Reference Work Entry

Encyclopedia of Algorithms

pp 1-99

# Nash Equilibria and Dominant Strategies in Routing

2005; Wang, Li, Chu
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Truthful; Nash; BB </p></section></body></html><!--4.0--> <!DOCTYPE html SYSTEM "about:legacy-compat"> <html xmlns="http://www.w3.org/1999/xhtml" lang=""><head><title/><meta charset="utf-8"/><script type="text/x-mathjax-config"> MathJax.Hub.Config({ /* load MathML extension */ extensions: ["mml2jax.js"], /* configure input and output */ jax: ["input/TeX", "input/MathML", "output/HTML-CSS"], /* align display equations to the left */ displayAlign: "left", /* set zoom trigger */ menuSettings: { zoom: "Click" }, /* configuration of the tex2jax preprocessor: - set delimiters for inline and display equations - preview while equations are processed is "TeX" - allow \ to represent a literal dollar sign */ tex2jax: { inlineMath: [ ["\\(","\"] ], displayMath: [ ['$$','$$'], ["\$","\$"] ], preview: ["TeX"], processEscapes: true }, /* configuration of the mml2jax preprocessor: - preview while equations are processed is "MathML" */ mml2jax: { preview: ["MathML"] }, /* configuration of the HTML-CSS output processor: - available fonts are STIX and TeX - preferred font is STIX - use TeX as web-based font if none of the above is available on the user's computer - use TeX font for image fallback mode */ "HTML-CSS": { availableFonts: ["STIX","TeX"], preferredFont: ["STIX"], webFont: ["TeX"], imageFont: ["TeX"], styles: { '.MathJax_Display': { "margin": 0 } } }, TeX: { TagSide: "right", Macros: { upalpha: '{\\unicode{x03B1}}', upbeta: '{\\unicode{x03B2}}', upgamma: '{\\unicode{x03B3}}', updelta: '{\\unicode{x03B4}}', upepsilon: '{\\unicode{x03F5}}', upvarepsilon: '{\\unicode{x03B5}}', upzeta: '{\\unicode{x03B6}}', upeta: '{\\unicode{x03B7}}', uptheta: '{\\unicode{x03B8}}', upvartheta: '{\\unicode{x03D1}}', upiota: '{\\unicode{x03B9}}', upkappa: '{\\unicode{x03BA}}', uplambda: '{\\unicode{x03BB}}', upmu: '{\\unicode{x03BC}}', upnu: '{\\unicode{x03BD}}', upxi: '{\\unicode{x03BE}}', upomicron: '{\\unicode{x03BF}}', uppi: '{\\unicode{x03C0}}', uprho: '{\\unicode{x03C1}}', upsigma: '{\\unicode{x03C3}}', uptau: '{\\unicode{x03C4}}', upupsilon: '{\\unicode{x03C5}}', upphi: '{\\unicode{x03C6}}', upchi: '{\\unicode{x03C7}}', uppsi: '{\\unicode{x03C8}}', upomega: '{\\unicode{x03C9}}', Upalpha: '{\\unicode{x0391}}', Upbeta: '{\\unicode{x0392}}', Upgamma: '{\\unicode{x0393}}', Updelta: '{\\unicode{x0394}}', Upepsilon: '{\\unicode{x0395}}', Upzeta: '{\\unicode{x0396}}', Upeta: '{\\unicode{x0397}}', Uptheta: '{\\unicode{x0398}}', Upvartheta: '{\\unicode{x03F4}}', Upiota: '{\\unicode{x0399}}', Upkappa: '{\\unicode{x039A}}', Uplambda: '{\\unicode{x039B}}', Upmu: '{\\unicode{x039C}}', Upnu: '{\\unicode{x039D}}', Upxi: '{\\unicode{x039E}}', Upomicron: '{\\unicode{x039F}}', Uppi: '{\\unicode{x03A0}}', Uprho: '{\\unicode{x03A1}}', Upsigma: '{\\unicode{x03A3}}', Uptau: '{\\unicode{x03A4}}', Upupsilon: '{\\unicode{x03A5}}', Upphi: '{\\unicode{x03A6}}', Upchi: '{\\unicode{x03A7}}', Uppsi: '{\\unicode{x03A8}}', Upomega: '{\\unicode{x03A9}}', permille: '{\\unicode{x2030}}', hfill: '{\\enspace\\enspace}', enskip: '{\\enspace}', copyright: '{\\unicode{x00A9}}', dag: '{\\unicode{x2020}}', ddag: '{\\unicode{x2021}}', ointop: '{\\unicode{0x222E}}', P: '{\\unicode{0x00B6}}', textregistered: '{\\unicode{0x00AE}}', lhook: '{\\hookrightarrow}', rhook: '{\\hookleftarrow}', fancyscript: ['{\\scr #1}',1], varvec: ['\\pmb{#1}',1], parbox: ['\\mbox{#2}',2], AA: '{\\unicode{x00C5}}' } }, /* configuration of the math menu: - allow the user to select what font to use */ MathMenu: { showFontMenu: true } }); 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data.math = data.math.replace(/\\text{\\scriptsize{([^}]+)}}/g, "\\scriptscriptstyle{\\text{$1}}"); data.math = data.math.replace(/\\text{\\tiny{([^}]+)}}/g, "\\scriptscriptstyle{\\text{$1}}"); data.math = data.math.replace(/\\mathop ([^{]+?)