The Lovely but Lonely Vickrey Auction | Combinatorial Auctions | MIT Press Scholarship Online

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js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244776406" aria-owns=sublist-headings-244776406 role="treeitem" tabindex="-1"> <span class="tocLink-text at-tocLink-text"> Dedication </span> </a> </div> <ul id="sublist-headings-244776406" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244776406" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244776425" aria-owns=sublist-headings-244776425 role="treeitem" tabindex="-1"> <span class="tocLink-text at-tocLink-text"> Foreword </span> </a> </div> <ul id="sublist-headings-244776425" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244776425" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244776472" aria-owns=sublist-headings-244776472 role="treeitem" tabindex="-1"> <span class="tocLink-text at-tocLink-text"> Acknowledgements </span> </a> </div> <ul id="sublist-headings-244776472" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244776472" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244776527" aria-owns=sublist-headings-244776527 role="treeitem" tabindex="-1"> <span class="tocLink-text at-tocLink-text"> Introduction to Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244776527" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244776527" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-down" data-sectionid="244776706" data-targeturl="javascript:;"> <span class="screenreader-text">Collapse</span> </i> </button> <button class="tocLink js-tocLink active at-highlighted-chapter js-nav-tree-link" aria-owns=sublist-toc-244776706 aria-expanded=true role="treeitem" tabindex="-1"> <span class="tocLink-label"> I </span> <span class="tocLink-text at-tocLink-text"> Mechanisms </span> </button> </div> <ul id="sublist-toc-244776706" class="js-headings-placeholder collections-child-list js-nav-tree-sublist" data-sectionid="244776706" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-down" data-sectionid="244776729" data-targeturl="/mit-press-scholarship-online/book/29406/chapter/244776729"> <span class="screenreader-text">Collapse</span> </i> </button> <button class="tocLink js-tocLink active at-highlighted-chapter js-nav-tree-link" aria-owns=sublist-headings-244776729 aria-expanded=true role="treeitem" tabindex="-1"> <span class="tocLink-label"> 1 </span> <span class="tocLink-text at-tocLink-text"> The Lovely but Lonely Vickrey Auction </span> </button> </div> <ul id="sublist-headings-244776729" class="js-headings-placeholder collections-child-list chapter-headings-wrap js-nav-tree-sublist" data-sectionid="244776729" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776744" href="#244776744" role="treeitem" tabindex="-1"> <span class="tocLink-label">1.1</span> <span> Introduction</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776744"> <span class="tocLink-label">1.1</span> <span> Introduction</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="244776756" data-targeturl="#244776756"> <span class="screenreader-text">Expand</span> </i> </button> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776756" href="#244776756" aria-owns=sublist-244776756 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-label">1.2</span> <span> Description of the General Vickrey (VCG) Design</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776756"> <span class="tocLink-label">1.2</span> <span> Description of the General Vickrey (VCG) Design</span> </span> </div> <ul id="sublist-244776756" class="js-headings-placeholder collections-child-list head-level__1 hide js-nav-tree-sublist" data-sectionid="244776756" data-targeturl="#244776756" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776786" href="#244776786" role="treeitem" tabindex="-1"> <span>Theorem 1.1</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776786"> <span>Theorem 1.1</span> </span> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="244776804" data-targeturl="#244776804"> <span class="screenreader-text">Expand</span> </i> </button> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776804" href="#244776804" aria-owns=sublist-244776804 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-label">1.3</span> <span> Virtues of the VCG Mechanism</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776804"> <span class="tocLink-label">1.3</span> <span> Virtues of the VCG Mechanism</span> </span> </div> <ul id="sublist-244776804" class="js-headings-placeholder collections-child-list head-level__2 hide js-nav-tree-sublist" data-sectionid="244776804" data-targeturl="#244776804" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776813" href="#244776813" role="treeitem" tabindex="-1"> <span>Theorem 1.2</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776813"> <span>Theorem 1.2</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776834" href="#244776834" role="treeitem" tabindex="-1"> <span>Theorem 1.3</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776834"> <span>Theorem 1.3</span> </span> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776843" href="#244776843" role="treeitem" tabindex="-1"> <span class="tocLink-label">1.4</span> <span> Weaknesses of the VCG Mechanism</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776843"> <span class="tocLink-label">1.4</span> <span> Weaknesses of the VCG Mechanism</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="244776908" data-targeturl="#244776908"> <span