REPRESENTATION AS A COORDINATION GAME
PRESENTER: DAVID LORENZ

 Changes in quality
 Horizontal v. Vertical
 Vertical
 Quality Differences
 Agreement on low v. high quality
 Examples
 First Class v. Coach Plane Tickets (vertical)
 spicy v. mild food (horizontal)

 No firm producing a quality consumers demand
 Profit from entering this market
 Realistically, most industries have:
 Very many or a couple firms
 All producing multiple qualities at different prices
 Example: Multiple car companies producing different cars at different prices
 Therefore, competition arises at every quality when collusion is not present

 Computer Industry
 Lots of different qualities of computers
 Some people demand higher quality computers than others
 Suppose only two computer producers
 Apple and Dell
 Suppose only two types of consumers
 Professional users and Personal users
 Professional users demand higher quality

 Quality (z) between 0 GB and 750 GB
 500,000 personal users and 1,000,000 professional users
 Utility Functions
 U
Pro
= 2 (z – 250) – P
 U
Per
= z – P
 Company goals
 create two products for different consumer types
 maximize price by minimizing Utility

 z
L
– P
L
≥ 0
 Low consumer must buy (assume all buy at U = 0)
 L means lower quality, H means higher quality
 2 (z
H
– 250) – P
H
 High must buy
≥ 0
 2 (z
H
– 250) – PH ≥ 2 (z to low quality
L
– 250) – P
L
 High must have more utility from high compared
 Otherwise nobody buys high

 Imagine MC
H
= 600, MC
L
= 350
 Using constraints…
 Proof in Appendix A if interested
 All consumers buy…
 P
H
= 1,000, z
H
= 750 GB
 P
L
= 500, z
L
= 500 GB
 Profit High = 400,000,000
 Profit Low = 75,000,000

 Limited resources, can only produce one quality
 R & D top secret, don’t know what quality other firm is producing
 Enter market at the same time
 If Apple enters the same quality market as Dell, a price war arises
 Bertrand Competition results, P = MC, profits = 0

development secret and therefore, the competing firms do not know what quality the other firm is developing until they release the product. Both firms move simultaneously once and release their product at the same time. If the firms produce separate qualities, they essentially have a monopoly on that section of the market, and receive the profits shown above in “Outcome.”
If firms produce the same quality, a price war develops because each firm can make additional profits by slightly undercutting the other firm so they serve the entire market. By serving the entire market, they increase profits by increasing the amount of computers sold. This price war is known as Bertrand Competition and it continues until price is equal to marginal cost.
In this model, we assume that both firms serve the entire market and in result, they only change price not quantity. The payoffs each firm receives are not immediate, but over a period of time.
In summary, if both firms produce the same quality a price war will take place until price equals
Representation as a Coordination Game (payoffs in millions of profit):
Dell!
H!
L!
H!
0, 0 *400, 75
Apple!
L!
*75, 400 0, 0
*Nash Equilibrium
In the payoff matrix above, there are multiple Nash equilbria, both of which are Pareto efficient. At a Nash equilibria, neither player can be made better off by deviating. This game is a coordination game because there are multiple equilibria and both players must “coordinate” with the other player to produce different quality goods in order to maximize profit and end up at

 Sequential Outcome: first firm produces high, second firm produces low
 Mixed Strategy
 Suppose multiple periods
 Indifferent when other firm produces high with probability of
84.21%
 If Dell plays high with a probability over 84.21%, Apple produces low and vice versa
 If Dell plays high with a probability under 84.21%, Apple produces high and vice versa

 Both firms can increase their profits
 Agree to create different products
 Producing for different consumers
 Instead of competing, hold a monopoly on different markets
 One firm makes more profit
 But suppose one year Apple produces high and Dell produces Low, and they next year they switch…
 Customer allocation
 Illegal, creating a Cartel
 DOJ will prosecute
 Serve consumers, maximize consumer utility by creating and enforcing rules against collusive/cartel behavior

 DOJ defines customer allocation as “agreements [that] involve some arrangement between competitors to split up customers, such as by geographic area, to reduce or eliminate competition.”
 What is punishable by Antitrust law?
 Likely not: company serving new consumer type by new quality
 Other firms likely to follow in product differentiation
 If firms specifically agreed to produce different qualities to split up consumers and serve different markets…
 this would likely be a violation
 competition would be reduced or eliminated

either equilibria. In addition, it is a coordination game because no strategy is dominated. It is likely that, because the game is played simultaneously, the game may not end up at an equilibria.
The mixed strategy equilibrium is that Apple and Dell play high if the other firm plays high with a probability higher than 15.79%, they are indifferent at 15.79%, and they play low if the other firm plays high with a probability lower than 15.79%.
2
If the firms could communicate or if the game was played sequentially, the firms would end up at one of the equilibria. If the game was played sequentially, the firm moving first would choose to produce the high quality good and the firm moving second would produce the low quality good.
3
Policy Analysis
Let’s consider the aggregate consumer welfare in this model. Using the utility functions
Dell!
H!
L!
H!
400 0
Apple!
L!
0 75
The payoff matrix above shows that consumers are better off if the firms enter the same market to create the same quality good because prices will be lower since the monopoly effect disappears. Outside of chance, the only way for producers to maximize profits is to
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
2 !
For!Proof,!see!Appendix!B!
3 !
Using!backward!induction,!the!firm!moving!first!knows!the!firm!moving!second!would!produce!the!opposite!
quality!good!and!400!million!is!greater!than!75!million.
!
4 !
For!Proof,!see!Appendix!C!

 Small number of Cartels are actually detected
 Whistleblower law has helped
 Today, estimate of only 10 – 33% detected
 For our model lets say it is 20%
 Punishment
 Damages Trebled, possible jail time for executives
 Damages = extra amount the firm was able to increase prices (overcharge) due to collusion * amount they sold during cartel’s existence

Dell!
H!
L!
H!
0, 0 160, 45
Apple!
L!
45, 160 0, 0
Due to the fact that most cartels are not detected, the table above suggests that firms still have an incentive to collude despite the threat of trebled damages. This must be the case in actual markets as well, because otherwise cartels and collusion would not exist. Upon this analysis, I believe damages must be more then trebled to eliminate cartels. Based on the numbers above, to eliminate cartels, damages must be multiplied by a factor greater than 5.
6
6
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
See!Appendix!E!for!proof!

 Based on this model, they still have an incentive to collude
 Payoffs = profit-profit*.20*3
 The damages would have to be multiplied by a factor of
5 for the firms to be indifferent between colluding and competing
 To help consumers of goods, the DOJ must be more effective in finding cartels, or have harsher penalties for those involved
 Because it is not likely that cartel detection will increase, they should focus on harsher penalties