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Recursive Multiple-Priors

<!DOCTYPE html> <HTML lang="en"> <HEAD> <TITLE>Recursive Multiple-Priors</TITLE> <meta charset="utf-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css" integrity="sha384-Gn5384xqQ1aoWXA+058RXPxPg6fy4IWvTNh0E263XmFcJlSAwiGgFAW/dAiS6JXm" crossorigin="anonymous"> <link rel="stylesheet" href="/css/font-awesome.min.css"> <!-- <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/fork-awesome@1.2.0/css/fork-awes ome.min.css" integrity="sha256-XoaMnoYC5TH6/+ihMEnospgm0J1PM/nioxbOUdnM8HY=" crossorigin="anonymous">--> <!-- <link rel="stylesheet" href="https://site-assets.fontawesome.com/releases/v6.2.0/css/all.css" />--> <link href="/css/normalnew.css" rel="stylesheet" type="text/css"/> <link href="/css/pushy.css" rel="stylesheet" type="text/css"/> <link rel="icon" type="image.jpg" href="/favicon.ico"> <!--[if lte IE 9]> <script src="/css/html5shiv.min.js"></script> <script src="/css/respond.min.js"></script> <![endif]--> <script type='text/javascript'> var captchaContainer = null; var loadCaptcha = function() { captchaContainer = grecaptcha.render('captcha_container', { 'sitekey' : '6LdQebIaAAAAACSKxvbloyrkQ_q-MqhOAGgD5PQV', 'callback' : function(response) { console.log(response); } }); }; </script> <META NAME="handle" CONTENT="RePEc:roc:rocher:485"><META NAME="description" CONTENT="Downloadable! This paper axiomatizes an intertemporal version of multiple-ptiors utility. A central axiom is dynamic consistency, which leads to a recursive structure for utility, to 'rectangular' sets of priors and to prior-by-prior Bayesian updating as the updating rule for such sets of priors. It is argued that dynamic consitency is intuitive in a wide range of situations and that the model is consistent with a rich set of possibilities for dynamic behavior under ambiguity."> <META NAME="keywords" CONTENT="ambiguity; updating; recursive utility; dynamic consistency; multiple-priors; Bayesian updating; robust decision-making; model uncertainty"> <META NAME="jel_code" CONTENT="D80; D81; D90"> <META NAME="author" CONTENT="Larry G. Epstein & Martin Schneider"> <META NAME="author_shortid" CONTENT="pep2; psc69"> <META NAME="title" CONTENT="Recursive Multiple-Priors"> <META NAME="download" CONTENT="1"> <META NAME="freedownload" CONTENT="1"> <META NAME="date" CONTENT="2001-02-02"> <META NAME="citation_publication_date" CONTENT="2001/08"> <META NAME="citation_authors" content="Larry G. Epstein; Martin Schneider"> <META NAME="citation_title" content="Recursive Multiple-Priors"> <META NAME="citation_abstract" content="This paper axiomatizes an intertemporal version of multiple-ptiors utility. A central axiom is dynamic consistency, which leads to a recursive structure for utility, to 'rectangular' sets of priors and to prior-by-prior Bayesian updating as the updating rule for such sets of priors. It is argued that dynamic consitency is intuitive in a wide range of situations and that the model is consistent with a rich set of possibilities for dynamic behavior under ambiguity."