Talk:Arrow–Debreu model

Anonymous nature of the markets

I don't know whether my brains is playing tricks on me, but I thought the central feature of Arrow-Debreu model is more to do with the anonymous nature of the markets. Ie Nobody care who supplies chair or steel in the market or who buy the same goods. I didn't see that from the Arrow-Debreu model article. The definition above is from "Toward new paradigm in monetary economics" by Stiglitz

I agree that the description is somewhat narrow and have added an introduction with reference to the economic theory pages on the subject. I agree with the original author(s) that in financial economics the term is typically used with reference to AD-securities.

I would like to hear more on what BIC's are (from the original author(s) or anybody else informed on that subject).--Olejasz 14:18, 9 October 2005 (UTC)[reply]

BICS

BICs are nonsense. You can read some discussion at http://wilmott.com/messageview.cfm?catid=11&threadid=24700, or the official site http://www.4bics.com for the self-published books of "Obi-Wan Yoda". --Ogdred 04:40, 8 March 2006 (UTC)[reply]

Removed the re-addition of the BICs claim. I have looked, and cannot not even find so much as a definition of these anywhere (outside of the author's self-published work). Ogdred 19:50, 2 April 2006 (UTC)[reply]

Well, I will step out, and leave it to some other editor to decide the fate of BICs here. I am sure that the truth lies somewhere in between my offhand dismissal of them as "nonsense", and the author's press release describing them as "the most significant theoretical and practical contribution to derivatives analysis since the Black Scholes analysis or even since financial mathematics pioneer Louis Bachelier."

Honestly, Arrow-Debreu securities are a fundamental concept in finance. It seems strange, to say the least, to spend a third of this article on discussing an unproven concept (indeed, explained by the author himself). Wikipedia is not a place for original research and self-promotion, and the presence of a discussion of BICs in this article is entirely misleading -- anyone coming to this page wanting to know what an Arrow-Debreu security is would think this is a concept that actually has seen some acceptance in the finance community, which as of writing it certainly has not.

This just begs the question -- why not create an article on Basis Instrument Contracts, and take the proselytizing out of this page? --Ogdred 00:59, 4 April 2006 (UTC)[reply]

Obi-Wan: If you checked, there is an article on BICs created April 3rd, 2006. There was an article before that date, I guess it was vandalized by another uninformed "wilmotter" or the like on a vendetta. This is not proselytizing. Anyone who is interested in Arrow Debreu securities would want to know about BICs. It is a "for further study reference" properly qualified as "emerging concept" -[User:Ogdred|Ogdred]] 00:59, 4 April 2006 (UTC)

Hello, My name is Obi-Wan Yoda author of the BICs books. I have been recovering from a PPS condition and that has delayed the effort to bring awareness to BICs.

I see there is an individual by the name of Ogred determined to erase my work from any outside mention. A lot of uninformed individuals have written strange things about the book in the wilmott forum. I thought it was a forum for discussion on quant finance. Between relapses, I tried to register several times to have an opportunity to explain, but was never allowed to post. This individual slandering(Ogdred) the book or BICs on that forum BICs seem to have turned to wikipedia with the same agenda.

My only expllanation so far is that BICs is perceived as unsettling the willmott business. But it need not.

Contrary to Mr./Ms. Ogred, to this date, I have not seen a single individual who has read the material and disputed a single claim in it. Lack of extensiveefforts to develop awareness is simply due to lack of resources

I have put this post on watch and will respond to all courteous exchanges. If Mr./Ms. Ogred, would want to receive a copy of the book and engage here in a thoughtful and unbiased discussion here and on wilmott(after asking for my being allowed to speak there too), I'll gladly send him a copy free of charge.

Obi-Wan Yoda

Note:

Definition: A Basis Instrument Contract or BIC is a representative derivative contract that is an element of a set of classes of equivalence of contracts. Together, these contracts uniquely enable the static replication of any derivatives contract in a multi-period trading market without any model assumption.

Hence, BICs are derivatives contracts of reference through which any derivatives contract, however complex or illiquid can be decomposed. This absence of model assumption is the critical differentiating factor with the Black Scholes Merton replication method by continuous delta hedging or more generally, the derivatives hedging approach by greeks hedging. The characteristic features of BICs and the rationale for those are as follows:

1) A Basis Instrument Contract or BIC identifies two parties: one or more buyer(s) named A and one or more seller(s) named B.

