<p>It depends on what you assume the firms know about each other.  Under full information / rationality assumptions, with identical firms, second-mover advantage disappears because the first-mover will recognize the credible threat of undercutting, and set P = MC and that will be that.</p>

<p>If the firms are not identical (e.g., different marginal costs) then turn order is irrelevant, because only one firm has the ability to make a credible threat of undercutting.  That firm will capture the market, whether it moves first or second.</p>

<p>Only if you drop the assumption of full information / rationality is it feasible that turn order would matter for Bertrand competition, because then the assessment of credible threat becomes a probabilistic one.</p>

CC BY-SA 4.0
2019-11-27T19:43:33.800Z
This assumes that products offered by both firms are homogeneous. Differentiation in products allows firms to price above marginal cost. This may add some clarity.
lunar_props
CC BY-SA 4.0
2019-11-27T19:51:56.273Z
@lunar_props I'm familiar with the classic Bertrand model.  My point is that relaxing those assumptions is the only way to yield a practical turn-order advantage.  This is to be contrasted with, e.g., a Cournot duopoly, in which there is a clear first-mover advantage even under the classic assumptions.
heh
CC BY-SA 4.0
2019-11-27T20:06:21.443Z
I take your point. This is one way to yield a turn-order advantage. However, with differentiated products, price competition will yield a turn-order advantage for the follower even in the presence of full information.
lunar_props
CC BY-SA 4.0
2019-11-27T20:14:33.690Z
Not under full info and rationality assumption.  In that case, firms know each others' production functions and best-response functions.  In particular, the stronger firm (by virtue of having a lower $MC = p_1$) will know that the weaker firm cannot make a credible threat to reduce price below $p_1$.  Since $p_2 > p_1$, whether the weaker firm moves first or second, it will not be able to capture the market on price.
heh
CC BY-SA 4.0
2019-11-27T21:26:05.497Z
I am having difficulties understanding this last comment. I am not sure what "lower $MC = p_1$" means, since $MC$ is a function of quantity sold, and that is also dependent on $p_2$, so it seems like something is missing here. Also, w.r.t. the last sentence: is capturing the entire market necessary for second mover advantage? Cannot I just be better off compared to the simultaneous equilibrium without capturing the entire market?
Giskard
CC BY-SA 4.0
2019-11-27T21:35:19.867Z
@Giskard These things all follow from the core assumptions of the classic Bertrand model (e.g., the one typically presented in classrooms and which the OP is most likely to be making reference to). In particular, marginal costs are exogenous and fixed, and it is assumed that consumers will all choose to purchase from the firm that offers the lowest price.
heh
CC BY-SA 4.0
2019-11-27T22:09:21.653Z
But you were responding to lunar_props's comment which clearly talks about differentiated products. Him/her: "*with differentiated products, price competition will yield a turn-order advantage for the follower even in the presence of full information.*" You: "*Not under full info and rationality assumption.*"
Giskard
CC BY-SA 4.0
2019-11-27T22:25:21.323Z