class="screenreader-text">Expand</span> </i> </button> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776908" href="#244776908" aria-owns=sublist-244776908 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-label">1.5</span> <span> VCG Outcomes and the Core</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776908"> <span class="tocLink-label">1.5</span> <span> VCG Outcomes and the Core</span> </span> </div> <ul id="sublist-244776908" class="js-headings-placeholder collections-child-list head-level__3 hide js-nav-tree-sublist" data-sectionid="244776908" data-targeturl="#244776908" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776937" href="#244776937" role="treeitem" tabindex="-1"> <span>Theorem 1.4</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776937"> <span>Theorem 1.4</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776944" href="#244776944" role="treeitem" tabindex="-1"> <span>Theorem 1.5</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776944"> <span>Theorem 1.5</span> </span> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="244776967" data-targeturl="#244776967"> <span class="screenreader-text">Expand</span> </i> </button> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776967" href="#244776967" aria-owns=sublist-244776967 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-label">1.6</span> <span> Conditions on the Coalitional Value Function</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776967"> <span class="tocLink-label">1.6</span> <span> Conditions on the Coalitional Value Function</span> </span> </div> <ul id="sublist-244776967" class="js-headings-placeholder collections-child-list head-level__4 hide js-nav-tree-sublist" data-sectionid="244776967" data-targeturl="#244776967" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776983" href="#244776983" role="treeitem" tabindex="-1"> <span>Definition 1.1</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776983"> <span>Definition 1.1</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244776988" href="#244776988" role="treeitem" tabindex="-1"> <span>Theorem 1.6 The following three statements are equivalent:</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244776988"> <span>Theorem 1.6 The following three statements are equivalent:</span> </span> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="244777016" data-targeturl="#244777016"> <span class="screenreader-text">Expand</span> </i> </button> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244777016" href="#244777016" aria-owns=sublist-244777016 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-label">1.7</span> <span> Conditions on the Goods Valuation Functions</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244777016"> <span class="tocLink-label">1.7</span> <span> Conditions on the Goods Valuation Functions</span> </span> </div> <ul id="sublist-244777016" class="js-headings-placeholder collections-child-list head-level__5 hide js-nav-tree-sublist" data-sectionid="244777016" data-targeturl="#244777016" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244777029" href="#244777029" role="treeitem" tabindex="-1"> <span>Theorem 1.7</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244777029"> <span>Theorem 1.7</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244777051" href="#244777051" role="treeitem" tabindex="-1"> <span>Lemma 1.1</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244777051"> <span>Lemma 1.1</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244777075" href="#244777075" role="treeitem" tabindex="-1"> <span>Theorem 1.8</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244777075"> <span>Theorem 1.8</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244777130" href="#244777130" role="treeitem" tabindex="-1"> <span>Theorem 1.9</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244777130"> <span>Theorem 1.9</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244777147" href="#244777147" role="treeitem" tabindex="-1"> <span>Theorem 1.10</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244777147"> <span>Theorem 1.10</span> </span> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244777189" href="#244777189" role="treeitem" tabindex="-1"> <span class="tocLink-label">1.8</span> <span> Conclusion</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244777189"> <span class="tocLink-label">1.8</span> <span> Conclusion</span> </span> </div> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244777201" href="#244777201" aria-owns=sublist-244777201 role="treeitem" tabindex="-1"> <span>Notes</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244777201"> <span>Notes</span> </span> </div> <ul id="sublist-244777201" class="js-headings-placeholder collections-child-list head-level__6 hide js-nav-tree-sublist" data-sectionid="244777201" data-targeturl="#244777201" role="group"> <li class="js-toc-chapter-link js-toc-notes-link js-nav-tree-item hide"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-jumplink at-tocLink js-nav-tree-link" data-sectionid="244777218" href="#244777218" aria-owns=sublist-244777218 role="treeitem" tabindex="-1"> <span>References</span> </a> <span class="tocLink js-jumplink-span hide" data-sectionid="244777218"> <span>References</span> </span> </div> <ul id="sublist-244777218" class="js-headings-placeholder collections-child-list head-level__6 hide js-nav-tree-sublist" data-sectionid="244777218" data-targeturl="#244777218" role="group"> <li class="js-toc-chapter-link js-toc-notes-link js-nav-tree-item hide"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244777431" aria-owns=sublist-headings-244777431 