> <META NAME="citation_publisher" content="University of Rochester - Center for Economic Research (RCER)"> <META NAME="citation_journal_title" content="RCER Working Papers"> <META NAME="citation_keywords" content="ambiguity; updating; recursive utility; dynamic consistency; multiple-priors; Bayesian updating; robust decision-making; model uncertainty"> <META NAME="citation_abstract_html_url" content="https://ideas.repec.org/p/roc/rocher/485.html"> <META NAME="citation_abstract_pdf_url" content="https://ideas.repec.org/p/roc/rocher/485.html"> <META NAME="redif-type" content="paper"> <META NAME="citation_type" content="redif-paper"> <META NAME="citation_technical_report_number" content="485"> <META NAME="citation_year" content="2001"> <META NAME="citation_number_of_pages" content="41 pages"> <META NAME="twitter:card" content="summary_large_image"> <META NAME="twitter:site" content="@repec_org"> <META NAME="twitter:title" content="Recursive Multiple-Priors, by Larry G. 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A central axiom is dynamic consistency, which leads to a recursive structure for utility, to 'rectangular' sets of priors an"> <META PROPERTY="og:url" content="https://ideas.repec.org//p/roc/rocher/485.html"> <META PROPERTY="og:image" content="https://ideas.repec.org/cgi-bin/twimage.cgi?p&roc:rocher:485"> <script type="application/ld+json"> { "@context": "http://schema.org", "@graph": [ { "@id": "#periodical", "@type": "Periodical", "name": "RCER Working Papers", "publisher": "University of Rochester - Center for Economic Research (RCER)", "url": "https://ideas.repec.org/s/roc/rocher.html", "requiresSubscription": "false" }, { "@id": "#number", "@type": "PublicationIssue", "datePublished": "2001-08", "issueNumber": "485" }, { "@id": "#article", "@type": "ScholarlyArticle", "name": "Recursive Multiple-Priors", "url": "https://ideas.repec.org//p/roc/rocher/485.html", "description": "This paper axiomatizes an intertemporal version of multiple-ptiors utility. 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xhttp.send(); } function myFunction(xhttp) { document.getElementById("response").innerHTML = xhttp.responseText; } </script><span id="response"></span> </div> </div> <div id="content-block"> <div id="title"> <h1>Recursive Multiple-Priors</h1></div> <div> <ul class="nav nav-pills" id="myTab" role="tablist"> <li class="nav-item"> <a class="nav-link active" id="author-abstract-tab" data-toggle="tab" href="#author-abstract" role="tab" aria-controls="author-abstract" aria-selected="true">Author & abstract</a> </li> <li class="nav-item"> <a class="nav-link download-tab" id="download-tab" data-toggle="tab" href="#download" role="tab" aria-controls="download" aria-selected="false">Download &amp; other version</a> </li> <li class="nav-item"> <a class="nav-link" id="refs-tab" data-toggle="tab" href="#refs" role="tab" aria-controls="refs" aria-selected="false">21 References</a> </li> <li class="nav-item"> <a class="nav-link" id="cites-tab" href="/r/roc/rocher/485.html" role="tab" aria-controls="cites" aria-selected="false">391 Citations</a> </li> <li class="nav-item"> <a class="nav-link" id="mrel-tab" data-toggle="tab" href="#mrel" role="tab" aria-controls="mrel" aria-selected="false">Most related</a> </li> <li class="nav-item"> <a class="nav-link" id="more-tab" data-toggle="tab" href="#more" role="tab" aria-controls="more" aria-selected="false">Related works & more</a> </li> <!