Market power, collusion, and oligopoly

1
Market power, collusion, and oligopoly

• Market power ability to influence market prices
• Acquiring market power mergers
• Horizontal mergers regulated by the DOJ/FTC
  guidelines (an interesting read!) based on loss
  of welfare due to the merger
  
• Welfare trade-off in a merger on the upside,
  mergers can decrease cost and also increase the
  range of products available. On the downside
  bigger firms have more market power, quantity
  produced is likely to decrease, resulting in
  higher prices and a welfare loss
• Overall, welfare effects of a merger are
  ambiguous a merger may increase or decrease
  welfare

2
Antitrust (I)

• Sherman Act (1890) and Clayton Act (1914) give
  courts power to prevent mergers that reduce
  competition
  
• A double monopoly two firms A and B, both
  monopolists in their product market. If A uses
  Bs output as an input, the outcome (evaluated in
  terms of welfare) is clearly worse than in the
  situation where As input were purchased in a
  competitive market
• 60k question whats worse than a monopoly?
• Answer a chain of monopolies.

3
Vertical mergers

• If the chain of monopolies becomes a single
  monopoly through vertical integration, consumers
  benefit
  
• But in general the welfare effects of a vertical
  merger are ambiguous mergers between competitive
  firms and monopolies may decrease welfare

4
Predatory pricing

• Acquiring market power revisited predatory
  pricing
  
• Decreasing price to drive out competition
• Price wars Intel and AMD
• The predator has to produce output it may incur
  losses if sells at a low price. The firm thats
  preyed upon may shut down during the price war
  
• Perhaps gaining reputation (warning to future
  entrants) is the best purpose of predatory
  pricing
  
• Predatory pricing (rather, some forms of price
  discrimination that tend to create a monopoly,
  lessen competition or injure competitors)
  illegal under the Robinson-Patman (1938) act

5
A bit of game theory

• Collusion firms set prices and quantities. Two
  forms really by direct contact and tacit
  collusion
  
• What price and quantity is most likely to occur
  from collusion?
  
• Monopoly profits highest possible profits
  achieved
  
• Smoking gun Christies and Sothebys posted on
  their website that talks between their
  representatives enabled them to set the
  commissions

6
Prisoners dilemma

• Want to play a game? Go to Mike Shors website
  at Owen
  
• Two suspects (A and B) committed a crime and were
  arrested
  
• Interrogated separately they may confess (C) or
  deny (D)
  
• Payoffs more is preferred to less!

7
Prisoners dilemma
Crook B
D
C
C
2,2
10,-1
Crook A
-1,10
6,6
D
As payoff is the first number in each cell the
second is Bs payoff
8
Solving the PD

• Best outcome (D,D) Pareto Optimal
• But theres always an incentive for a player to
  deviate from (D,D)
  
• In fact, choosing C always gets you a better
  payoff than choosing D Check this!
  
• Nash Equilibrium a pair of strategies (SA, SB)
  if A sticks to his NE strategy SA, B has no
  profitable deviation and similar for B.
  
• Alternatively No unilateral profitable
  deviations from the Nash equilibrium exist!

9
Games

• Find the NE of the following 2-player game

Player B
D
C
C
2,3
-1,5
Player A
3,-1
-2,-2
D
Check for profitable deviations Player A first,
then player B.
Are any strategies dominated?
10
Repeated PD

• If play for a finite number of times the same PD
  game, start with the last period. What would you
  do if you were Mr. A?
  
• Go to the next-to-last period. What would you do
  if you were Mr. A?
  
• Collusion? There is no collusion in the
  finite-period repeated PD?
  
• What if the game is repeated an infinite (or
  random) number of times?
  
• If players put enough weight on future streams of
  income, collusion may be enforced.

11
The infinitely repeated PD

• Refer to the payoffs in the table on p. 7 both
  players would be better off if they played in
  each period (D,D). They choose to play C because
  of the incentive that the opponents have to
  cheat by playing C.
• Mr. A offers the following plan to Mr. B he
  will start by playing D in the first round will
  continue to play D as long as Mr. B plays D if a
  deviation is detected, Mr. A will play C forever.
  This is a grim trigger strategy (deviation from
  D triggers punishment of the opponent forever).

12
Infinitely repeated PD (contd)

• To analyze the conditions under which the trigger
  strategy is an equilibrium, we have to see if
  there are any unilateral profitable deviations.
  
• A bit of notation is required since the game is
  played in discrete time periods t1,2,3, let the
  value of 1 in period t1 be equal to d in
  period t (d is usually referred to as the
  discount factor and incorporates the effect of
  a non-zero interest rate d1/(1r) where r is
  the inter-period interest rate thus, d must be
  less than 1).
• d may be interpreted as the present value of 1
  that is obtained one period in the future.
  
• Intuitively to have 100 in your bank account
  one year from now, you have to put less than 100
  in your bank account today the amount is exactly
  100/(1r)100 d

13
Trigger strategies

• If Mr. B plays D forever, his payoff is
• 66 d 6d26 d3
• If he defects/cheats by playing C, his payoff is
  102 d2 d22 d3
  
• Helpful aa da d2 ad3a/(1- d) for any
  number a and for any d that is less than 1 and
  greater than zero
  
• Compare the two payoffs above if
• 6/(1- d)102 d/(1- d)
• Thus, for the trigger strategy to be an
  equilibrium, we need d1/2.
  
• Intuition if the discount factor is large enough
  (i.e., if you care enough about future payoffs),
  the collusive outcome (D,D) may be enforced in
  all periods.

14
Mixed strategies

• If you play paper-rock-scissors, announcing a
  strategy to your opponent (e.g., you will play S)
  and sticking to it guarantees that your payoff
  will be equal to zero (your opponent will choose
  R and will win).
• The only way to win in this game is to randomize
  over strategies choose P, R and S with some
  probability.
  