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 2 </span> <span class="tocLink-text at-tocLink-text"> Iterative Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244777431" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244777431" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244779611" aria-owns=sublist-headings-244779611 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 3 </span> <span class="tocLink-text at-tocLink-text"> Ascending Proxy Auctions </span> </a> </div> <ul id="sublist-headings-244779611" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244779611" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244780329" aria-owns=sublist-headings-244780329 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 4 </span> <span class="tocLink-text at-tocLink-text"> Simultaneous Ascending Auctions </span> </a> </div> <ul id="sublist-headings-244780329" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244780329" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244780875" aria-owns=sublist-headings-244780875 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 5 </span> <span class="tocLink-text at-tocLink-text"> The Clock-Proxy Auction: A Practical Combinatorial Auction Design </span> </a> </div> <ul id="sublist-headings-244780875" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244780875" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244781446" aria-owns=sublist-headings-244781446 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 6 </span> <span class="tocLink-text at-tocLink-text"> PAUSE: A Computationally Tractable Combinatorial Auction </span> </a> </div> <ul id="sublist-headings-244781446" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244781446" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> </ul> <ul id="sublist-headings-244776706" class="js-headings-placeholder collections-child-list chapter-headings-wrap js-nav-tree-sublist" data-sectionid="244776706" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="244783321" data-targeturl="javascript:;"> <span class="screenreader-text">Expand</span> </i> </button> <button class="tocLink js-tocLink js-nav-tree-link" aria-owns=sublist-toc-244783321 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-label"> II </span> <span class="tocLink-text at-tocLink-text"> Bidding and Efficiency </span> </button> </div> <ul id="sublist-toc-244783321" class="js-headings-placeholder collections-child-list hide js-nav-tree-sublist" data-sectionid="244783321" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244783362" aria-owns=sublist-headings-244783362 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 7 </span> <span class="tocLink-text at-tocLink-text"> Pseudonymous Bidding in Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244783362" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244783362" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244785745" aria-owns=sublist-headings-244785745 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 8 </span> <span class="tocLink-text at-tocLink-text"> From the Assignment Model to Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244785745" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244785745" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244787625" aria-owns=sublist-headings-244787625 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 9 </span> <span class="tocLink-text at-tocLink-text"> Bidding Languages for Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244787625" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244787625" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244788129" aria-owns=sublist-headings-244788129 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 10 </span> <span class="tocLink-text at-tocLink-text"> Preference Elicitation in Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244788129" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244788129" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244788786" aria-owns=sublist-headings-244788786 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 11 </span> <span class="tocLink-text at-tocLink-text"> The Communication Requirements of Combinatorial Allocation Problems </span> </a> </div> <ul id="sublist-headings-244788786" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244788786" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> </ul> <ul id="sublist-headings-244783321" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244783321" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="244789364" data-targeturl="javascript:;"> <span class="screenreader-text">Expand</span> </i> </button> <button class="tocLink js-tocLink js-nav-tree-link" aria-owns=sublist-toc-244789364 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-label"> III </span> <span class="tocLink-text at-tocLink-text"> Complexity and Algorithmic Considerations </span> </button> </div> <ul id="sublist-toc-244789364" class="js-headings-placeholder collections-child-list hide js-nav-tree-sublist" data-sectionid="244789364" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244789405" aria-owns=sublist-headings-244789405 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 12 </span> <span class="tocLink-text at-tocLink-text"> The Winner Determination Problem </span> </a> </div> <ul id="sublist-headings-244789405" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244789405" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244790115" aria-owns=sublist-headings-244790115 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 