Talk:Stackelberg competition

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[edit] term missing?

I just edited the equation for Pi_1, but on second thought it occurs to me that there may be a term missing. Shouldn't it be the total differential as follows?

\frac{d \Pi_1}{d q_1} = (\frac{\partial P(q_1+q_2)}{\partial q_1} + \frac{\partial P(q_1+q_2)}{\partial q_2}.\frac{\partial q_2(q_1)}{\partial q_1}).q_1 + P(q_1+q_2(q_1)) - \frac{\partial C_1 (q_1)}{\partial q_1}

Common Man 08:56, 19 October 2005 (UTC)

[edit] Nash equilibrium?

Stackelberg's model has many Nash Equilibrium, isn't this describing subgame perfect equilibrium? Smmurphy 17:37, 16 November 2005 (UTC)

[edit] Vandalism

There is obvious vandalism in the first part of the page. A knowledgeable person should correct it. —The preceding unsigned comment was added by 155.232.128.10 (talk) 20:22, 28 March 2007 (UTC).

[edit] Correct version of page

The link below seems to be the version of the page free of vandalism.

http://en.wikipedia.org/w/index.php?title=Stackelberg_competition&oldid=118524910

I have just done a humongous revert to the material from december 2006. It seems everything since then has been vandalism (or changes from british to american spelling). nadav 06:41, 1 May 2007 (UTC)

[edit] Jargon-free explanation

For those of us who aren't game theorists, it would be nice for the article to explain some terms that are used in the introduction. What does it mean for firms to

  • "compete on quantity"
  • "go first". Do what first?
  • "commit to a future non-Stackelberg follower action"
  • "have commitment power"

It seems that the second paragraph under "Nash equilibrium" is a much better introduction to what the game is actually about for those who don't already know. LachlanA 20:30, 2 August 2007 (UTC)

[edit] Conditions for Equilibria

Setting the first derrivative of follower's payoff (conditional on leader's output) to zero does not guarantee a maximum -there could be many or no solutions. The function does not even have to be differentiable. Some conditions on the cost and price functions are necessary.

I suggest adding the following conditions (sufficient but not necessary):

1) Supposing that the functions p(q1,q1), c1(q1), and c2(q2) are differentiable. (For price function, at least want 1st partials, don't really need differentiability).

2) First partials of of p are non-positive 3) Derrivatives of cost functions are non-negative —Preceding unsigned comment added by 149.173.6.51 (talk) 20:09, 20 May 2008 (UTC)