-- Placeholder usernotes pill--> <li class="nav-item"> <a class="nav-link" id="correct-tab" data-toggle="tab" href="#correct" role="tab" aria-controls="correct" aria-selected="false">Corrections</a> </li> </ul> <div class="tab-content" id="myTabContent"> <div class="tab-pane fade show active" id="author-abstract" role="tabpanel" aria-labelledby="author-abstract-tab"> <h2>Author</h2> <div id="author-body"> <div id="authortable"> <div id="listed-authors">Listed: <ul id="authorlist"><li class="authorname">Larry G. Epstein<p class="authorcontact"> (<a href="http://www.econ.rochester.edu/Faculty/Epstein.html">University of Rochester</a>)</p></li> <li class="authorname">Martin Schneider<p class="authorcontact"> (UCLA)</p></li> </ul></div><div id="registered-authors"> <a href="https://authors.repec.org/">Registered:</a> <ul id="authorregistered"><li><a href="/e/pep2.html">Larry G. Epstein </A></li> <li><a href="/e/psc69.html">Martin Schneider </A></li> </ul> </div> </div> </div> <h2 style="clear:left">Abstract</h2><div id="abstract-body">This paper axiomatizes an intertemporal version of multiple-ptiors utility. A central axiom is dynamic consistency, which leads to a recursive structure for utility, to 'rectangular' sets of priors and to prior-by-prior Bayesian updating as the updating rule for such sets of priors. It is argued that dynamic consitency is intuitive in a wide range of situations and that the model is consistent with a rich set of possibilities for dynamic behavior under ambiguity.</div> <h2>Suggested Citation</h2> <div id="biblio-body"> <LI class="list-group-item downfree"> Larry G. Epstein & Martin Schneider, 2001. "<B><A HREF="/p/roc/rocher/485.html">Recursive Multiple-Priors</A></B>," <A HREF="/s/roc/rocher.html">RCER Working Papers</A> 485, University of Rochester - Center for Economic Research (RCER). </li> Handle: <i style="word-break:break-all">RePEc:roc:rocher:485</i> <form method="post" action="/cgi-bin/refs.cgi" enctype="multipart/form-data" target="refs" class="form-inline" role="form" style="margin-bottom: 10px;"> <input type="hidden" name="handle" value="RePEc:roc:rocher:485"> <div class="pull-left" style="padding-right: 2px;"> <input type="submit" class="btn btn-default fa" name="ref" value="Export reference &#xf08e;"> as </div> <div class="col-xs-8" style="padding-left: 0;"> <select name="output" size="1"> <option value="0">HTML</option> <option value="0.5">HTML with abstract</option> <option value="1">plain text</option> <option value="1.5">plain text with abstract</option> <option value="2">BibTeX</option> <option value="3">RIS (EndNote, RefMan, ProCite)</option> <option value="4">ReDIF</option> <option value="6">JSON</option> </select> </div> </form></div> </div> <div class="tab-pane fade" id="download" role="tabpanel" aria-labelledby="download-tab"> <h2>Download full text from publisher</h2><p></p> <FORM METHOD=GET ACTION="/cgi-bin/get_doc.pl" target="_blank"> <INPUT TYPE=HIDDEN NAME="urn" VALUE="RePEc:roc:rocher:485"><INPUT TYPE="radio" NAME="url" VALUE="http://rcer.econ.rochester.edu/RCERPAPERS/rcer_485.pdf" checked><B>File URL:</B> <span style="word-break:break-all">http://rcer.econ.rochester.edu/RCERPAPERS/rcer_485.pdf</span><BR><B>File Function:</B> full text<BR><B>Download Restriction:</B> None<BR> <font size="+2" color="red">---><INPUT TYPE="SUBMIT" class="btn fa" VALUE="Download the selected file &#xf08e;" style="color:white;background-color:#2d4e8b;"><---</font></FORM><P><h2>Other versions of this item:</h2> <div class="publishedas"><UL><LI class="list-group-item downgate"> Epstein, Larry G. & Schneider, Martin, 2003. "<B><A HREF="https://ideas.repec.org/a/eee/jetheo/v113y2003i1p1-31.html">Recursive multiple-priors</A></B>," <A HREF="https://ideas.repec.org/s/eee/jetheo.html">Journal of Economic Theory</A>, Elsevier, vol. 113(1), pages 1-31, November. </UL></div> </div> <div class="tab-pane fade" id="refs" role="tabpanel" aria-labelledby="refs-tab"><h2>References