Talk:Bertrand competition

Critics

They are quite inconsistent. These models works in an ideal perfect homogeneity market, they are models. To sell the same good in America or Europe, well that's not the same good. — Preceding unsigned comment added by 2.229.153.38 (talk) 11:33, 14 July 2015 (UTC)

Bertrand model concludes that each firm will set P=MC. (So each firm's profit is zero just as in perfect competition.) But if FC > 0, then AC > MC. In this case P=MC will induce to a negative profit since a zero profit is attained at P=AC. So in Bertrand model with FC > 0, each firm should set P=AC, not P=MC.

Prose

Have expanded the first section to have prose explanation. Will continue to alter the rest of the article. Will keep the nice section with best response figures, but maybe add some maths in terms of the payoff function when I have the time.Byronmercury (talk) 21:17, 13 September 2012 (UTC)

Have reorganized some of the material and made into prose. Just need to improve the Bertrand vs Cournot section (references to Kreps and Scheinkman etc.) when I have the time.Byronmercury (talk) 13:49, 19 September 2012 (UTC)

Hi! I am an economic university student and for my assignment I'm tasked to contribute to this page. Can you give me any further advice for improving this article?--Kumar74922 (talk) 11:23, 25 April 2022 (UTC)

A technical issue on best responses

The article correctly sates that:

Firm 1s optimum price (which will be a best response) depends on what it believes firm 2 will set prices at.

However there is a misconception on the continuing lines, namely:

If firm 1 expects firm 2 to price below marginal cost, then its best strategy is to price higher, at marginal cost.

According to Wikipedia a best response is the strategy (or strategies) which produces the most favorable immediate outcome for the current player, taking other players' strategies as given.

Therefore, in the context of Bertrand interaction when firm 1 prices below marginal cost firms' 2 best response will be to not sell any positive amount. However price equal to cost is just oneway of achieving this outcome, any price above the price of firm 1 will be a best response.

The original idea of a best response is a correspondence, i.e. given the action of player i, player j may react in various different ways (as opposed to a function). Consequently the graphs of the best responses are flawed.

This does not affect the main outcome or the general presentation of the article.

--I agree with the above. Even though it does not affect the outcome, I still think it is an important point which may lead to misunderstandings. —Preceding unsigned comment added by 131.111.220.6 (talk) 22:14, 28 April 2008 (UTC)

Yeah, that's related to Edgeworth price cycles. It probably should be dealt with. Cretog8 (talk) 06:56, 19 June 2008 (UTC)

There is another error in the best response functions. Since prices are continuous, when firm 2 is pricing below monopoly profit but above marginal cost, there is no best response. If firm 1 undercuts its rival by a small amount it sells to the whole market and increases profit, but there is no best "small amount." Therefore the best response correspondence for firm 1 to prices of firm 2 is the empty set for prices of firm 2 between the monopoly price and marginal cost (inclusive). 130.56.65.25 (talk) 06:41, 5 June 2009 (UTC)

This is also somewhat technically correct. What really matters is that any price above marginal cost is strictly dominated by any price below it. Basically I think the article is incorporating the language from the version of Bertrand game with differentiated goods where there are best responses. Here there's just the p=marginal cost equilibrium.radek (talk) 07:11, 5 June 2009 (UTC)

Looking at the article again I don't think this is a very serious problem here. To be precise the best response graph should have a shaded area (open set) in the shape of a triangle for firm two pricing below MC, then a jump then a flat line after the monopoly price. I know that below I say we should be precise but here I think the presentation as it is makes it much easier for a non-math, non-econ reader to understand. I'll go dig out some books and see how they deal with it.radek (talk) 07:16, 5 June 2009 (UTC)

A technical issue on best responses (2)

Hi, I am the one that posted the first comment, and I think there is another part that is actually wrong.

The article states: "There are two plausible outcomes: colluding to charge the monopoly price and supplying one half of the market each, or not colluding and charging marginal cost, which is the non-cooperative Nash equilibrium outcome."

However, collusion is Not a solution of the Bertrand problem using a single shot game and the Nash equilibrium (which are the assumptions of the article). Collusion only occurs when there are repeated interaction among firms, if firms have prices as a decision variable then the only pure strategy Nash equilibrium is charging price=marginal cost (assuming equal cost as well)

The issue would be Why is collusion a plausible outcome? there is no rationale provided

It's outside-the-model thinking. Boy, there's a technical term for that, which I can't think of. Essentially, the point is if they could figure out how to collude, they could charge the monopoly price. How they manage to collude is a different question. Some repeated game constructions can get collusion, or there are other ways.Cretog8 (talk) 21:21, 26 June 2008 (UTC)

"Off-the equilibrium path"?radek (talk) 06:56, 5 June 2009 (UTC)

But why would you state that this is one of the two plausible outcomes? If you think outside the model, as you say, you can also consider the possibility of one of the competitors retiring form the game and the other giving him a certain amount to do so. This would have the same result as coordinating and I don't see why you can't consider this result as "plausible". I don't think this has anything to do with the result of Bertrand interaction whatsoever —Preceding unsigned comment added by 87.86.38.62 (talk) 14:29, 30 June 2008 (UTC)

I agree with anon here - we should be precise. And once you start talking about off equilibrium paths almost any outcome is plausible for some definition of "plausible" (that's my Folk Theorem).radek (talk) 07:00, 5 June 2009 (UTC)

Search Cost effect

I changed the search cost effects on equilibrium pricing. Previous statements were not correct. Anyone care to verify? —Preceding unsigned comment added by Qauz (talk • contribs) 23:16, 14 November 2010 (UTC)