{"id":152,"date":"2020-05-18T22:11:27","date_gmt":"2020-05-18T22:11:27","guid":{"rendered":"https:\/\/www.rasmusen.org\/blog1\/?p=152"},"modified":"2020-05-18T22:11:27","modified_gmt":"2020-05-18T22:11:27","slug":"splitting-a-pie-mixed-strategies-in-bargaining-under-complete-information","status":"publish","type":"post","link":"https:\/\/www.rasmusen.org\/blog1\/splitting-a-pie-mixed-strategies-in-bargaining-under-complete-information\/","title":{"rendered":"&#8220;Splitting a Pie: Mixed Strategies in Bargaining under Complete Information,&#8221;"},"content":{"rendered":"<p>We submitted this to <em>Economic Theory<\/em> yesterday, after being rejected at<em> Econometrica.<\/em> Comments welcomed. <\/p>\n<p>&#8220;Splitting a Pie: Mixed Strategies in Bargaining under Complete Information,&#8221; with Christopher Connell. We characterize the mixed-strategy equilibria for the bargaining game in which two players simultaneously bid for a share of a pie and receive shares proportional to their bids, or zero if the bids sum to more than 100%. Of particular interest is the symmetric equilibrium in which each player&#8217;s support is a single interval. This consists of a convex increasing density $f_1(p)$ on $[{a}, 1-{a}]$ and an atom of probability at $a$, and is unique for given $a \\in (0, .5)$. The two outcomes with highest probability are breakdown and a 50-50 split. We use the same approach to characterize all symmetric and asymmetric equilibria over multiple intervals, and all equilibria (such as &#8220;hawk-dove&#8221;) that mix over a finite set of bids instead of intervals. <\/p>\n<p><a href=\"http:\/\/www.rasmusen.org\/papers\/mixedpie.pdf\" rel=\"noopener noreferrer\" target=\"_blank\">http:\/\/www.rasmusen.org\/papers\/mixedpie.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We submitted this to Economic Theory yesterday, after being rejected at Econometrica. Comments welcomed. &#8220;Splitting a Pie: Mixed Strategies in Bargaining under Complete Information,&#8221; with Christopher Connell. We characterize the mixed-strategy equilibria for the bargaining game in which two players simultaneously bid for a share of a pie and receive shares proportional to their bids, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[15,16,14],"class_list":["post-152","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-bargaining","tag-game-theory","tag-papers"],"_links":{"self":[{"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/posts\/152","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/comments?post=152"}],"version-history":[{"count":1,"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/posts\/152\/revisions"}],"predecessor-version":[{"id":153,"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/posts\/152\/revisions\/153"}],"wp:attachment":[{"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/media?parent=152"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/categories?post=152"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rasmusen.org\/blog1\/wp-json\/wp\/v2\/tags?post=152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}