\\limits/g, "\\mathop{$1}\\limits"); data.math = data.math.replace(/\$big|Big|bigg|Bigg) *{([^}]+)}/g, "\\1 2"); data.math = data.math.replace(/\\textsc *{([^}]+)}/g, "{\\rm ~#~1~#~}"); data.math = data.math.replace(/\\upvarphi/g, "\\varphi"); var reg = new RegExp("~#~(.*?)~#~", "g"); var m; while (m = reg.exec(data.math)) { var result = ""; for (var index=0; index != m[1].length; index++) { var char = m[1].substr(index, 1); if (char.match(/[a-z]/)) { result += "{\\small "+ char.toUpperCase() + "}"; } else { result += char; } } data.math = data.math.replace(/~#~.*?~#~/, result); } }); } ); </script><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML-full.js"> </script></head><body><section id="Sec2_254" class="Section1 RenderAsSection1"><h2 class="Heading">Problem Definition</h2><p class="Para">This problem is concerned with the multicast routing and cost sharing in a selfish network composed of relay terminals and receivers. This problem is motivated by the recent observation that the selfish behavior of the network could largely degraded existing system performance, even dysfunction. The work of Wang, Li and Chu [<span class="CitationRef"><a href="#CR7_254">7</a></span>] first presented some negative results of the strategyproof mechanism in multicast routing and sharing, and then proposed a new solution based on Nash Equilibrium that could greatly improve the performance.</p><p class="Para">Wang, Li and Chu modeled a network by a link weighted graph <span class="InlineEquation" id="IEq1_254">\( { G=(V,E,\textbf{c}) }$</span>, where <em class="EmphasisTypeItalic ">V</em> is the set of all nodes and <span class="InlineEquation" id="IEq2_254">${ \textbf{c} }$</span> is the cost vector of the set <em class="EmphasisTypeItalic ">E</em> of links. For a multicast session, let <em class="EmphasisTypeItalic ">Q</em> denote the set of all receivers. In game theoretical networking literatures, usually there are t ...</p></section></body></html><!--4.0--> </div> <div class="excerpt-message"></div> </div> <div id="kb-nav--aside" class="col-aside" role="complementary"> <div class="cover"> <div class="look-inside cover-image-animate"> <div id="reader-overlay"> <div id="reader-page-template"> <div id="page-%P"> <div class="page-number"> Page %P </div> <div class="pdf-page" id="page-img-container-%ID"> <img id="pdf-page-image-%ID" class="pdf-image" src="/static/1.738/images/pdf-preview/spacer.gif" alt="Loading..." width="%W" style="width:%Wpx;" data-loaded="false"/> </div> </div> </div> <div class="reader-position"> <div id="reader"> <div id="reader-buttons"> <a href="#close" id="pdf-close" class="btn btn-close right"> Close </a> <a href="#close" id="toggletext" class="btn" title="Toggle plain text"> Plain text </a> </div> <div id="viewer" class="show-pdf"> <div id="scroller"></div> </div> <div class="top-shadow"></div> <div 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xmlns:meta="http://www.springer.com/app/meta" xmlns:epub="http://www.idpf.org/2007/ops" class="FulltextWrapper"><aside class="Bibliography" id="Bib1_254"><h3 class="Heading">Recommended Reading</h3><ol class="BibliographyWrapper"><li class="Citation"><div class="CitationNumber">1.</div><div class="CitationContent" id="CR1_254">Feigenbaum, J., Papadimitriou, C.H., Shenker, S.: Sharing the cost of multicast transmissions. J. Comput. Syst. Sci. <strong class="EmphasisTypeBold ">63</strong>, 21–41 (2001)<span class="Occurrences"><span class="Occurrence OccurrenceZLBID"><a href="http://www.emis.de/MATH-item?$0996.68026"><span><span>MATH</span></span></a></span><span class="Occurrence OccurrenceDOI"><a href="http://dx.doi.org/10.1006/jcss.2001.1754"><span><span>CrossRef</span></span></a></span><span class="Occurrence OccurrenceAMSID"><a href="http://www.ams.org/mathscinet-getitem?mr=1868835"><span><span>MathSciNet</span></span></a></span></span></div></li><li class="Citation"><div class="CitationNumber">2.</div><div class="CitationContent" id="CR2_254">Kao, M.-Y., Li, X.