{"id":4712,"date":"2024-04-13T10:50:18","date_gmt":"2024-04-13T10:50:18","guid":{"rendered":"https:\/\/prosperity.newai.com.au\/?p=4712"},"modified":"2025-04-13T12:45:36","modified_gmt":"2025-04-13T12:45:36","slug":"optimal-bidding-strategy-in-round-1-a-mathematical-approach-to-fish-market-trading","status":"publish","type":"post","link":"https:\/\/prosperity.newai.com.au\/index.php\/2024\/04\/13\/optimal-bidding-strategy-in-round-1-a-mathematical-approach-to-fish-market-trading\/","title":{"rendered":"Optimal Bidding Strategy in Round 1: A Mathematical Approach to Fish Market Trading"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"4712\" class=\"elementor elementor-4712\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a90b744 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a90b744\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-986612e\" data-id=\"986612e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bb276d1 elementor-widget elementor-widget-text-editor\" data-id=\"bb276d1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.6.7 - 03-07-2022 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#818a91;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#818a91;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>For Round 1&#8217;s algo portion, it&#8217;s identical to last year&#8217;s, so I reused my 2023 code. Interested friends can refer to last year&#8217;s posts.<\/p>\n<p><b>Manual Part Analysis:<\/b><br>There&#8217;s a group of fish selling items with reserve prices uniformly distributed between 900 and 1000:<\/p>\n<p>\u2981 Minimum probability at 900<\/p>\n<p>\u2981 Maximum probability at 1000<\/p>\n<p>\u2981 Linear probability distribution in between<\/p>\n<p>We need to set two bid prices. Any fish with reserve price below our bids will sell to us at the lowest bid that exceeds their reserve price. We can then resell all acquired items at 1000.<\/p>\n<p><b>Example:<\/b><br>If I bid 930 and 970:<\/p>\n<p>\u2981 Fish with reserves 900-929 sell at 930<\/p>\n<p>\u2981 Fish with reserves 930-969 sell at 970<\/p>\n<p>\u2981 Fish with reserves 970-1000 don&#8217;t trade<\/p>\n<p><b>Mathematical Optimization:<\/b><br>Assuming fish quantity follows an arithmetic sequence:<\/p>\n<p>\u2981 1 fish at 900<\/p>\n<p>\u2981 2 fish at 901<\/p>\n<p>\u2981 &#8230;<\/p>\n<p>\u2981 101 fish at 1000<\/p>\n<p>For lower bid X:<br>Number of willing fish = \u03a3 from 900 to X-1 = (X-900)(X-901)\/2<br>Profit E1 = (X-900)(X-901)\/2 \u00d7 (1000-X)<\/p>\n<p>For higher bid Y:<br>Number of willing fish = \u03a3 from X to Y-1 = (X+Y-1801)(Y-X)\/2<br>Profit E2 = (X+Y-1801)(Y-X)\/2 \u00d7 (1000-Y)<\/p>\n<p>Total profit E = E1 + E2<br>Maximizing E requires solving \u2202E\/\u2202X = 0 and \u2202E\/\u2202Y = 0<br>Optimal solution found at X\u2248952, Y\u2248978<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>For Round 1&#8217;s algo portion, it&#8217;s identical to last year&#8217;s, so I reused my 2023 code. Interested friends can refer to last year&#8217;s posts. Manual Part Analysis:There&#8217;s a group of fish selling items with reserve prices uniformly distributed between 900 and 1000: \u2981 Minimum probability at 900 \u2981 Maximum probability at 1000 \u2981 Linear probability [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":4537,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[35],"tags":[],"class_list":["post-4712","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-2024r1"],"acf":[],"_links":{"self":[{"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/posts\/4712","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/comments?post=4712"}],"version-history":[{"count":4,"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/posts\/4712\/revisions"}],"predecessor-version":[{"id":4716,"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/posts\/4712\/revisions\/4716"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/media\/4537"}],"wp:attachment":[{"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/media?parent=4712"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/categories?post=4712"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/prosperity.newai.com.au\/index.php\/wp-json\/wp\/v2\/tags?post=4712"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}