{"id":1657,"date":"2023-07-09T20:45:34","date_gmt":"2023-07-09T11:45:34","guid":{"rendered":"https:\/\/saraheee.com\/?p=1657"},"modified":"2023-07-09T20:45:36","modified_gmt":"2023-07-09T11:45:36","slug":"game-theory-11-chap22-job-market-signaling","status":"publish","type":"post","link":"https:\/\/saraheee.com\/ko\/2023\/07\/game-theory-11-chap22-job-market-signaling\/","title":{"rendered":"Game Theory 11 \u2013 chap22. Job-market signaling"},"content":{"rendered":"<p>5. Dynamic Bayesian Games<br>5.3 Dynamic Bayesian Games: Signaling<br>Application I : Job-Market Signaling (Chapter 29, Spence (1973))<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Job-Market Signaling, Michael Spence (1973)<\/h3>\n\n\n\n<p>In most job markets, a job hunter&#8217;s productive capability on the job is <em>not perfectly observable<\/em> when an employer makes a hiring decision<\/p>\n\n\n\n<p>Instead, the employer is able to observe a plethora of personal data and certain attributes such as:<br>education, previous work experiences, race, age, sex, etc<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignleft size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"183\" height=\"275\" src=\"https:\/\/saraheee.com\/wp-content\/uploads\/2023\/07\/image-8.png\" alt=\"\" class=\"wp-image-1658\"\/><\/figure><\/div>\n\n\n<p>Michael Spence &#8211; Nobel laureate in 2001<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-global-color-15-color\">MICHAEL SPENCE (1973)<\/mark><\/strong> classifies the set of attributes into <em>indices<\/em> and <em>signals<\/em> according to its alterability<\/p>\n\n\n\n<p>In his pioneering work, a job hunter is represented by a pair of his productivity and one signal,<\/p>\n\n\n\n<p>(\\(\\theta\\),<em>e<\/em>),<\/p>\n\n\n\n<p>where \\(\\theta\\) his unobservable innate talent and <em>e<\/em> is the level of education<\/p>\n\n\n\n<p>The textbook presents a simple version of his job-market signaling model:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The worker&#8217;s type 0 is either high or low<\/li>\n\n\n\n<li>The common prior is Pr(\\(\\theta\\) = H) =1\/3<\/li>\n\n\n\n<li>After observing \\(\\theta\\), the worker decides whether to obtain an education or not<\/li>\n\n\n\n<li><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-global-color-8-color\">Education is costly<\/mark><\/strong>, 4 to the high type and 7 to the low type<\/li>\n\n\n\n<li>After observing the worker&#8217;s choice, the firm decides whether to appoint him as a manager or a clerk<\/li>\n\n\n\n<li>The firm earns a profit of 10 (0) by putting the high (low) type in the management position<\/li>\n\n\n\n<li>When appointed as a clerk, both types yield a profit of 4 to the firm<\/li>\n\n\n\n<li>The manager receives a wage of 10, whereas the clerk receives 4<\/li>\n<\/ul>\n\n\n\n<p>The dynamic game can be put in the extensive form: <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"478\" src=\"https:\/\/saraheee.com\/wp-content\/uploads\/2023\/07\/image-9-1024x478.png\" alt=\"\" class=\"wp-image-1661\" srcset=\"https:\/\/saraheee.com\/wp-content\/uploads\/2023\/07\/image-9-1024x478.png 1024w, https:\/\/saraheee.com\/wp-content\/uploads\/2023\/07\/image-9-300x140.png 300w, https:\/\/saraheee.com\/wp-content\/uploads\/2023\/07\/image-9-768x358.png 768w, https:\/\/saraheee.com\/wp-content\/uploads\/2023\/07\/image-9-1536x717.png 1536w, https:\/\/saraheee.com\/wp-content\/uploads\/2023\/07\/image-9.png 2002w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-global-color-15-color\">separate equilibrium: High Type E, Low Type N&#8217;<br>(Since there is no intensive debated, because of M for q and C&#8217; for p)<\/mark><\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-global-color-15-color\">pooling equilibrium: High Type N, Low Type N&#8217;<br>expected payoff: 10\/3 &lt; 4 so C&#8217; is Best Response<\/mark><\/p>\n\n\n\n<p>&lt;(NN&#8217;, C&#8217;C), p = 1\/3, q &lt;= 2\/5><\/p>\n\n\n\n<p>This signaling game has a unique PBE in <em>separating strategies<\/em> satisfying the Cho-Kreps criterion:<br>\u27e8(\\(E^H N^L, C^N M^E\\)), p = 0, q = 1\u27e9<\/p>\n\n\n\n<p>This highlights the <strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-global-color-8-color\">signaling role<\/mark><\/strong> of education in job markets<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Although it does not improve productivity, education could still have economic value to the worker<\/li>\n\n\n\n<li>High-type workers are willing to obtain more education in order to signal their productivity, and this costly signaling is compensated with high pay in the market<\/li>\n<\/ul>\n\n\n\n<p>&#8220;<em>the sheepskin<\/em> (diploma) effect&#8221;<\/p>\n\n\n\n<p>Spence&#8217;s work sparked subsequent empirical research investigating whether this effect indeed exists in the real world<\/p>\n\n\n\n<p>We study how to compute a PBE by going through the next classic example<\/p>\n\n\n\n<p><mark style=\"background-color:var(--global-color-10)\" class=\"has-inline-color\">EXAMPLE 5.7 (THE BEER-QUICHE GAME, CHO AND KREPS (1987))<\/mark>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Player 1 can be weak (w) or strong (s), and let Pr(\\(t_1\\) = w) = 0.1. The strong type likes beer for breakfast, while the weak likes quiche.<\/li>\n\n\n\n<li>Player 1 is ordering his breakfast, and player 2 is watching and contemplating whether to pick a fight with player 1. Player 2 wants to fight with the weak type but walk away from the strong type.<\/li>\n\n\n\n<li>Player 1 likes to avoid a fight: he gets a payoff of one from the preferred breakfast, and a payoff of two from avoiding the fight.<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Reference: Chang-Koo Chi, (40\/50) Game Theory and Applications 11 \u2013 Job-market signaling, Jul 15, 2020,\u00a0<a href=\"https:\/\/youtu.be\/O19madhZ2rE\" rel=\"noopener\">https:\/\/youtu.be\/O19madhZ2rE<\/a><\/li>\n<\/ul>\n\n\n\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>Learn about the first application of signaling, job-market signaling by Michael Spence.<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[82,4,112,114,113],"class_list":["post-1657","post","type-post","status-publish","format-standard","hentry","category-game-theory-and-applications","tag-bayesian-games","tag-game-theory","tag-job-market-signaling","tag-jul-9-2023","tag-michael-spence"],"_links":{"self":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/1657"}],"collection":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/comments?post=1657"}],"version-history":[{"count":6,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/1657\/revisions"}],"predecessor-version":[{"id":1843,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/posts\/1657\/revisions\/1843"}],"wp:attachment":[{"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/media?parent=1657"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/categories?post=1657"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/saraheee.com\/ko\/wp-json\/wp\/v2\/tags?post=1657"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}