Transcript price leadership

Corporate Social Responsibility or
Asymmetry of Payoff ?: An
Investigation of Endogenous
Timing Game
joint work with Akira Ogawa
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Our works related to this paper
(1) Payoff Dominance and Risk Dominance in the
Observable Delay Game: A Note (JoE 2009, joint work
with Akira Ogawa).
(2) On the Robustness of Private Leadership in Mixed
Duopoly (AEP 2010, with Akira Ogawa)
(3) Randomized Strategy Equilibrium and
Simultaneous-Move Outcome in the Action
Commitment Game with Small Cost of Leading (ORL
2011, with Takeshi Murooka and Akira Ogawa).
(4) Price leadership in a homogeneous product market
(JoE 2011, with Daisuke Hirata)
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price leadership
The leader announces the price change first, and
then other firms follow this price change.
Some researchers suspect that this is a collusive
pricing, implicit cartel.
However, if we regard this as a price version
Stackelberg, it is natural that a higher price of the
leader induces a higher price of the follower
(strategic complements)
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price leadership (Ono, 1978)
Homogeneous product market, no supply
obligation, duopoly, increasing marginal cost,
price-setting.
One firm chooses the price and then the other firm
chooses its price after observing the price of the
rival. (Stackelberg)
He compares the equilibrium payoffs when the firm
with higher cost is the leader to those when the
firm with lower cost is the leader.
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Asymmetric Costs
MC
the MC of the
higher cost firm
the MC of the
lower cost firm
0
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Follower's pricing
(1) Suppose that the leader's price is higher than the
monopoly price of the follower. Then, the follower
names its monopoly price and obtains the whole
market.
(2) Suppose that the leader's price is lower than the
monopoly price of the follower. Then,
(a) names a higher price than the leader and obtains
the residual demand, or
(b) the follower names the price slightly lower than the
rival's and obtains the whole market. (price undercutting)
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Firm 1's pricing
Ono (1978) assume that the follower undercuts the
leader's price. Predicting this behavior of the
follower, the leader chooses its price.
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Residual demand
MC
Follower's MC
P
residual demand of the leader
D
P1
0
Y2
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residual demand
MC
Follower's MC
P
residual demand of the leader
D
0
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Residual Demand
MC
P
residual demand of the leader
Follower's MC
D
0
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price leadership
Suppose that the firm with lower cost becomes the
follower.→It produces a lot as a price taker
→Predicting this aggressive behavior, the firm with
higher cost names a low price.
Suppose that the firms with higher cost becomes the
follower.→It does not produces a lot as a price taker
→Predicting this less aggressive behavior, the firm with
higher cost names a high price. ~ beneficial for both
firms.
He concludes that the lower cost firm takes price
leadership if the cost difference between two firms is
large.
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Contribution of Ono (1978)
(1) pioneering work on Timing Game
(2) pioneering work on Price Leadership
～the lower cost firm becomes the leader
(3) Mutually beneficial price leadership can appear
when the cost difference between two firms are
sufficiently large.
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Subsequent Works
・Ono (1982) Oligopoly Version
・Denekere and Kovenock (1992)
~Capacity Constraint
→The firm with more capacity becomes the leader.
・ Amir and Stepanova (2006)～differentiated product
market
→The firm with lower cost firm becomes the leader
and it is mutually beneficial if cost difference is large.
・Ishibashi (2007)
~Capacity Constraint＋repeated game
→The firm with more capacity becomes the leader.
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Problems in Ono(1978)
(1) Is mutually beneficial leadership is always realized
in equilibrium？
・He did not formulate the Timing Game.
(a) Is the outcome where the lower cost firm becomes
the leader always an equilibrium？
(b) Is it a unique equilibrium?
(c) If not, the equilibrium with lower cost firm's
leadership is robust？
~No game theoretic foundation
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Problems in Ono(1978)
(2) Is price undercutting is always best reply?
The answer is NO. undercutting is not always best reply.
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Dastidar (2004)
Consider a Stackelberg duopoly with common
increasing marginal cost in a homogeneous product
market.
Firm 1 names the price and after observing the price
firm names the price.
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price-undercutting
P
MC
Firm 2's MC
D
P1
0
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Y
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no price-undercutting
P
MC
Firm 2's MC
D
P2
Residual Demand
P1
0
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Y
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price-undercutting vs nonundercutting
A decrease in the price of the leader makes the
undercutting strategy more profitable and nonundercutting strategy less profitable.