listed on IDEAS</h2><form method="post" action="/cgi-bin/refs.cgi" enctype="multipart/form-data" target="refs" class="form-inline" role="form" style="margin-bottom: 10px;"> <input type="hidden" name="handle" value="repec:ecm:emetrp:v:62:y:1994:i:2:p:283-322#repec:eee:jetheo:v:75:y:1997:i:1:p:194-204#repec:roc:rocher:474#repec:ime:imemes:v:19:y:2001:i:s1:p:213-227#repec:ecm:emetrp:v:46:y:1978:i:1:p:185-200#repec:cup:macdyn:v:6:y:2002:i:01:p:85-110_02#repec:aea:aecrev:v:91:y:2001:i:2:p:55-59#repec:cla:levarc:596#repec:eee:jetheo:v:92:y:2000:i:1:p:35-65#repec:hal:journl:hal-00481334#repec:eee:dyncon:v:27:y:2003:i:7:p:1253-1288#repec:eee:mateco:v:18:y:1989:i:2:p:141-153#repec:eee:jetheo:v:59:y:1993:i:1:p:33-49#repec:nbr:nberwo:7490#repec:ecm:emetrp:v:57:y:1989:i:3:p:571-87#repec:fip:fedfpr:y:1999:x:5#repec:wsi:wschap:9789814578127_0005#repec:oup:qjecon:v:75:y:1961:i:4:p:643-669.#repec:hal:journl:hal-00753237#repec:roc:rocher:478#repec:icr:wpmath:17-2001#repec:ags:isfiwp:275405#repec:ecm:emetrp:v:70:y:2002:i:4:p:1403-1443#repec:oup:restud:v:66:y:1999:i:4:p:873-907.#repec:eee:jetheo:v:31:y:1983:i:1:p:133-152#repec:cla:levarc:7662#repec:hal:journl:hal-00753150#repec:cla:levarc:625018000000000009#repec:spr:joecth:v:12:y:1998:i:2:p:293-312#repec:cmu:gsiawp:63#repec:qed:wpaper:699#repec:ecm:emetrp:v:57:y:1989:i:4:p:937-69#repec:red:issued:v:4:y:2001:i:3:p:519-535#repec:wsi:wschap:9789814417358_0012#repec:wsi:wschap:9789814578127_0003#repec:ecm:emetrp:v:71:y:2003:i:6:p:1897-1908#repec:kap:jrisku:v:17:y:1998:i:2:p:87-119#repec:nwu:cmsems:924#repec:clt:sswopa:1127#repec:aea:aecrev:v:91:y:2001:i:2:p:60-66"> <div class="pull-left" style="padding-right: 2px;"> <input type="submit" class="btn btn-default fa" name="ref" value="Export references &#xf08e;"> as </div> <div class="col-xs-8" style="padding-left: 0;"> <select name="output" size="1"> <option value="0">HTML</option> <option value="0.5">HTML with abstract</option> <option value="1">plain text</option> <option value="1.5">plain text with abstract</option> <option value="2">BibTeX</option> <option value="3">RIS (EndNote, RefMan, ProCite)</option> <option value="4">ReDIF</option> <option value="6">JSON</option> </select> </div> </form> <ol class="list-group"><LI class="list-group-item downgate"> Lars Peter Hansen & Thomas J Sargent, 2014. "<B><A HREF="/h/wsi/wschap/9789814578127_0005.html">Robust Control and Model Uncertainty</A></B>," <A HREF="/s/wsi/wschap.html">World Scientific Book Chapters</A>, in: <A HREF="/b/wsi/wsbook/9028.html">UNCERTAINTY WITHIN ECONOMIC MODELS</A>, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd.. <div class="publishedas"><UL> <LI class="list-group-item downgate"> Thomas J. Sargent & LarsPeter Hansen, 2001. "<B><A HREF="/a/aea/aecrev/v91y2001i2p60-66.html">Robust Control and Model Uncertainty</A></B>," <A HREF="/s/aea/aecrev.html">American Economic Review</A>, American Economic Association, vol. 91(2), pages 60-66, May. </UL></div> <LI class="list-group-item downnone"> Zengjing Chen & Larry Epstein, 2002. "<B><A HREF="/a/ecm/emetrp/v70y2002i4p1403-1443.html">Ambiguity, Risk, and Asset Returns in Continuous Time</A></B>," <A HREF="/s/ecm/emetrp.html">Econometrica</A>, Econometric Society, vol. 70(4), pages 1403-1443, July. <div class="otherversion"><UL> <LI class="list-group-item downfree"> Zengjing Chen & Larry G. Epstein, 2000. "<B><A HREF="/p/roc/rocher/474.html">Ambiguity, risk and asset returns in continuous time</A></B>," <A HREF="/s/roc/rocher.html">RCER