-Y., Wang, W.: Towards truthful mechanisms for binary demand games: A general framework. In: ACM EC, pp. 213–222, Vancouver, Canada (2005)</div></li><li class="Citation"><div class="CitationNumber">3.</div><div class="CitationContent" id="CR3_254">Herzog, S., Shenker, S., Estrin, D.: Sharing the “cost” of multicast trees: an axiomatic analysis. IEEE/ACM Trans. Netw. <strong class="EmphasisTypeBold ">5</strong>, 847–860 (1997)<span class="Occurrences"><span class="Occurrence OccurrenceDOI"><a href="http://dx.doi.org/10.1109/90.650144"><span><span>CrossRef</span></span></a></span></span></div></li><li class="Citation"><div class="CitationNumber">4.</div><div class="CitationContent" id="CR4_254">Moulin, H., Shenker, S.: Strategyproof sharing of submodular costs: budget balance versus efficiency. Econ. Theory <strong class="EmphasisTypeBold ">18</strong>, 511–533 (2001)<span class="Occurrences"><span class="Occurrence OccurrenceZLBID"><a href="http://www.emis.de/MATH-item?\$1087.91509"><span><span>MATH</span></span></a></span><span class="Occurrence OccurrenceDOI"><a href="http://dx.doi.org/10.1007/PL00004200"><span><span>CrossRef</span></span></a></span><span class="Occurrence OccurrenceAMSID"><a href="http://www.ams.org/mathscinet-getitem?mr=1877085"><span><span>MathSciNet</span></span></a></span></span></div></li><li class="Citation"><div class="CitationNumber">5.</div><div class="CitationContent" id="CR5_254">Wang, W., Li, X.-Y., Sun, Z., Wang, Y.: Design multicast protocols for non-cooperative networks. In: Proceedings of the 24th IEEE INFOCOM. vol. 3, pp. 1596–1607, Miami, USA (2005)</div></li><li class="Citation"><div class="CitationNumber">6.</div><div class="CitationContent" id="CR6_254">Wang, W., Li, X.-Y., Wang, Y.: Truthful multicast in selfish wireless networks. In: Proceedings of the 10th ACM MOBICOM, pp. 245–259, Philadelphia, USA (2004)</div></li><li class="Citation"><div class="CitationNumber">7.</div><div class="CitationContent" id="CR7_254">Wang, W., Li, X.-Y., Chu, X.: Nash equilibria, dominant strategies in routing. In: Workshop for Internet and Network Economics (WINE). Lecture Notes in Computer Science, vol. 3828, pp 979–988. Springer, Hong Kong, China (2005)</div></li></ol></aside></div> </div> </div> </div> </div> <div id="abstract-about" class="expander expander-open"> <div class="expander-title"> <div class="heading"> <button> <h2>About this Reference Work Entry</h2> </button> </div> </div> <div class="expander-content"> <div class="expander-content-inner"> <div class="summary"> <dl> <dt>Title</dt> <dd id="abstract-about-title">Nash Equilibria and Dominant Strategies in Routing</dd> <dt>Reference Work Title</dt> <dd id="abstract-about-publication"> <a href="/book/10.1007/978-0-387-30162-4">Encyclopedia of Algorithms</a> </dd> <dt id="dt-abstract-about-book-chapter-page-ranges">Pages</dt> <dd id="abstract-about-book-chapter-page-ranges">pp 1-99</dd> <dt id="dt-abstract-about-book-chapter-copyright-year">Copyright</dt> <dd id="abstract-about-book-chapter-copyright-year">2008</dd> <dt>DOI</dt> <dd id="abstract-about-book-chapter-doi" class="doi">10.1007/978-0-387-30162-4_254</dd> <dt id="dt-abstract-about-book-print-isbn">Print ISBN</dt> <dd id="abstract-about-book-print-isbn">978-0-387-30770-1</dd> <dt id="dt-abstract-about-book-online-isbn">Online ISBN</dt> <dd id="abstract-about-book-online-isbn">978-0-387-30162-4</dd> <dt id="dt-abstract-about-publisher">Publisher</dt> <dd id="abstract-about-publisher">Springer US</dd> <dt id="dt-abstract-about-book-copyright-holder">Copyright Holder</dt> <dd id="abstract-about-book-copyright-holder">Springer-Verlag</dd> <dt>Additional Links</dt> <dd id="abstract-about-additional-links"> <ul> <li> <a class="external" href="http://www.springer.com/978-0-387-30770-1?wt_mc=ThirdParty.SpringerLink.3.EPR653.About_eBook" target="_blank" title="It opens in new window">About this Reference Work</a> </li> </ul> </dd> </dl> <dl> <dt>Topics</dt> <dd itemprop="genre"> <ul