@Giskard indeed. And I clearly talked about heterogenous firms in my answer to the OP.  Allowing for differing marginal costs is a simple way of tweaking a model for heterogeneity while still keeping marginal costs exogenous and fixed.  We can move this to chat if you wish, but the gist is that if the weak firm moves first the stronger firm can undercut to claim the full market.  If the strong firm moves first, it anticipates that setting price greater than the weak firm's MC allows the weak firm to undercut, and so it sets price below the weak firm's MC.
heh
CC BY-SA 4.0
2019-11-27T22:27:08.293Z
So you did not address lunar_props's comment? I am mistaken, and your comment after his is a merely an illusory answer?
Giskard
CC BY-SA 4.0
2019-11-27T22:28:20.787Z
@Giskard I am struggling to grasp what your angle is, here.  lunar_props' comment was addressed in the original answer I provided to the OP.
heh
CC BY-SA 4.0
2019-11-27T22:29:48.837Z
I mean, I can quote the two consequential comments again, but I don't understand why it is necessary. lunar_props: "with differentiated products, price competition will yield a turn-order advantage for the follower even in the presence of full information." You: "Not under full info and rationality assumption." You are claiming that these consequential lines have nothing to do with each other?
Giskard
CC BY-SA 4.0
2019-11-27T22:31:20.247Z
@Giskard, it may serve to post a question to the community seeking clarity on how product differentiation in the context of fixed, exogenous costs is typically expressed by allowing firms marginal costs to differ.
heh
CC BY-SA 4.0
2019-11-27T22:32:16.947Z
Are you being a politician right now? Why can't you admit that you made a mistake in your comments? It is not even in your answer! Did you make your comment in answer to lunar_props comment or not?
Giskard
CC BY-SA 4.0
2019-11-27T22:32:41.883Z
Homogenous firms: $MC_1 = MC_2$.  Heterogenous firms: $MC_1 \neq MC_2$.
heh
CC BY-SA 4.0
2019-11-27T22:33:32.190Z
I tire of this doubletalk.
Giskard
CC BY-SA 4.0
2019-11-27T22:34:54.813Z
@Giskard evidently not, since you began it and cannot help but to continue it.  There is no controversy here.  I have invited you to discus further to determine where you are being confused.  You elected not to.  Whatever it is you're trying to accomplish here, you are clearly not seeking clarity in good faith.
heh
CC BY-SA 4.0
2019-11-27T22:35:51.177Z
Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/101572/discussion-between-giskard-and-heh).
Giskard
CC BY-SA 4.0
2019-11-27T22:54:02.197Z
What followed was a somewhat unpleasant conversation in which heh claimed differentiated Bertrand is "breaking the Bertrand framework". The following comment by heh (starting with "Well, to be fair") is also true. (Note "wholly unrelated products")
Giskard
CC BY-SA 4.0
2019-11-27T22:55:33.163Z
Well, to be fair, I suggested that if @Giskard thinks the OP wanted to contemplate a scenario in which the two firms produced wholly unrelated products facing different demand functions, he can offer an answer to that effect.  Evidently he has elected not to.
heh
CC BY-SA 4.0
2019-11-27T19:10:11.797Z
2019-11-27T19:10:11.797Z
heh
<p>For example, in the case of Bertrand competition, is the Stackelberg leader worse off relative to the follower? If so, why? Is this because the first mover can always undercut until marginal cost is reached?</p>

