<?php
require_once $_SERVER['DOCUMENT_ROOT'] . '/sys/includes/wwwlib.php';
$formare_root = '../../';
require_once $formare_root . 'macros.php';
$title = 'Auction Theory Toolbox (ATT)';
SetHeaderTitle($title);
SetPageTitle($title);
SetMaintainer('Christoph Lange', '*****@*****.**');
AddStylesheet($formare_root . 'formare.css');
HTMLHeader();
PageStart();
?>
<p>This is an output of the <a href="../..">ForMaRE</a> research project. We particularly focus on</p>
<ul>
<li><a href="#maskin">proving theorems about static single-good auctions</a></li>
<li><a href="#sound-verif">checking the soundness of more complex auctions and generating verified software.</a></li>
</ul>
<p>Both will be detailed below.</p>
<h2 id="maskin">Proving theorems about static single-good auctions</h2>
<p>Our formalisation is guided by Eric Maskin's 2004 review article “<a href="http://scholar.harvard.edu/maskin/publications/unity-auction-theory">The unity of auction theory: Milgrom's master class</a>” (Journal of Economic Literature 42.4, p. 1102–1115). As this article makes rather high-level statements, we have elaborated them to more detail on paper.</p>
<p>We have used different languages for the formalisation. The table below lists the current state of formalising the propositions given in Maskin's review article. For the research background and first results, please see our paper “<a href="../../publications.php#cicm2013-comparison">A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory</a>” (in: Conference on Intelligent Computer Mathematics, 2013).</p>
<p>Further contributions are highly welcome; this includes</p>
<ul>
<li>formalisations of propositions not yet covered</li>
<li>re-formalisations in new languages</li>
<li>improvements to existing formalisations</li>
</ul>
<p>For any questions, please contact us via <a href="mailto:formare-discuss@cs.bham.ac.uk?subject=Auction%20Theory%20Toolbox">formare-discuss@cs.bham.ac.uk</a>. (You need to <a href="https://mailman.cs.bham.ac.uk/mailman/listinfo/formare-discuss">subscribe</a> first.)</p>
<p>Downloadable files are linked below. If you would like to contribute to the latest developments, please have a look at our <a href="https://github.com/formare/auctions">GitHub repository</a>.</p>
<p>The table below shows the following information:</p>
<?php
require_once $_SERVER['DOCUMENT_ROOT'] . '/sys/includes/wwwlib.php';
$formare_root = '../../../';
require_once $formare_root . 'macros.php';
$title = 'Auction Theory Toolbox (ATT) – Theorema';
SetHeaderTitle($title);
SetPageTitle($title);
SetMaintainer('Christoph Lange', '*****@*****.**');
AddStylesheet($formare_root . 'formare.css');
HTMLHeader();
PageStart();
?>
<h2>Files relevant to the Theorema formalisation</h2>
<ul>
<li><a href="https://github.com/formare/auctions/tree/master/theorema">Source repository on GitHub</a>.</li>
<li><a href="theorema.zip">all-in-one ZIP archive for download</a></li>
<li><a href="Vickrey.nb">Theorema formalisation</a></li>
<li><a href="Vickrey.pdf">PDF export</a></li>
</ul>
<h2>How to run</h2>
<ol>
<li>Get a licence of <a href="http://www.wolfram.com/mathematica/">Mathematica 8</a>.</li>
<li>For now, please contact <a href="http://www.risc.jku.at/people/wwindste/">Wolfgang Windsteiger</a> for a copy of Theorema and for installation instructions.</li>
<li>Open the Theorema formalisation in Mathematica.</li>
<li>Evaluate the cell that reads <code>Needs["Theorema`"]</code> by placing the cursor there and pressing Shift+Return, or evaluate all initialization cells via <em>Evaluation→Evaluate Initialization Cells</em>.</li>
</ol>
<p style="text-align:right; font-style:italic"><? echo $timestamp ?></p>
<?php
PageEnd();
HTMLFooter();