13 </span> <span class="tocLink-text at-tocLink-text"> Tractable Cases of the Winner Determination Problem </span> </a> </div> <ul id="sublist-headings-244790115" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244790115" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244790311" aria-owns=sublist-headings-244790311 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 14 </span> <span class="tocLink-text at-tocLink-text"> Optimal Winner Determination Algorithms </span> </a> </div> <ul id="sublist-headings-244790311" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244790311" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244791404" aria-owns=sublist-headings-244791404 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 15 </span> <span class="tocLink-text at-tocLink-text"> Incentive Compatibility in Computationally Feasible Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244791404" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244791404" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244792202" aria-owns=sublist-headings-244792202 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 16 </span> <span class="tocLink-text at-tocLink-text"> Noncomputational Approaches to Mitigating Computational Problems in Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244792202" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244792202" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> </ul> <ul id="sublist-headings-244789364" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244789364" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="244792379" data-targeturl="javascript:;"> <span class="screenreader-text">Expand</span> </i> </button> <button class="tocLink js-tocLink js-nav-tree-link" aria-owns=sublist-toc-244792379 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-label"> IV </span> <span class="tocLink-text at-tocLink-text"> Testing and Implementation </span> </button> </div> <ul id="sublist-toc-244792379" class="js-headings-placeholder collections-child-list hide js-nav-tree-sublist" data-sectionid="244792379" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244792401" aria-owns=sublist-headings-244792401 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 17 </span> <span class="tocLink-text at-tocLink-text"> Observations and Near-Direct Implementations of the Ascending Proxy Auction </span> </a> </div> <ul id="sublist-headings-244792401" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244792401" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244793347" aria-owns=sublist-headings-244793347 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 18 </span> <span class="tocLink-text at-tocLink-text"> A Test Suite for Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244793347" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244793347" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244794435" aria-owns=sublist-headings-244794435 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 19 </span> <span class="tocLink-text at-tocLink-text"> Empirical Hardness Models for Combinatorial Auctions </span> </a> </div> <ul id="sublist-headings-244794435" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244794435" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> </ul> <ul id="sublist-headings-244792379" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244792379" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="244795075" data-targeturl="javascript:;"> <span class="screenreader-text">Expand</span> </i> </button> <button class="tocLink js-tocLink js-nav-tree-link" aria-owns=sublist-toc-244795075 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-label"> V </span> <span class="tocLink-text at-tocLink-text"> Applications </span> </button> </div> <ul id="sublist-toc-244795075" class="js-headings-placeholder collections-child-list hide js-nav-tree-sublist" data-sectionid="244795075" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244795089" aria-owns=sublist-headings-244795089 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 20 </span> <span class="tocLink-text at-tocLink-text"> Auctions for the Safe, Efficient, and Equitable Allocation of Airspace System Resources </span> </a> </div> <ul id="sublist-headings-244795089" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244795089" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244795700" aria-owns=sublist-headings-244795700 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 21 </span> <span class="tocLink-text at-tocLink-text"> Combinatorial Auctions for Truckload Transportation </span> </a> </div> <ul id="sublist-headings-244795700" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244795700" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244797074" aria-owns=sublist-headings-244797074 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 22 </span> <span class="tocLink-text at-tocLink-text"> Auctioning Bus Routes: The London Experience </span> </a> </div> <ul id="sublist-headings-244797074" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244797074" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244797750" aria-owns=sublist-headings-244797750 role="treeitem" tabindex="-1"> <span class="tocLink-label"> 23 </span> <span class="tocLink-text at-tocLink-text"> Industrial Procurement Auctions </span> </a> </div> <ul id="sublist-headings-244797750" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244797750" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> </ul> <ul