Stackelberg

Michael Anderson Rabina Sherchan

[|Heinrich von Stackelberg] is a German economist who published //Marktform und Gleichgewicht// in [|1934] which describes the Stackelberg leadership model. This model is a economic strategic game which the leader firm moves first and then the follower firms move sequentially. Stackelberg is also known for his contributions to game theory and oligopoly theory.

This model is similar to [|game theory] where players are a //leader// and a //follower// competing on quantity. The leader moves first, choosing a quantity. The follower observes the leader's choice and then picks a quantity. The Stackelberg leader is also known as the Market Leader.

There are constraints within the Stackelberg model which include:
 * The leader knowing //[|ex ante]// that the follower observes his action.
 * The follower must have no means of committing to a future non-Stackelberg follower actions.
 * Leaders must know that followers have no means to commit to non-Stackelberg future actions.
 * Leaders having perfect information
 * All players are rational

The Stackelberg model also assumes that barriers to entry exist and all firm possess some type of market power. Indeed, if the 'follower' could commit to a Stackelberg leader action and the 'leader' knew this, the leader's best response would be to play a Stackelberg follower action.

Firms may engage in Stackelberg competition if they have any advantage enabling them to move first. The leader must have commitment power. Besides committing by moving first, once the leader has moved, it cannot undo its decision and is committed to that action. This first-mover advantage is similar to a situation if the leader was in an industry where they were an incumbent monopoly and the follower was a new entrant. Players must keep in mind that sometimes the first mover advantage is truly a disadvantage which can affect the outcome of the game and other players’ decisions. Other forms of commitment can include holding excess capacity is another means of commitment.

Stackelberg’s model leads towards solving the Nash Equilibrium, where each players’ strategy is optimized through assessing and considering the strategies of other players. Often times the Stackelberg model can be analyzed and better understood utilizing a decision tree to show the combination of outputs and payoffs for a firm’s decision.

Stackelberg is also known for developing the //Stackelberg Oligopoly,// which one firm makes an output decision in an industry before any other firm can act. An industry is chacterized by a //Stackelberg Oligopoly if://

- There are few firms serving many consumers - Firms either produce differentiated or homogenous products - A single firm (the leader) chooses an output before all other firms choose their outputs. - All other firms (the follows) take the output set by leader and choose outputs that maximize profits given the leaders output. - Barriers to entry exist

Equilibrium Outputs in a //Stackelberg Oligopoly:

P = a - b (Q1 + Q2)//


 * __Graphical Model__**

The above figure demonstrates the Stackelberg model. Leader firm would produce at q1, total Stackelberg output at Q, and competitive output at Qc. Leader firm would produce where Residual MR=MC and follower firm would produce q2, determined by Q-q1.

In comparison with other oligopoly models,
 * __Comparison with other oligopoly models__**
 * The aggregate Stackelberg output is greater than the aggregate Cournot output, but less than the aggregate Bertrand output.
 * The Stackelberg price is lower than the Cournot price, but greater than the Bertrand price.
 * The Stackelberg consumer surplus is greater than the Cournot consumer surplus, but lower than the Bertrand consumer surplus.
 * The aggregate Stackelberg output is greater than pure monopoly or cartel, but less than the perfectly competitive output.
 * The Stackelberg price is lower than the pure monopoly or cartel price, but greater than the perfectly competitive price.

__**Example**__ Firm that discovers and develops a new product has a natural first-mover advantage. Lets suppose there are two firms F1 and its rival FCost function of each of the two firms : C = 0,28q (no fixed costs, to simplify). Market demande curve : q = 1000 – 1000p Market Price function : p = 1- 0,001q Suppose firm F1 is the leader and the firm F2 the follower. Firm F1 realizes that once it sets its output, the follower firm F2 will use its Cournot best-response function to pick its optimal q2. The output choosen by F1 is 360 units. Then the output choosen by F2 is calculated by using the best-response function : [q2 =360 - 0,5q1]= 180 units

__**Test Questions:**__ 1) Which statement does not apply to Stackelberg Oligopoly?

a) There are many firms serving many consumers b) Firms wither produce differentiated or homogenous products c) A single firm (the leader) chooses an output before all other firms choose their outputs d) There is barriers to entry and exit


 * The answer is A. Oligopoly is a market structure where there are only few firms.**

2) (True/False) In a Stackelberg Oligopoly, all other firms follow a leaders decision and attempt to maximize their output based on the leaders output decision.
 * Answer: True**

3) (True/False) A Stackelberg Oligopoly has firms that follow the leaders' output or pricing decisions.
 * Answer: True**

4) Since the leading firm in an Stackelberg Oligopoly knows that other firms will react to its output and pricing decisions it must:

a) choose a level of output that will maximize its profits given that the followers will react to whatever the leader does b) produce based upon the followers' reaction functions at any point on the curve c) produce based upon the followers' reaction functions at the point that maximizes revenue d) None of the above e) A & C f) A & B


 * The answer is C.**

5) What are some of the similarities between a Stackleberg Oligopoly and a Bertrand Oligopoly?

a) Both have few firms serving many customers b) Both oligopolies have barriers to entry c) Both oligopolies //only// produce homogeneous products d) There are no similarities between the two oligopolies e) A & B


 * The answer is E.**

6) (True/False) A Stackelberg Oligopoly is characterized by a firm that is considered to have first-mover advantage in production or pricing. **Answer: True**

7) (True/False) In a Stackelberg Oligopoly, a follower will not react to a leaders' output decision by using a Cournot reaction function. **Answer: False**

1. Picture of Henrich von Stackelberg http://cepa.newschool.edu/het/profiles/image/stackel.gif 2. Works of [|Heinrich von Stackelberg] 3. http://64.233.167.104/search?q=cache:AqhUlUckTQwJ:www.aae.wisc.edu/fsrg/publications/wp2005-03.pdf+stackelberg+companies&hl=en&ct=clnk&cd=11&gl=us 4. http://64.233.167.104/search?q=cache:X0VGFGAcEFIJ:in3.dem.ist.utl.pt/master/06micro/06_Oligopoly.pps+stackelberg+companies&hl=en&ct=clnk&cd=15&gl=us 5. http://64.233.167.104/search?q=cache:3Ioox4R36qQJ:courses.ttu.edu/econ3320-kdesilva/Chap009.pdf+stackelberg+companies&hl=en&ct=clnk&cd=19&gl=us 6. http://ideas.repec.org/p/wpa/wuwpio/0506013.html 7. http://ideas.repec.org/a/spr/reecde/v3y1997i1p29-43.html 8. http://www.ecofine.com/strategy/The%20Stackelberg%20Equilibrium.htm
 * __Links to explore__**
 * //Grundlagen einer reinen Kostentheorie (Foundations of Cost Theory)//, [|Vienna], 1932
 * //Marktform und Gleichgewicht (Market and Equilibrium)//, Vienna 1934
 * //Grundlagen der theoretischen Volkswirtschaftslehre (Principles of theoretical Economics)//, 2. Aufl., [|Berne] 1951
 * //Theorie der Vertriebspolitik und Qualitätsvariation (Theory of Distribution Policy and Quality Differentiation)//, in: Ott, A. E., //Preistheorie//, [|Cologne] 1965, S. 230-318