→There exists p* such that the follower takes nonundercutting strategy if and only if p≦p*.
In equilibrium, firm 1 names P1= p* , firm 2 takes nonundercutting strategy, and two firms obtain the same
profits.
Two prices appear in the homogeneous product market.
The leader engages in marginal cost-pricing, while the
follower is not.
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Problems in Ono(1978)
(3) The assumption of price-undercutting is innocuous?
The answer is NO. This assumption changes the results
In equilibrium, the follower does not undercut the price.
(i) The price leadership by the higher price firm is
mutually beneficial even when the cost difference is
small.
(ii) It is a unique equilibrium, or it is the risk-dominant
equilibrium.
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Hirata and Matsumura (2011)
(i) The price leadership by the higher price firm is
mutually beneficial even when the cost difference is
small.
(ii) It is a unique equilibrium, or it is the risk-dominant
equilibrium.
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price-undercutting
P
MC
Firm 2's MC
D
P1
0
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Y
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no price-undercutting
P
Firm 1's MC
MC
Firm 2's MC
D
P2
Residual Demand
P1
0
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Y
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Intuition behind the results
Suppose that the leader has a higher cost. ～It is easy
to induce the follower to take non-undercutting
strategy (taking a residual demand).
It can name the relatively higher price, and it is
mutually beneficial.
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Stackelberg or Cournot
Cournot (Bertrand) model and Stackelberg model yield
different results.
Simultaneous move model and sequential move model
yield different results.
Which model should we use? Which model is more
realistic?
An incumbent and a new entrant competes
→sequential-move model
There is no such asymmetry between firms
→simultaneous-move model
However, in reality, firms can choose both how much
they produce and when they produce.
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Timing Games
Firms can choose when to produce.
Formulating a model where Cournot outcome and
Stackelberg outcome can appear, and
investigating whether Cournot or Stackelberg
appear in equilibrium.
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Stackelberg Duopoly
Firm 1 and firm 2 compete in a homogeneous
product market.
Firm 1 chooses its output Y1∈[0, ∞). After observing
Y1, firm 2 chooses its output Y2∈[0, ∞).
Each firm maximizes its own profit Πi.
Πi＝P(Y)YiーCi(Yi), P: Inverse demand function,
Y: Total output, Yi: Firm i's output, Ci: Firm i's cost
function
I assume that P'+P''Y1<0 (strategic substitutes)
⇒First-Mover Advantage
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Stackelberg's discussion on the
market instability
In the real world, it is not predetermined which firm
becomes the leader.
Because of the first-mover advantage, both firms want
to be the leaders.
Straggle for becoming the leader make the market
instable.
～This is just the idea for endogenous timing game.
But he himself did not present a model formally.
Some papers discussing this problem appeared at the
end of 70s.
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Four representative timing games
(1) Observable delay game
(2) Action commitment game
(3) Infinitely earlier period model
(4) Seal or disclose
(5) Two production period model
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Observable Delay Game
Duopoly
First stage: Two firm choose period 1 or period 2.
Second Stage: After observing the timing,
the firm choosing period 1 chooses its action.
Third Stage: After observing the actions taking at
the second stage, the firm choosing period 2
chooses its action.
Payoff depends only on its action (not period).
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Possible Outcomes
Both firms choose period 1 ⇒Cournot
Both firms choose period 2 ⇒Cournot
Only firm 1 chooses period 1 ⇒Stackelberg
Only firm 2 chooses period 1 ⇒Stackelberg
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Equilibrium in Observable Delay
Game
Strategic Substitutes
⇒Both firms choose period 1 (Cournot)
since Leader ≫ Cournot ≫ Follower
Strategic Complements
⇒Only firm1 chooses period 1 (Stackelberg) or
Only firm2 chooses period 1 (Stackelberg)
since Leader ≫ Cournot
and Follower ≫ Cournot.
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Asymmetric Cases
It is possible that two firms have different payoff
ranking.
e.g., Price Leadership
Firm 1 Leader ≫ Follower >> Bertrand
Firm 2 Follower >> Leader >> Bertrand
It is quite natural to think that firm 1 becomes a
leader in equilibrium. cf Ono (1978,1982)
Is it true?