id="sublist-headings-244795075" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244795075" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <button type="button" class="show-headings-button js-show-headings-button js-nav-tree-toggle" aria-hidden="true" tabindex="-1"> <i class="show-headings-icon js-show-headings-icon icon-general-arrow-filled-right" data-sectionid="-2073881583" data-targeturl="javascript:;"> <span class="screenreader-text">Expand</span> </i> </button> <button class="tocLink js-tocLink js-nav-tree-link" aria-owns=sublist-toc--2073881583 aria-expanded=false role="treeitem" tabindex="-1"> <span class="tocLink-text at-tocLink-text"> End Matter </span> </button> </div> <ul id="sublist-toc--2073881583" class="js-headings-placeholder collections-child-list hide js-nav-tree-sublist" data-sectionid="-2073881583" role="group"> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244798385" aria-owns=sublist-headings-244798385 role="treeitem" tabindex="-1"> <span class="tocLink-text at-tocLink-text"> Combinatorial Auction Glossary </span> </a> </div> <ul id="sublist-headings-244798385" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244798385" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244798433" aria-owns=sublist-headings-244798433 role="treeitem" tabindex="-1"> <span class="tocLink-text at-tocLink-text"> Contributors </span> </a> </div> <ul id="sublist-headings-244798433" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244798433" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-chapter-footnotes js-nav-tree-link" href="#chapter-footnotes" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> <li class="js-toc-chapter-link js-toc-notes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink js-notes-link-end-notes js-nav-tree-link" href="#endNotesTargetLocation" role="treeitem" tabindex="-1"><span>Notes</span></a> </div> </li> </ul> </li> <li class="js-toc-chapter-link js-nav-tree-item" role="none"> <div class="section-title-wrap js-section-title-wrap"> <a class="tocLink js-nav-tree-link" href="/mit-press-scholarship-online/book/29406/chapter/244798469" aria-owns=sublist-headings-244798469 role="treeitem" tabindex="-1"> <span class="tocLink-text at-tocLink-text"> Index </span> </a> </div> <ul id="sublist-headings-244798469" class="js-headings-placeholder collections-child-list chapter-headings-wrap hide js-nav-tree-sublist" data-sectionid="244798469" role="group"> <li class="js-toc-chapter-link js-toc-footnotes-link hide js-nav-tree-item" role="none"> <div class="js-section-title-wrap"> <a class="tocLink js-jumplink 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src="https://oup.silverchair-cdn.com/oup/backfile/content_public/books/29406/book/1/m_9780262033428.jpeg?Expires=1734592609&Signature=iI0hOKk77QrZxq6s6eEcp-wW01NTO1ZqX9Rq0MG6DtPvYqvnD~ErMqYjlTKPyGZGSo71z2OXaEdxtpP5xsTaj0Oc3n-iZwVLho5W4JXzvI8d2Dutq8vwSVLxrKxde8lMVC~17K25pTTAHesyiZ-cZOkfs5ED0YulSmXGHI1NLPCjfRFfvHY7RVMshpC-LXdBa0x4sDr-pK2cJLGzU4DDqKV44M75N1cHSzVZ5qk8Wv4dByctZIOlsLwkyFXeoZp4nAEqQwHIPvChstZ7PwQreesyOiFTKpmDF1GkWOTg39s6rUlIl00onMtJ9KK3vBdWClMHAba9uX0Ba1mma4tMrQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA" class="book-info__cover-img" alt="Combinatorial Auctions"> <span class="book-info__title" href="https://academic.oup.com/mit-press-scholarship-online/book/29406"> Combinatorial Auctions </span> </a> <div class="article-browse-top article-browse-mobile-nav js-mobile-nav"> <div class="article-browse-mobile-nav-inner js-mobile-nav-inner"> <button class="toggle-left-col toggle-left-col__article btn-as-link"> Contents </button> </div> </div> <div class="article-browse-top 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</span> <span class="chapter-title-without-label"> <span class="xrefLink" id="jumplink-upso-9780262033428-chapter-2-milestone-37"></span>The Lovely but Lonely Vickrey Auction </span> </h1> <a href="#no-access-message" class="get-access get-access-jumplink at-get-access-jumplink js-no-access-jumplink"> <span class="get-access-text">Get access</span> <img class='get-access-icon' src='/UI/app/svg/chevron-right-white.svg' alt='Arrow' aria-hidden='true'> </a></div> <div class="chapter-authors at-ChapterAuthors"> <div class="al-authors-list chapter__author-list"> <div class="al-author-name book-info__author js-flyout-wrap"> <a class="linked-name js-linked-name book-info__author-link stats-author-info-trigger" href="javascript:;">Lawrence M. Ausubel</a><span class='delimiter al-author-delim'>, </span> <div class="al-author-info-wrap arrow-up book-info__author-info stats-author-info-panel"> <div id="authorInfo_ChapterTopInfoChapter" class="info-card-author authorInfo_ChapterTopInfoChapter"> <div class="name-role-wrap"> <div class="info-card-name"> Lawrence M. 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It presents several virtues of a VCG auction, which include the dominant strategy property and its scope of application, and its weaknesses that are responsible for the rarity of the VCG mechanism in practice. In this mechanism, efficient allocation of all packages is made in order to maximize total value and the winner achieves a profit that is similar to his incremental contribution to the total value. The chapter emphasizes that more practical procedures are required to remove imperfections and other limitations of the Vickrey auction that are decisive for most practical applications. These shortcomings include the possibility of generating very low revenues and the chances of discouraging value-creating mergers among bidders. 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