Working Papers</A> 474, University of Rochester - Center for Economic Research (RCER). </UL></div> <LI class="list-group-item downgate"> Gilboa Itzhak & Schmeidler David, 1993. "<B><A HREF="/a/eee/jetheo/v59y1993i1p33-49.html">Updating Ambiguous Beliefs</A></B>," <A HREF="/s/eee/jetheo.html">Journal of Economic Theory</A>, Elsevier, vol. 59(1), pages 33-49, February. <div class="otherversion"><UL> <LI class="list-group-item downfree"> Itzhak Gilboa & David Schmeidler, 1991. "<B><A HREF="/p/nwu/cmsems/924.html">Updating Ambiguous Beliefs</A></B>," <A HREF="/s/nwu/cmsems.html">Discussion Papers</A> 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science. <LI class="list-group-item downnone"> Itzhak Gilboa & David Scheidler, 1993. "<B><A HREF="/p/hal/journl/hal-00753150.html">Updating Ambiguous Beliefs</A></B>," <A HREF="/s/hal/journl.html">Post-Print</A> hal-00753150, HAL. </UL></div> <LI class="list-group-item downgate"> Ben-Porath, Elchanan & Gilboa, Itzhak & Schmeidler, David, 1997. "<B><A HREF="/a/eee/jetheo/v75y1997i1p194-204.html">On the Measurement of Inequality under Uncertainty</A></B>," <A HREF="/s/eee/jetheo.html">Journal of Economic Theory</A>, Elsevier, vol. 75(1), pages 194-204, July. <div class="otherversion"><UL> <LI class="list-group-item downnone"> Itzhak Gilboa & Elchanan Ben-Porath & David Schmeidler, 1997. 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"<B><A HREF="/p/nbr/nberwo/7490.html">Robust Monetary Policy Under Model Uncertainty in a Small Model of the U.S. Economy</A></B>," <A HREF="/s/nbr/nberwo.html">NBER Working Papers</A> 7490, National Bureau of Economic Research, Inc. </UL></div> <LI class="list-group-item downgate"> Lars Peter Hansen & Thomas J. Sargent, 2001. "<B><A HREF="/a/red/issued/v4y2001i3p519-535.html">Acknowledging Misspecification in Macroeconomic Theory</A></B>," <A HREF="/s/red/issued.html">Review of Economic Dynamics</A>, Elsevier for the Society for Economic Dynamics, vol. 4(3), pages 519-535, July. <LI class="list-group-item downgate"> Epstein, Larry G., 1983. "<B><A HREF="/a/eee/jetheo/v31y1983i1p133-152.html">Stationary cardinal utility and optimal growth under uncertainty</A></B>," <A HREF="/s/eee/jetheo.html">Journal of Economic Theory</A>, Elsevier, vol. 31(1), pages 133-152, October. <LI class="list-group-item downgate"> Kreps, David M & Porteus, Evan L, 1978. "<B><A HREF="/a/ecm/emetrp/v46y1978i1p185-200.html">Temporal Resolution of Uncertainty and Dynamic Choice Theory</A></B>," <A HREF="/s/ecm/emetrp.html">Econometrica</A>, Econometric Society, vol. 46(1), pages 185-200, January. <div class="otherversion"><UL> <LI class="list-group-item downfree"> David M Kreps & Evan L Porteus, 1978. "<B><A HREF="/p/cla/levarc/625018000000000009.html">Temporal Resolution of Uncertainty and Dynamic Choice Theory</A></B>," <A HREF="/s/cla/levarc.html">Levine's Working Paper Archive</A> 625018000000000009, David K. Levine. </UL></div> </ol> <A TARGET="_blank" HREF="http://citec.repec.org/cgi-bin/get_data.pl?h=RePEc:roc:rocher:485&o=all"><B>Full references</B> <i class="fa fa-external-link"></i></A> (including those not matched with items on IDEAS)<P> </div> <div class="tab-pane fade" id="mrel" role="tabpanel" aria-labelledby="mrel-tab"> <h2>Most related items</H2> These are the items that most often cite the same works as this one and are cited by the same works as this one. <ol class="list-group"><LI class="list-group-item downgate"> Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "<B><A HREF="/a/eee/jetheo/v144y2009i3p930-976.html">Recursive smooth ambiguity preferences</A></B>," <A HREF="/s/eee/jetheo.html">Journal of Economic Theory</A>, Elsevier, vol. 144(3), pages 930-976, May. <div class="otherversion"><UL> <LI class="list-group-item downfree"> Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2006. 