Competitive
Strategy
Key Concept:




Demand elasticity controls profitability and
Demand elasticity depends on reactions of
competitors.
If competitors match price moves, demand
is relatively inelastic but
If they don’t match, demand may be very
elastic.
Competitors’ Responses



To assess demand conditions and efficacy of
a pricing strategy,
Need to predict how rivals will respond.
No simple general answer - we will review
several different frameworks for analyzing
this.
Pharmaceutical Example

New drug goes through various life stages:




On patent - no competition.
Still on patent but another patented competitor.
Off patent - generic competitors.
Clearly pricing policy differs by stage.
Pharmaceutical Example


We know how to price in the first stage here
- set MR = MC, and possibly price
discriminate.
Follow through the other stages. First
assume one other competitor with a patented
drug with similar therapeutic value.
Monopolistic Competition and Oligopoly
Suppose two competitors 1 & 2 face the
following market demand curve:
P = 30 - Q
where Q is the total production of both firms
(i.e., Q = Q1 + Q2).
Also, suppose both firms have marginal cost:
MC1 = MC2 = 0
Price
30
Demand curve
Quantity
30
Two Competitors


Each tries to choose production level in
response to output of the other.
In choosing output level, firm indirectly
chooses (or determines) price, as price is
determined by total output (it and the
competitor) and market demand conditions.
Reaction Curve


A reaction curve for firm 1 specifies for each
output level of firm 2 what is firm 1’s best
response, i.e. firm 1’s most profitable output
level given that of firm 2.
A reaction curve for firm 2 is the same with
the 1s and 2s interchanged.
Determine the reaction curve for Firm
1.
To maximize profit, the firm sets
marginal revenue equal to marginal
cost. Firm 1’s total revenue R1 is
given by:
R1 = PQ1 = (30 - Q)Q1
= 30 Q1 - (Q1 + Q2)Q1
= 30 Q1 - (Q1)2 - Q2Q1
The firm’s marginal revenue MR1 is
just the incremental revenue R1
resulting from an incremental change
in output Q1:
MR1 = R1/Q1 = 30 - 2 Q1 - Q2
Now, setting MR1 equal to zero (the firm’s
marginal cost), and solving for Q1, we find:
Firm 1’s Reaction Curve: Q1 = 15 - 1/2 Q2 (*)
The same calculation applies to Firm 2:
Firm 2’s Reaction Curve: Q2 = 15 - 1/2 Q1 (**)
Duopoly Example
Q1
30
Firm 2’s
Reaction Curve
Cournot Equilibrium
10
Firm 1’s
Reaction Curve
10
30
Q2
Figure shows reaction curves and the CournotNash equilibrium.
Note that Firm 1’s reaction curve shows its
output Q1 in terms of Firm 2’s output Q2
Similarly, Firm 2’s reaction curve shows Q2 in
terms of Q1. (Since the firm’s are identical, the
two reaction curves have the same form. They
look different because one gives Q1 in terms of
Q2, and the other gives Q2 in terms of Q1)
The equilibrium output levels are the values for
Q1 and Q2 that are at the intersection of the two
reaction curves, i.e., that are the solution to
equations (*) and (**).
By replacing Q2 in firm 1’s reaction curve with
the expression on the right-hand side of firm 2’s,
you can verify that the equilibrium output levels
are:
Cournot Equilibrium: Q1 = Q2 = 10
The total quantity produced is therefore
Q = Q1 + Q2 = 20
so the equilibrium market price is
P = 30 - Q = 10
The equilibrium is at the intersection of the
two curves. At this point each firm is
maximizing its own profit, given its
competitor’s output
We have assumed that the two firms compete
with each other. Suppose, instead, that the
antitrust laws were relaxed and the two firms
could collude.
Suppose the firms set their outputs to maximize
total profit of the two taken together, and agree to
split that profit evenly
Total profit is maximized by choosing total
output Q so that marginal revenue equals
marginal cost, which in this example is zero
Total revenue for the two firms is:
R = PR = (30 - Q)Q = 30Q - Q2
so the marginal revenue is
MR = R/Q = 30 - 2Q
Setting MR equal to zero, total profit
is maximized when Q = 15
Duopoly Example
Q1
30
Firm 2’s
Reaction Curve
For the firm, collusion is the best
outcome followed by the Cournot
Equilibrium and then the
competitive equilibrium
Competitive Equilibrium (P = MC; Profit = 0)
15
Cournot Equilibrium
Collusive Equilibrium
10
7.5
Firm 1’s
Reaction Curve
Collusion
Curve
7.5 10
15
30
Q2
Any combination of outputs Q1 and Q2 that add up to
15 maximizes total profit
The curve Q1 + Q2 = 15, called the contract curve, is
therefore all pairs of outputs Q1 and Q2 that
maximize total profit.
If the firms agree to share the profits equally, they will
each produce half of the total output:
Q1 = Q2 = 7.5
More Competition