2) The definition of each BIC comprises three dates:

The contract agreement date t0, which is the date at which the binding rights and obligations on both sides of the contract are agreed upon.

The premium payment date ti , with ,which is the date at which the party identified in the contract as the buyer A complies with its part of the agreement by paying the seller B an amount in units of basis currency known as the premium of the contract or the premium payment amount. The premium payment amount may be expressed as a function of the values of the fluctuating variables between time t0 and time ti

The contract expiry date, also known as maturity or payout payment date tj, with tj > ti = ti+1, is the date at which the party(ies) identified in the contract as the seller(s) B complies with its (their) part of the agreement by paying the buyer(s) A an amount in units of basis currency as determined as the payout of the individual BIC.

3) A BIC admits notional amounts that may be functions of the realized values of underlyings and related derivatives contracts whose value shall be known by the premium payment date ti at the latest. With their pre-agreement features, BICs may be somewhat reminiscent of Forward Rate Agreements (FRAs) and Forwards. However, unlike FRAs or forwards, we do not know in general the numerical value of the notional of a BIC at contract agreement time.

The payout format of BICs at each payout payment date defined in what we call the BIC set format. Bics

Predictably enough, Mr./Ms. Ogred had no interest in the truth or objectivity. No intellectual curiosity as all the other Wilmott special interests panderers...

Clueless Slander is so much fun ... it seems. Bics

BICs again

It's been a long while, and there seems to be no useful addition on BICs. There's no Wikipedia page or reference within this article. So I'm pulling BICs out.Cretog8 (talk) 13:05, 25 June 2008 (UTC)[reply]

Model

Please, could someone write the model? Lbertolotti —Preceding unsigned comment added by Lbertolotti (talk • contribs) 23:56, 18 February 2009 (UTC)[reply]

Resolved

Lbertolotti (talk) 20:09, 11 June 2024 (UTC)[reply]

Uniqueness

An IP editor wrote the following Kiefer.Wolfowitz 09:24, 14 April 2012 (UTC):[reply]

"there can be any countable number of equilibria in general equilibrium models in which utility functions are strongly convex and twice continuously differentiable. This is not an external reference but the fact that the claim is false is correctly stated in the linked article. A proposed final edit would be to delete everything in the preceding sentence from the semi colon on."

I did not find a discussion of strong concavity in the cited article. I thought that I took the uniqueness result from Mas-Colell's monograph. Kiefer.Wolfowitz 09:29, 14 April 2012 (UTC)[reply]

In fact, the conditions for uniqueness were from a reliable source, which cited Smale's foundations of general equilibrium theory. I believe that the IP editor may have misunderstood something. Kiefer.Wolfowitz 13:49, 14 April 2012 (UTC)[reply]

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Merger proposal

I propose that Arrow–Debreu model be merged into Complete market. The model is but an expression of the complete-market notion. It all comes down to the same exact ideas, expressed differently. Wikipedia users would benefit from having the model as a (large) section of the "complete markets" article. What do others think? (Note: Discussing the merger will be done, according to the rules, in the target article's talk page, and specifically here). Take care, all. -The Gnome (talk) 09:56, 4 April 2018 (UTC)[reply]

Requested move 4 July 2018

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: no clear consensus to move the page to any particular title at this time, per the discussion below. Dekimasuよ! 06:27, 26 July 2018 (UTC)[reply]

Arrow–Debreu model → Arrow-Debreu-McKenzie model – It has become clear in recent years that McKenzie deserves just as much credit as Arrow and Debreu do for proving the existence of efficient general equilibria (if not more credit, given that McKenzie's proof appeared in Econometrica BEFORE Arrow and Debreu's). Moreover, we now know from archival research that Debreu, as one of the referees of McKenzie's paper, tried to delay its publication, and withheld knowledge of McKenzie's paper from Arrow. This matter has been exhaustively researched by Roy Weintraub at Duke; see his paper "Retrospectives . . ." in Journal of Economic Perspectives, and his book with Princeton University Press, FINDING EQUILIBRIUM. Further, the proof is already frequently referred to using the names of all three authors, and this class of models as the "Arrow-Debreu-McKenzie model" (or, less frequently, the "McKenzie-Arrow-Debreu model"). 32.216.57.128 (talk) 20:32, 4 July 2018 (UTC)--Relisting. Dekimasuよ! 16:36, 12 July 2018 (UTC) --Relisting. Anarchyte (work | talk) 12:05, 22 July 2018 (UTC)[reply]

