Talk:Bertrand paradox (economics)

two Bertrand paradoxes
Hi, please consider the 2 entries in wikipedia (I am refering to the Bertrand's Paradox entry and the Bertrand Paradox entry). Are they refering to the same paradox? Or did Bertrand came up with 2 different paradoxes. I search for Bertrand's paradox on google and it appears that the paradox on probability is the more common find: that is what is the probability that a randomly picked chord of a circle will have a length greater than the side of an equilateral triangle inscribed in the circle.

Translation from de WP
Here is a start at translating the material from the German Wikipedia entry (as requested on the page for BertrandParadox). Feel free to add to this - this is just the first paragraph, but the text is not long.

Bertrand model of price competition

In a market with a homogeneous good (e.g. water), there are two suppliers, A and B (duopoly). These suppliers compete solely through the simultaneous announcement of their prices. Al consumers buy only from the supplier with the lowest price. This suplier then satisfy the entire demand. If both suppliers offer the same price, they share the market, i.e. 50% of the consumers go to supplier A, with the rest going to supplier B. The fixed costs are negligible.

Claim

There exists a unique "Nash equlibrium", in which the following holds: Price of supplier A = Price of supplier B = marginal cost.

Proof

(sorry, it is not marginal cost. It is smallest possible cost larger than zero-profit). Assume that Price of A = Price of B at any price greater than no profit.

Now, for either company, decrease of price will increase profit for that company. However, the other company will do likewise.

Neither company will reduce to the zero-profit level, because that actually decreases profit rather than increases it.

So, the price will decrease to zero-profit plus epsilon. Unlike pure mathematics, where epsilon is arbratrarly small, in economics, epsilon is finite.

The limits of epsilon involve smallest available monetary unit and granularity of measurements, and must be calculated separately for every such situation.

Wikification
I've wikified the article and removed the wikify tag at the top. Also cleaned up the translation a bit (thanks for the translation in the first place, by the way!). Ryan McDaniel 23:24, 22 February 2006 (UTC)

Definition of oligopoly
hello - the definition of oligopoly in this artile differs from the (in my opinion correct) definition given in the oligopoly article:

"An oligopoly is a market form in which a market or industry is dominated by a small number of sellers (oligopolists). The word is derived from the Greek for few sellers. Some industries which are oligopolies are referred to as the "Big Three" or the "Big Four." Because there are few participants in this type of market, each oligopolist is aware of the actions of the others. Oligopolistic markets are characterised by interactivity. The decisions of one firm influence, and are influenced by the decisions of other firms. Strategic planning by oligopolists always involves taking into account the likely responses of the other market participants. This causes oligopolistic markets and industries to be at the highest risk for collusion."

you mean "pure collusion" or "collusive oligopoly" I think

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84.68.169.155 18:57, 30 June 2007 (UTC)

Merge with Bertrand competition
The result was stale, inclusive, default to keep separate from Bertrand competition. nb. since this is clearly not controversial anyone who feels strongly enough to pursue the merge proposal should consider being bold and doing it, per the process described at WP:Merge. -- Debate   木  09:54, 16 July 2008 (UTC)

Seems to me this covers exactly the same material as the Bertrand competition page. Good candidate for a merger i think. adcock1689 19:43, 15 May 2007


 * Long time no talk about this merge proposal. Any new thoughts? Cretog8 (talk) 02:46, 16 June 2008 (UTC)

Dr. De Francesco's comment on this article
Dr. De Francesco has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"1. Nowhere in the entry is it mentioned that the Bertrand paradox rests, among other things, on the constancy of marginal cost. For instance, instead of "Suppose two firms […], each with the same cost of production and distribution", one should write "[… ] each with the same constant marginal cost".

2. The sentence "It follows that demand is infinitely price-elastic" is a bit ambiguous. A more clear statement would be "it follows that the demand forthcoming to one firm is infinitely elastic to its own price at a price equal to the rival's price."

3. Some hint should be given as to why, under "capacity constraints", the Bertrand paradox does not necessarily arise. It should be stated that, under capacity constraints, the outcome of the strategic interaction on prices might not be the competitive outcome in which total demand and total industry supply are equal. A classic reference on this topic is Vives X. (1986). Incidentally, it would be appropriate to consider under the heading “Capacity constraints” also the case of increasing marginal cost (see point 4 below).

4. The treatment of “Integer pricing” is misleading. As it stands, the main text is (implicitly) referring to the implications of integer pricing when there are no capacity constraints and marginal cost is constant (and identical across the firms), i.e., the Bertrand context. In such a contex, discrete pricing in a duopoly just implies that an additional Nash equilibrium exists in which both prices are one cent above marginal cost (Harrington J. E., 1989). But this is a minor implication of integer pricing and is not the focus of the reference given in the text (Dixon, 1993). Dixon is in fact concerned with the case of increasing marginal cost, where a pure strategy equilibrium does not exist so long as the price is viewed as a continuous choice variable. As proved by Dixon, things are much different under discrete pricing since pure strategy equilibria – and an array of such equilibria, which might or might not include competitive pricing - may then exist.

5. Some hint should be given to why competitive pricing need not emerge under “repeated price competition”. The Folk Theorem should be mentioned in this connection.

6. The argument in the paragraph “More money for higher price” is obscure.

7. The last paragraph seems to refer to “Collusion” rather than “Oligopoly”. Also, the argument is unclear and potentially overlapping with the argument for “Dynamic competition”.

References

Dixon H. D. (1993), "Integer pricing and Bertrand-Edgeworth oligopoly with strictly convex costs: is it worth more than a penny?, Bulletin of Economic Research 45, pp. 257-268.

Harrington J. E. (1989), “A re-evaluation of perfect competition as the solution to the Bertrand price game”, Mathematical Social Sciences 17, pp. 315-328

Vives X. (1986), “Rationing rules and Bertrand-Edgeworth equilibria in large markets”, Economics Letters, Vol. 21, No. 2, pp. 113-116."

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. De Francesco has expertise on the topic of this article, since he has published relevant scholarly research:


 * Reference : Massimo A. De Francesco, 2004. "Pricing and matching under duopoly with imperfect buyer mobility," Department of Economics University of Siena 439, Department of Economics, University of Siena.

ExpertIdeasBot (talk) 18:44, 26 July 2016 (UTC)

Dr. Sunde's comment on this article
Dr. Sunde has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"Typo: Some reasons the Bertrand paradox does not strictly apply:"

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Sunde has expertise on the topic of this article, since he has published relevant scholarly research:


 * Reference : Rudi Stracke & Wolfgang Hochtl & Rudolf Kerschbamer & Uwe Sunde, 2014. "Optimal prizes in dynamic elimination contests: Theory and experimental evidence," Working Papers 2014-08, Faculty of Economics and Statistics, University of Innsbruck.

ExpertIdeasBot (talk) 16:41, 2 August 2016 (UTC)