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

Quantity

30

30

Demand curve

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 (**)

Firm 1’sReaction Curve

Firm 2’sReaction Curve

Duopoly ExampleQ1

Q2

30

30

10

10

Cournot Equilibrium

Figure shows reaction curves and the Cournot-Nash 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

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

Total revenue for the two firms is:

Firm 1’sReaction Curve

Firm 2’sReaction Curve

Duopoly ExampleQ1

Q2

30

30

10

10

Cournot Equilibrium15

15

Competitive Equilibrium (P = MC; Profit = 0)

CollusionCurve

7.5

7.5

Collusive Equilibrium

For the firm, collusion is the bestoutcome followed by the Cournot

Equilibrium and then the competitive equilibrium

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 ExampleQ1

Q2

30

30

10

10

Cournot Equilibrium (2 firms)

15

15

Competitive Equilibrium (many firms)

Monopolist

More competition: profits & prices fall

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

Firm 2Price 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.

P r o f i t s F i r m 2 P r i c e H i g h L o w

F i r m 1 H i g h 1 0 , 1 0 5 , 1 2

L o w 1 2 , 5 7 , 7

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:

P r o f i t s F i r m 2P r i c e H i g h L o w

F i r m 1 H i g h 1 0 , 1 0 6 , 1 2

L o w 1 2 , 5 5 , 7

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:

P r o f i t s F i r m 2P r i c e H i g h L o w

F i r m 1 H i g h 1 0 , 1 0 6 , 1 2

L o w 1 2 , 6 5 , 5

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:

P r o f i t s F i r m 2P r i c e H i g h L o w

F i r m 1 H i g h 1 0 , 1 0 5 , 1 2

L o w 1 2 , 5 7 , 7

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 CaseCalculation of Expected Value

1 3 0.0512 6 0.1623 10 0.374 17 0.795 28 1.5966 18 1.2067 8 0.6168 4 0.3489 3 0.19410 1 0.10711 1 0.11712 1 0.12713 1 0.137EV: 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