Iff this rationale is valid, then move to Arrow–Debreu–McKenzie model (with en dashes) per MOS:DASH. The nominator has mistakenly swapped the correct en dash for an incorrect hyphen. I have no idea about the merits of the underlying rationale; assertion that sources frequently use all three names isn't citing the sources to prove it. — SMcCandlish ☏ ¢ 😼 05:31, 5 July 2018 (UTC)[reply]
Support with en dashes like in this source and this. Dicklyon (talk) 06:36, 5 July 2018 (UTC)[reply]
Oppose barring other evidence. A check of Google Scholar of 2008 forward (that is, excluding old sources) shows that Arrow-Debreu-McKenzie has a mere 300 hits, some of which are weak hits even on the first page, while Arrow-Debreu has 15,100 hits, many of which look extremely high quality and relevant. This may be unfair to McKenzie, but it does not appear scholarly use has shifted on calling this plain Arrow-Debreu. SnowFire (talk) 13:19, 11 July 2018 (UTC)[reply]
Neutral, but please fix the incorrect hyphens (-) to en-dashes (–) per MOS:DASH and other articles. Paintspot Infez (talk) 01:33, 22 July 2018 (UTC)[reply]

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

uniqueness

The claim that (strict) concavity of utility functions yields uniqueness of equilibrium is ridiculous. 2603:8001:7402:7D0C:3441:449:CDB5:5402 (talk) 15:29, 24 January 2023 (UTC)[reply]

strongly concave and twice continuously differentiable pony in a strange land (talk) 18:31, 25 January 2023 (UTC)[reply]

Sorry, I checked again and yes, the proper statement is that equilibrium is unique generically, but not always. It is fixed (with proper reference). pony in a strange land (talk) 18:47, 25 January 2023 (UTC)[reply]

I looked up your reference and of course it says no such thing (not surprisingly since it is a completely false assertion). My guess is that you are referring to the well-known generic local (!) uniqueness result, emanating with Debreu (1970 as I recall). Local uniqueness means that equilibria are isolated, so that they are finite in number, but there could be, say, a 1001 of them (it's generically an odd number). This is sometimes called determinacy, as opposed to there being a continuum of equilibria (indeterminacy), which is the non-generic thing (at least in finite-dimensional models). Strong convexity, a rather mild assumption, doesn't have much to do with all this. It so happens that I am an expert in the field, but any well-educated graduate student ought to know that you can't get uniqueness of equilibrium so cheaply. 2603:8001:7402:7D0C:C55B:B017:D5CD:5584 (talk) 06:34, 7 February 2023 (UTC)[reply]

I see that you actually wrote "strongly concave," but that is even weirder, since that would be a cardinal, not an ordinal property. It's not very difficult to draw an Edgeworth box with say three equilibria where the preferences are as nice as you might wish, as was well-known to, say, Marshall. 2603:8001:7402:7D0C:C55B:B017:D5CD:5584 (talk) 06:43, 7 February 2023 (UTC)[reply]

A more interesting and pertinent question, which I didn't notice you addressing, is why is there a separate entry for the Arrow-Debreu model, as opposed to the general entry for general equilibrium theory. Answers to this might involve the assumption in the A-D model of a given number of producers (as well as consumers, as well as goods), as opposed to, say, the McKenzie model, with a variable number of producers. One might also contrast these finiteness assumptions against OLG models (infinite number of goods and consumers) or Aumann models (a continuum of consumers) or Mas-Colell type product differentiation models (an infinite number of goods). It turns out to make a difference, e.g. the first theorem of welfare economics can fail with an infinite number of goods or consumers. 2603:8001:7402:7D0C:C55B:B017:D5CD:5584 (talk) 07:03, 7 February 2023 (UTC)[reply]

It's not usually in my character to work for free, but I am worried that the younger generation has not only made few advances in economic theory in this millenium but that it has also forgotten what was formerly well known. It's not really their fault I suppose since it is now much easier to concentrate on data. I fear that all this misinformation on the internet will corrupt impressionable minds. Getting it right on this site may mean that ChatGPT learns what is correct, which could prove important in the future (I tested and it was woefully ignorant of economic theory: I wonder where it got its ideas; perhaps it does not have access to the literature, which is often hidden behind paywalls). 2603:8001:7402:7D0C:112F:EF32:D428:33EF (talk) 18:26, 7 February 2023 (UTC)[reply]

