* - c2)QC2 = (A - 2c2 + c1)2/9.

• equilibrium output is less than the competitive level

• product (burgers) is produced inefficiently

• In the idealistic condition, Burger King (Firm 2) should produce all of the burgers, since the lower cost of production will it make it possible for Burger King to produce more burgers than if Firm 1 and Firm 2 both produces burgers.

Page 19: Ppt Oi Final

Concentration and Profitability

• Firms operating in an oligopoly market will want to know how large its concentration and how profitable is the firm compared to other firms in the industry

• let’s take an example of the shampoo industry which has Pantene Shampoo, Sunsilk Shampoo, and other shampoo brands such as Dove, Rejoice, and other brands in the market

• Let’s assume that we have N number of firms in the market with different marginal costs

• Demand for Pantene (Firm 1) will be P = (A - BQ-1) - Bq1.

• The demand for the i firm (any other shampoo producers in the market except for Pantene) will be equal to P = (A - BQ-

i) - BQi.

Page 20: Ppt Oi Final

Concentration and Profitability

•A - BQ-i - 2Bqi = ci

• This can be reorganized into the equilibrium function of A - B(Q*-i + q*i) - Bq*i - ci = 0• P* - Bq*i - ci = 0 or P* - ci = BQ*i.

• If we take P* - ci = Bq*I and divided it by Q*/Q* we will obtain the following:

MRMRii = MC = MCii

•BQ*/P* = 1/ and q*i/Q* = si

Page 21: Ppt Oi Final

Concentration and Profitability

•What does this mean?

• the operating profit of Pantene Shampoo will depend on

• how large the size of Pantene compared to other firms in the industry as a whole (its market share)

• how attached consumers in the market are to Pantene Shampoo (demand elasticity twoards Pantene Shampoo)

As the industry concentration gets higher (more concentrated and less competitive), we can conclude that the operating profit (price-cost margin) will be higher for each firm especially the firm who are the market players.

Page 22: Ppt Oi Final

Conclusion• in oligopoly markets, firms are interdependent of each other.

• how the quantity produced by a firm is actually a reaction function to how it perceives the other firm will produce

• Nash Equilibrium happens when firms choose the strategy that will give them the best pay-off regardless of how the other firms act.

• As many more firms exist in the market, the price will tend to adjust to the marginal cost, making each firm’s profit less than what it would have been with only a few players in the market.

• operating profit of each firm is dependent on its market share and demand elasticity in the market

Firms will have to find a way to lower down its cost (cost leadership strategy)

or

differentiate its product in the market (differentiation strategy)

to be able to grab consumers and stay in the market.