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"<B><A HREF="/a/eee/dyncon/v90y2018icp30-44.html">Continuous-time smooth ambiguity preferences</A></B>," <A HREF="/s/eee/dyncon.html">Journal of Economic Dynamics and Control</A>, Elsevier, vol. 90(C), pages 30-44. <LI class="list-group-item downgate"> Lorenzo Bastianello & José Heleno Faro, 2023. "<B><A HREF="/a/spr/joecth/v75y2023i4d10.1007_s00199-022-01438-0.html">Choquet expected discounted utility</A></B>," <A HREF="/s/spr/joecth.html">Economic Theory</A>, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1071-1098, May. <LI class="list-group-item downgate"> Ghirardato, Paolo & Marinacci, Massimo, 2002. "<B><A HREF="/a/eee/jetheo/v102y2002i2p251-289.html">Ambiguity Made Precise: A Comparative Foundation</A></B>," <A HREF="/s/eee/jetheo.html">Journal of Economic Theory</A>, Elsevier, vol. 102(2), pages 251-289, February. <LI class="list-group-item downgate"> Zimper, Alexander, 2012. "<B><A HREF="/a/eee/dyncon/v36y2012i4p610-628.html">Asset pricing in a Lucas fruit-tree economy with the best and worst in mind</A></B>," <A HREF="/s/eee/dyncon.html">Journal of Economic Dynamics and Control</A>, Elsevier, vol. 36(4), pages 610-628. </ol> </div> <div class="tab-pane fade" id="more" role="tabpanel" aria-labelledby="more-tab"> <H2> More about this item</H2> <h3>Keywords</h3> <A HREF="/cgi-bin/htsearch2?q=%22ambiguity%22" rel="nofollow">ambiguity</A>; <A HREF="/cgi-bin/htsearch2?q=%22updating%22" rel="nofollow">updating</A>; <A HREF="/cgi-bin/htsearch2?q=%22recursive+utility%22" rel="nofollow">recursive utility</A>; <A HREF="/cgi-bin/htsearch2?q=%22dynamic+consistency%22" rel="nofollow">dynamic consistency</A>; <A HREF="/cgi-bin/htsearch2?q=%22multiple-priors%22" rel="nofollow">multiple-priors</A>; <A HREF="/cgi-bin/htsearch2?q=%22Bayesian+updating%22" rel="nofollow">Bayesian updating</A>; <A HREF="/cgi-bin/htsearch2?q=%22robust+decision-making%22" rel="nofollow">robust decision-making</A>; <A HREF="/cgi-bin/htsearch2?q=%22model+uncertainty%22" rel="nofollow">model uncertainty</A>; <BR><A HREF="/cgi-bin/htsearch2?q=%22ambiguity%22 %22updating%22 %22recursive+utility%22 %22dynamic+consistency%22 %22multiple-priors%22 %22Bayesian+updating%22 %22robust+decision-making%22 %22model+uncertainty%22 " rel="nofollow">All these keywords</A>. <H3><A HREF="/j/">JEL</A> classification:</h3> <UL> <LI><A HREF="/j/D80.html"><B>D80</B></A> - Microeconomics - - Information, Knowledge, and Uncertainty - - - General</LI> <LI><A HREF="/j/D81.html"><B>D81</B></A> - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty</LI> <LI><A HREF="/j/D90.html"><B>D90</B></A> - Microeconomics - - Micro-Based Behavioral Economics - - - General</LI> </UL><P> <h3>Statistics</h3> <A HREF="http://logec.repec.org/scripts/paperstat.pl?h=RePEc:roc:rocher:485">Access and download statistics</A> </div> <!-- placeholder usernotes tab--> <div class="tab-pane fade" id="correct" role="tabpanel" aria-labelledby="correct-tab"> <h2>Corrections</H2> <P>All material on this site has been provided by the respective publishers and authors. 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