I see that you are a mathematician, as well as of course a pony, though perhaps not an economist (do you then know about ordinal vs cardinal?). The generic dimension zero of the equilibrium set is a straightfoward application of the transversality theorem in differential topology (so there is some truth to the stated need for differentiablity of demand) and the finiteness part comes from a side argument where though price space is not generally compact the demands are proper mappings over that domain. This then is the generic local uniqueness of the A-D model (not necessarily true in infinite dimensional models; see my previous aside on what makes an A_D model what it is) To get true uniqueness of equilibrium you usually look at the Poincare-Hopf index theorem. which fits the situation pretty well and then make some sort of very strong assumption forcing each zero to have index unity, in which case there can be but one (unity being the Euler characteristic of the price domain). The classical example of a strong assumption is the assumption (Dierker) that all the equilibrium are locally stable and hence have the requisite index one, so that there can then be but one equilibrium. 2603:8001:7402:7D0C:112F:EF32:D428:33EF (talk) 18:55, 7 February 2023 (UTC)[reply]

Perhaps you are getting strong concavity from consideration of what it takes to get a unique maximum to the optimization of a real-valued function, but here we are dealing with an equilibrium problem in multiple dimensions, not a maximization one (though rationality/maximization for the economic agent (consumer, producer) and then equilibrium for the entire economy are indeed the overriding principles of neoclassical economics). 2603:8001:7402:7D0C:112F:EF32:D428:33EF (talk) 19:13, 7 February 2023 (UTC)[reply]

Bothering to scroll up I see that the reference to uniqueness was already called into question in 2012! Of course, I am not calling into question such claims, I am telling you they are utterly wrong (that is no minor adjustment is going to fix up what is so very far from the truth). Luckily, I have the impression that no one has paid any attention to this site in a long time, else the "wisdom of the masses" would have prevailed long ago. 2603:8001:7402:7D0C:112F:EF32:D428:33EF (talk) 20:11, 7 February 2023 (UTC)[reply]

With a little effort one can locate many other problems with this exposition. While I agree that convexity is typically used in employing the Arrow-Debreu model, I wouldn't say it was necessary and certainly the mathematical statement that fixed point theorems fail without convexity is untrue. Let me point out the Eilenberg-Montgomery fixed point theorem which uses contractibility, a weaker notion than convexity and was employed by Debreu in his 1952 PNAS article. There are plenty of other dubious things in the article, though perhaps nothing as glaring as the statement about uniqueness. 2603:8001:7402:7D0C:112F:EF32:D428:33EF (talk) 03:24, 8 February 2023 (UTC)[reply]

query

I fail to understand why you do not react to what I have (patiently) explained above 2603:8001:7402:7D0C:3545:DFA7:7016:47B5 (talk) 03:04, 11 February 2023 (UTC)[reply]

My apologies. I don't have the talk page on my watch list to reduce mental load.

I submit that I am not well-informed on the classical literature in mathematical economics, and never took any formal course in economics. I simply worked through (Starr, 2011), and he devoted just one section to uniqueness issues, and I supplemented with reading some papers by Debreu and Smale. I believe you are far more qualified to write about it than I am.

In the interest of posterity and public education, I think it would be good for you to write something up, preferably here: https://wiki.riteme.site/wiki/General_equilibrium_theory#Uniqueness which currently has no inline citations or mention of the classical results you mentioned.

Wikipedia articles are quite widely used, so it's a very efficient way to impart your knowledge efficiently on the commons. For example, in the past 2 months, the AD model got 70 views per day, which isn't that much compared to classical books like Andreu Mas-Colell that students consult everyday, but it's quite a lot when compared to other online sources, like educative blogposts.

https://pageviews.wmcloud.org/?project=wiki.riteme.site&platform=all-access&agent=user&redirects=0&start=2023-01-11&end=2023-03-03&pages=General_equilibrium_theory%7CArrow%E2%80%93Debreu_model pony in a strange land (talk) 20:51, 4 March 2023 (UTC)[reply]