• Another example Matching pennies

15
Games

• Find the (pure strategy) NE of the following
  2-player game

Different
Tail
Head
Head
-1,1
1,-1
Same
-1,1
1,-1
Tail
Are any strategies dominated? No. In addition,
no NE in pure strategies exist!
16
Matching pennies

• The only way to (sometimes) win in this game (as
  in P-R-S) is to randomize over your choice of H
  and T.
  
• To find the equilibrium probabilities of playing
  H and T, observe that if a strategy (i.e.,
  playing H or T) is used in equilibrium, it must
  yield the same (expected) payoff as all the other
  strategies that are used in equilibrium. If a
  strategy has a higher expected payoff than all
  the others, you will only use that strategy!
• So suppose that the same player chooses H with
  probability p, and T with probability 1-p
  
• Similarly, the different player chooses H with
  probability r, and T with probability 1-r.
  
• Lets find p and r so that the expected payoff
  for the two players of playing H and T are the
  same.

17
Mixed strategies

• Mr. same if he plays H, his expected payoff
  is 1r -1(1-r) (he gets 1 if his opponent plays H
  this happens with probability r, and -1 if his
  opponent plays T, which happens with probability
  1-r.
• If Mr. same plays T, he gets -1r(1-r).
• By definition of a mixed strategy equilibrium,
  the expected payoffs from playing H and T should
  be the same, so we need 2r-11-2r, from which it
  follows that r.5.
• Same argument holds for Mr. different, thus, p
  must be equal to .5.

18
Matching pennies

• Interpretation to maximize expected payoff, each
  player in the game of matching pennies chooses to
  play T or H each with probability ½. If a higher
  probability is put on one of the strategies,
  expected payoff is strictly less (can you show
  this?).
• This game is known as a zero-sum game the sum
  of payoffs in each of the four possible outcomes
  is equal to zero.
  
• What is the equilibrium expected payoff for the
  two players?
  
• What are the corresponding probabilities and
  expected payoffs in the P-R-S game?

19
Oligopoly

• Price and quantity competition respective
  games are Bertrand and Cournot
  
• Cournot quantity competition. Two (or more)
  firms that share the market for a homogeneous
  good
  
• Inverse demand P(X) a b X gives market price
  when the quantity produced by the two
  oligopolists is equal to X.
  
• For simplicity both firms have constant marginal
  cost equal to c.

20
Exercise 8.1

• If market demand is D(P)50-2P, what is inverse
  demand?
  
• Write X 50-2P and solve for P. In this case
  P25-X/2.
  
• So P(X)25-X/2 is inverse market demand

21
Cournot (quantity competition)

• First firm chooses x1 to maximize its profit
  (P(x1x2)-c) x1 (revenue minus cost)
  
• Note that the optimal x1 will be a function of
  x2. This is the first firms reaction function
  x1R1(x2).
  
• Similarly, for firm 2, x2R2(x1)
• Graphically

22
x2
R1(x2)
X2
R2(x1)
x1
X1
23
Finding reaction functionsExercise 8.2

• P(X)5-X
• Marginal cost c1
• ?1 (5-(x1x2)-1)x1
• ?2 (5-(x1x2)-1)x2
• Differentiate ??1/?x14-2x1-x20
• ??1/?x14-2x2-x10
• First x1(4-x2)/2R1(x2) (1)
• Second x2(4-x1)/2R2(x1) (2)
• Solve for x1 and x2 take x2 from (2) and plug it
  into (1) get x1(4-(4-x1)/2)/2, so
  
• 2x1 2-x1/2 or 3x1/22 x14/3
• x2 will be equal to x1 (check this!)

24
What if

• P(X) a b X
• Marginal cost c
• Can you find the reaction functions?
• Can you find the Cournot quantities?
• Suppose there are three firms in a market
• Can you find the reaction functions?
• Can you find the Cournot quantities?

25
Bertrand model (price competition)

• Two firms, same marginal cost c, homogeneous
  product
  
• Puzzling result price charged by the two firms
  equals marginal cost
  
• Why?
• Suppose that a firm charges a higher price than
  the other. What is that firms profit?
  
• So both firms must charge the same price
• If price is above marginal cost
• Undercutting the rivals cost by a penny gets you
  all the market (a simplification, certainly)
  
• If price is below marginal cost
• Firms incur losses
• Is (c,c) a Nash Equilibrium?

26
Bertrand

• Yes there is no profitable deviation
• The profits of the two firms are 0
• Compare this with the profit with Cournot
  (quantity) competition

27
Collusion in the Bertrand (price competition)
model

• Both firms would be best off if they choose the
  monopoly price.
  
• Fear of being cheated (e.g., the opponent charges
  the monopoly price minus a penny) makes
  competitors choose a price that is equal to
  marginal cost.
• What if the price competition game is repeated an
  infinite number of times? Analysis of the
  infinitely repeated PD game suggests that if the
  discount rate is high enough, collusion may be
  enforced with infinite repetition.

28
Monopolistic competition

• Product differentiation products that differ
  across firms in their characteristics
  
• Pepsi and Coca-Cola?
• Demand more elastic than the one faced by a
  monopolist because elasticity of demand depends
  on the availability of substitutes
  
• Firms maximize profit MRMC
• In the short run a monopolistically competitive
  firm may earn positive profit, but long-run entry
  drives profits to zero

29
Monopolistic competition


Long Run
Short Run
MC
MC
AC
PSR
AC
Short run profit
SR demand
PLRAC Zero profit
MR
PLR
LR demand
LRMR
QLR
Quantity
QSR
Quantity