<game-theory><markets>
Does the case of strategic complements always result in a situation where the Stackelberg leader is worse off?
Aqqqq
# Does the case of strategic complements always result in a situation where the Stackelberg leader is worse off?

(Asked by: username_0 on 2019-11-27)

For example, in the case of Bertrand competition, is the Stackelberg leader worse off relative to the follower? If so, why? Is this because the first mover can always undercut until marginal cost is reached?

**Tags:** game-theory, markets


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## 1 answers

### Answer by username_1 on 2019-11-27. Score: 2 | Accepted answer

It depends on what you assume the firms know about each other. Under full information / rationality assumptions, with identical firms, second-mover advantage disappears because the first-mover will recognize the credible threat of undercutting, and set P = MC and that will be that.

If the firms are not identical (e.g., different marginal costs) then turn order is irrelevant, because only one firm has the ability to make a credible threat of undercutting. That firm will capture the market, whether it moves first or second.

Only if you drop the assumption of full information / rationality is it feasible that turn order would matter for Bertrand competition, because then the assessment of credible threat becomes a probabilistic one.

> **Comments:**
> **username_2**: This assumes that products offered by both firms are homogeneous. Differentiation in products allows firms to price above marginal cost. This may add some clarity.  
> **username_1**: @username_2 I'm familiar with the classic Bertrand model.  My point is that relaxing those assumptions is the only way to yield a practical turn-order advantage.  This is to be contrasted with, e.g., a Cournot duopoly, in which there is a clear first-mover advantage even under the classic assumptions.  
> **username_2**: I take your point. This is one way to yield a turn-order advantage. However, with differentiated products, price competition will yield a turn-order advantage for the follower even in the presence of full information.  
> **username_1**: Not under full info and rationality assumption.  In that case, firms know each others' production functions and best-response functions.  In particular, the stronger firm (by virtue of having a lower $MC = p_1$) will know that the weaker firm cannot make a credible threat to reduce price below $p_1$.  Since $p_2 > p_1$, whether the weaker firm moves first or second, it will not be able to capture the market on price.  
> **username_3**: I am having difficulties understanding this last comment. I am not sure what "lower $MC = p_1$" means, since $MC$ is a function of quantity sold, and that is also dependent on $p_2$, so it seems like something is missing here. Also, w.r.t. the last sentence: is capturing the entire market necessary for second mover advantage? Cannot I just be better off compared to the simultaneous equilibrium without capturing the entire market?  
> **username_1**: @username_3 These things all follow from the core assumptions of the classic Bertrand model (e.g., the one typically presented in classrooms and which the OP is most likely to be making reference to). In particular, marginal costs are exogenous and fixed, and it is assumed that consumers will all choose to purchase from the firm that offers the lowest price.  
> **username_3**: But you were responding to username_2's comment which clearly talks about differentiated products. Him/her: "*with differentiated products, price competition will yield a turn-order advantage for the follower even in the presence of full information.*" You: "*Not under full info and rationality assumption.*"  
> **username_1**: @username_3 indeed. And I clearly talked about heterogenous firms in my answer to the OP.  Allowing for differing marginal costs is a simple way of tweaking a model for heterogeneity while still keeping marginal costs exogenous and fixed.  We can move this to chat if you wish, but the gist is that if the weak firm moves first the stronger firm can undercut to claim the full market.  If the strong firm moves first, it anticipates that setting price greater than the weak firm's MC allows the weak firm to undercut, and so it sets price below the weak firm's MC.  
> **username_3**: So you did not address username_2's comment? I am mistaken, and your comment after his is a merely an illusory answer?  
> **username_1**: @username_3 I am struggling to grasp what your angle is, here.  username_2' comment was addressed in the original answer I provided to the OP.  
> **username_3**: I mean, I can quote the two consequential comments again, but I don't understand why it is necessary. username_2: "with differentiated products, price competition will yield a turn-order advantage for the follower even in the presence of full information." You: "Not under full info and rationality assumption." You are claiming that these consequential lines have nothing to do with each other?  
> **username_1**: @username_3, it may serve to post a question to the community seeking clarity on how product differentiation in the context of fixed, exogenous costs is typically expressed by allowing firms marginal costs to differ.  
> **username_3**: Are you being a politician right now? Why can't you admit that you made a mistake in your comments? It is not even in your answer! Did you make your comment in answer to username_2 comment or not?  
> **username_1**: Homogenous firms: $MC_1 = MC_2$.  Heterogenous firms: $MC_1 \neq MC_2$.  
> **username_3**: I tire of this doubletalk.  
> **username_1**: @username_3 evidently not, since you began it and cannot help but to continue it.  There is no controversy here.  I have invited you to discus further to determine where you are being confused.  You elected not to.  Whatever it is you're trying to accomplish here, you are clearly not seeking clarity in good faith.  
> **username_3**: Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/101572/discussion-between-username_3-and-heh).  
> **username_3**: What followed was a somewhat unpleasant conversation in which heh claimed differentiated Bertrand is "breaking the Bertrand framework". The following comment by heh (starting with "Well, to be fair") is also true. (Note "wholly unrelated products")  
> **username_1**: Well, to be fair, I suggested that if @username_3 thinks the OP wanted to contemplate a scenario in which the two firms produced wholly unrelated products facing different demand functions, he can offer an answer to that effect.  Evidently he has elected not to.  

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