class="abstract-about-subject"> <li> <a href="/search?facet-subject=%22Theory+of+Computation%22">Theory of Computation</a> </li> <li> <a href="/search?facet-subject=%22Electronic+and+Computer+Engineering%22">Electronic and Computer Engineering</a> </li> <li> <a href="/search?facet-subject=%22Applications+of+Mathematics%22">Applications of Mathematics</a> </li> <li> <a href="/search?facet-subject=%22Computing+Methodologies%22">Computing Methodologies</a> </li> <li> <a href="/search?facet-subject=%22Computational+Mathematics+and+Numerical+Analysis%22">Computational Mathematics and Numerical Analysis</a> </li> </ul> </dd> <dt>Industry Sectors</dt> <dd itemprop="genre"> <ul class="abstract-about-industrysectors"> <li> <a title="/industry/electronics" href="/industry/electronics">Electronics</a> </li> <li> <a title="/industry/telecom" href="/industry/telecom">Telecommunications</a> </li> <li> <a title="/industry/it" href="/industry/it">IT & Software</a> </li> </ul> </dd> <dt>eBook Packages</dt> <dd itemprop="genre"> <ul class="abstract-about-ebook-packages"> <li> <a href="/search?package=11645">eBook Package english Computer Science</a> </li> <li> <a href="/search?package=90011652">eBook Package english full Collection</a> </li> </ul> </dd> </dl> <dl> <dt>Editors</dt> <dd> <ul class="editors"> <li itemprop="editor" itemscope="itemscope" itemtype="http://schema.org/Person"> <a class="person" href="/search?facet-creator=%22Ming-Yang+Kao+Professor+of+Computer+Science%22" itemprop="name">Ming-Yang Kao Professor of Computer Science</a> <sup title="Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University">(1)</sup> </li> </ul> </dd> <dt>Editor Affiliations</dt> <dd> <ul class="editor-affiliations"> <li> <span class="position">1.</span> <span class="affiliation"> Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University </span> </li> </ul> </dd> <dt>Authors</dt> <dd> <ul class="authors"> <li itemprop="author" itemscope="itemscope" itemtype="http://schema.org/Person"> <a class="person" href="/search?facet-creator=%22Weizhao+Wang%22" itemprop="name">Weizhao Wang</a> <a class="envelope" href="mailto:weizhao.wang@gmail.com" title="weizhao.wang@gmail.com"><img src="/static/1.738/images/envelope.png" alt="weizhao.wang@gmail.com"/></a> <sup title="Google Inc.">(1)</sup> </li> <li itemprop="author" itemscope="itemscope" itemtype="http://schema.org/Person"> <a class="person" href="/search?facet-creator=%22Xiang-Yang+Li%22" itemprop="name">Xiang-Yang Li</a> <a class="envelope" href="mailto:xli@cs.iit.edu" title="xli@cs.iit.edu"><img src="/static/1.738/images/envelope.png" alt="xli@cs.iit.edu"/></a> <sup title="Department of Computer Science, Illinois Institute of Tech.">(2)</sup> </li> <li itemprop="author" itemscope="itemscope" itemtype="http://schema.org/Person"> <a class="person" href="/search?facet-creator=%22Xiaowen+Chu%22" itemprop="name">Xiaowen Chu</a> <a class="envelope" href="mailto:chxw@comp.hkbu.edu.hk" title="chxw@comp.hkbu.edu.hk"><img src="/static/1.738/images/envelope.png" alt="chxw@comp.hkbu.edu.hk"/></a> <sup title="Department of Computer Science, Hong Kong Baptist University">(3)</sup> </li> </ul> </dd> <dt>Author Affiliations</dt> <dd> <ul class="author-affiliations"> <li> <span class="position">1.</span> <span class="affiliation"> Google Inc., Irvine, CA, USA </span> </li> <li> <span class="position">2.</span> <span class="affiliation"> Department of Computer Science, Illinois Institute of Tech., Chicago, IL, USA </span> </li> <li> <span class="position">3.</span> <span class="affiliation"> Department of Computer Science, Hong Kong Baptist University, Hong Kong, China </span> </li> </ul> </dd> </dl> </div> </div> </div> </div> </div> </div> <div id="look-inside-interrupt" class="look-inside-interrupt"> <h3>Continue reading...</h3> <div class="col-1"> <p>To view the rest of this content please follow the download PDF link above.</p> </div> </div> </div> <div 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