As number of firms increases, equilibrium
output points moves towards “competitive
equilibrium.”
With more competition total output rises &
price falls, as do profits for each firm.
Competition makes each firm’s demand more
elastic & reduces its margin & its best output
level.
Duopoly Example
Q1
30
More competition: profits & prices fall
Competitive Equilibrium (many firms)
15
10
Cournot Equilibrium (2 firms)
Monopolist
10
15
30
Q2
A Different Model of
Competitive Interaction



Prisoners’ Dilemma model
Represents tension between cooperative and
competitive behavior.
Central feature in any cooperation between
potentially competitive entities - firms in a
cartel, OPEC members, opposed political
parties.
Prisoners’ Dilemma

Two competitors

Each has constant cost at $4 per unit

Two pricing options: $8 or $6

Both high: sell 2.5 million annually each

Both low: sell 3.5 million annually each
One high, one low, then former sells 1.25 million,
latter 6 million

Price
Firm 2
High
Low
Firm 1 High
2.5, 2.5
1.25, 6
Low
6, 1.25
3.5, 3.5
Note: profits = (price - cost) * sales = $(8-4) * 2.5 = 10,
etc.
Price
Firm 2
High
Low
Firm 1 High
10, 10
5, 12
12, 5
7, 7
Profits
Low
For each firm, a low price is the best
strategy, whatever the other firm does. It is
therefore a dominant strategy, a strategy
which is best whatever the choice of the
other player, so the outcome is (7, 7). This is
in spite of the fact that both could be better
off if both charged high prices. This is an
example of a prisoners’ dilemma game.
Note that (7, 7) is a Nash Equilibrium in the
sense that if firm 1 plays low then low is 2’s
best response and vice versa: at (7, 7) each is
making its best move given the move of the
other. This is the definition of a Nash
Equilibrium.
Collusion and PD



Collusive solution in previous diagrams has
a PD structure.
Stability of cartels - OPEC.
Christies, Sothebys and the Justice
Department.
Now change the payoff matrix slightly:
Profits
Price
Firm 2
High
Low
Firm 1 High
10, 10
6, 12
12, 5
5, 7
Low
Now low is no longer the dominant strategy for
firm 1: low is best for 1 if 2 plays high but high
is best if 2 plays low. Now 1 should always do
the opposite of 2. But for 2 nothing has
changed: low is dominant.
What will be the outcome?
1 cannot decide what to do unless it knows
what 2 will do. So it has to forecast 2’s
move. But 1 can tell that 2’s best move is
low, so 1 should forecast that 2 will choose
low. In this case, 1 should choose high:
hence the outcome will be (high, low) = (6,
12). This is a Nash Equilibrium. Here 2 has
no incentive to move to high.
Now consider this case:
Profits
Price
Firm 2
High
Low
Firm 1 High
10, 10
6, 12
12, 6
5, 5
Low
Neither firm has a dominant strategy: the best
move for each depends on what the other does -
presumable the most common case. What are
the Nash equilibria here? One is (low, high) =
(12, 6). Another is (high, low) = (6, 12).
Which is realized depends on who moves first,
or who stakes out a claim to a market of
product first. (Think of preemptive
announcements, “vaporware”, etc.)
Finally, go back to the prisoners’ dilemma case:
Profits
Price
Firm 2
High
Low
Firm 1 High
10, 10
5, 12
12, 5
7, 7
Low
Here low is a dominant strategy for each
firm, so the outcome should be (7, 7). Now
suppose the game is played repeatedly, say
every month the same two firms face each
other in the same market. Consider the
following strategy:
Firm 1 picks high in period 1 and in period 2.
Then firm 1 keeps on picking high as long as
firm 2 picked high in the previous period. But if
2 picked low in the previous period, firm 1 picks
low forever - or for a very long time. This is
called a “tit-for-tat” strategy or a “punishment”
strategy.
What is 2’s best response to this strategy? If it
plays low the payoff is (12, 12, 7, 7, 7, 7,…). If
it picks high the payoff is (10, 10, 10, 10,…).
Clearly the payoff to picking high is greater.
So the best response to the “punishment” or
“tit-for-tat” strategy is to cooperate and the (10,
10) outcome will result. This outcome is
sometimes referred to as “tacit collusion”.
Polystyrene Base Case
MAXCO-Gambit Case
Calculation of Expected Value
1
2
3
4
5
6
7
8
9
10
11
12
13
EV:
3
6
10
17
28
18
8
4
3
1
1
1
1
0.051
0.162
0.37
0.79
1.596
1.206
0.616
0.348
0.194
0.107
0.117
0.127
0.137
5.83
The MAXCO - Gambit Case

Suppose G believes M will bid EV (EV =
5.83)

What should G bid?

Not bid if true value < 5.83: bid 5.9 if true
value > 5.9

In particular, G will not bid true value if it
expects M to bid EV

Should M bid EV?

When does M win if it bids EV?

If G bids true value, then M loses if true value >
EV and

M wins in true value < EV

So for M bidding EV can lead to “winners curse”
if G bids true value