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Matsumura and Ogawa (2009)
Assumption UiL≧ UiC
Result If U1L＞ U1F and U2F＞ U2L,
(i) firm 1's leadership is the unique equilibrium
outcome,
(ii) equilibrium outcomes other than firm 1's
leadership is supported by weakly dominated
strategies,
or (iii) firm 1's leadership is risk dominant
⇒Pareto dominance implies risk dominance in the
observable delay game. ～foundation for Ono's
discussion.
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Pareto efficient outcome can fail to be
an equilibrium in general contexts
２
Ｃ
Ｄ
Ｃ
（3,3）
（0,4)
Ｄ
（4,0）
（1,1）
１
Pareto Dominance →(C,C)
Risk Dominance →(D,D)
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Pareto dominant equilibrium can fail to
be the risk dominant equilibrium in
general contexts
２
C
１
D
C
(3,3)
D
(-100,-1)
(-1,-100)
(1,1)
Pareto Dominance →(C,C)
Risk Dominance →(D,D)
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risk dominance
２
C
D
C
(3,3)
(-100,-1)
D
(-1,-100)
(1,1)
１
Consider a mixed strategy equilibrium. Suppose that in
the mixed strategy equilibrium each firm independently
chooses C with probability q. Then (C,C) is risk
dominant if and only if q <1/2.
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Observable Delay
２
1
2
1
(A,a)
(C,b)
2
(B,c)
(A,a)
１
C≧A, c≧a.
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Asymmetric Cases
It is possible that two firms have different payoff
ranking.
e.g., Mixed Duopoly
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Pal (1998):mixed duopoly, domestic
private firm, quantity-competition
２(private firm)
1
2
1
(A,a)
(C,b)
2
(B,c)
(A,a)
１
B>C>A, c>a, b>a
Question: Derive the equilibrium outcome.
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Matsumura(2003): mixed duopoly,
foreign private firm, quantitycompetition
２
1
2
1
(A,a)
(C,b)
2
(B,c)
(A,a)
１
C>A>B, c>a, b>a
Question: Derive the equilibrium outcome.
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Observable Delay, Matsumura
(2003)
２
1
2
1
(A,a)
(C,b)
2
(B,c)
(A,a)
１
C>A>B, c>a, b>a
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Barcena-Ruiz (2007) :mixed duopoly,
domestic private firm, pricecompetition
２
1
2
1
(A,a)
(C,b)
2
(B,c)
(A,a)
１
B>A>C, c>a>b
Question: Derive the equilibrium outcome.
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Barcena-Ruiz (2007)
２
1
2
1
(A,a)
(C,b)
2
(B,c)
(A,a)
１
B>A>C, c>a>b
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Mixed Duopoly
Mixed duopoly
Quantity-competition→Stackelberg
Price-Competition→Bertrand
Private duopoly
Quantity-competition→Cournot
Price-Competition→Stackelberg
Does asymmetry in objectives or welfare-maximizing
objective yield contrasting results in mixed duopoly?
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Social responsibility approach
Ghosh and Mitra (2010)
Payoff θΠ＋(1-θ)W
The same payoff of partially privatized firm
Difference ~ Both firm has the same payoff (no
asymmetry)
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Social responsibility approach
Quantity-competition→Cournot
Price-competition→Stackelberg
Asymmetry in objectives, not welfare-maximizing
objective, yields contrasting results in mixed duopoly.
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Endogenous Choice of PriceQuantity Contract
Firms choose whether to adopt price contract or
quantity contract, and then choose the prices or
quantities.
Singh and Vives (1984) showed that choosing the
quantity (price) contract is a dominant strategy for
each firm if the goods are substitutes (complements).
Intuition (substitutable goods case)： Choosing a
price contract increases the demand elasticity of the
rival, resulting in a more aggressive action of the rival.
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Endogenous Choice of PriceQuantity Contract in Mixed Duopoly
For the private firm, choosing a price contract increases
the demand elasticity of the rival, resulting in a less
aggressive action of the rival (substitutable goods case).
Thus, the private firm has an incentive to choose the
price contract, as opposed to the private duopoly.
For the public firm, choosing a price contract increases
the demand elasticity of the rival, resulting in a more
aggressive action of the rival . Thus, the public firm has
an incentive to choose the price contract.
→Bertrand competition appears in Mixed Duopoly
(Matsumura and Ogawa, 2012)
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Social responsibility approach
Quantity contract is chosen.
Asymmetry in objectives, not welfare-maximizing
objective, yields contrasting results in mixed duopoly.
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