{"id":39849,"date":"2022-07-05T16:45:34","date_gmt":"2022-07-05T09:45:34","guid":{"rendered":"https:\/\/www.princess-it-foundation.org\/pbl\/?p=39849"},"modified":"2022-07-05T17:09:52","modified_gmt":"2022-07-05T10:09:52","slug":"remember-that-and-you-will-which-is-are-decreasing","status":"publish","type":"post","link":"https:\/\/www.princess-it.org\/pbl\/?p=39849","title":{"rendered":"Remember that and you will , which is, are decreasing during the x"},"content":{"rendered":"<p><title>Remember that and you will , which is, are decreasing during the x<\/title><br \/>\nstep one Proof Proposition 1<\/h2>\n<p>There exists a unique x<sub>1<\/sub> , where 0 ? x<sub>1<\/sub> ? 1 , given that V<sub>t<\/sub>(q<sub>1<\/sub>, q<sub>2<\/sub>) is an increasing function in q<sub>1<\/sub> .<\/p>\n<p>Proof. When the strategic RA (RA1) gets a bad project, it will get pay-off if it gives the project a GramsR, and if it refuses rating. <sub>1<\/sub> and is increasing in x<sub>1<\/sub> . Given that V<sub>t<\/sub>(q<sub>1<\/sub>, q<sub>2<\/sub>) is increasing in q<sub>1<\/sub> , it is easy to see that ?(lie) is decreasing in x<sub>1<\/sub> and that ?(honest) is increasing in x<sub>1<\/sub> . Thus, if we define x<sub>1<\/sub> such that<\/p>\n<h2>2 Proof of Suggestion 2<\/h2>\n<p>Proof. Suppose that the strategic RA (RA1) gets a good project and that its strategy is x<sub>1<\/sub> . Let us examine whether RA1 wants to deviate:<\/p>\n<p>\u2022if x<sub>1<\/sub> = 1 , we have ?(lie) ? ?(honest) , or . If the RA1 gives NR to the good project, it will get and otherwise. Since RA1 does not want to deviate.<\/p>\n<p>\u2022if x<sub>1<\/sub> = 0 , , hence reputation becomes irrelevant and the RA does not have an incentive to give NR to the good project.<\/p>\n<p>\u2022if 0 &lt; x<sub>1<\/sub> &lt; 1 , we have ?(lie) = ?(honest) , so , and hence RA1 does not want to deviate.<\/p>\n<h2>3 Proof of Corollary 1<\/h2>\n<p>Proof. Suppose that the equilibrium strategy is x<sub>1<\/sub> = 0 . Then and we must have I + ?V<sub>t<\/sub>(q<sub>1<\/sub>, q<sub>2<\/sub>) ? ?V<sub>t<\/sub>(q<sub>1<\/sub> <a href=\"https:\/\/datingranking.net\/thaifriendly-review\/\">https:\/\/datingranking.net\/thaifriendly-review\/<\/a>, q<sub>2<\/sub>) . This is impossible as long as I &gt; 0 . Hence, x<sub>1<\/sub> = 0 cannot be an equilibrium strategy.<\/p>\n<h2>cuatro Evidence of Corollary dos<\/h2>\n<p>Suppose the model ends in period T. Then the equilibrium strategy of the strategic RA is x<sub>t<\/sub> = 1 at t = T ? step one, T .<\/p>\n<p>Proof. At t = T , the strategic RA does not have any reputational concerns. This implies that the strategy of strategic RA will be to always give GR if the project is bad, that is, x<sub>T<\/sub> = 1 .<\/p>\n<p>Similarly, from the t = T ? 1 , this new strategic RA are often lie. Imagine that an adverse enterprise involves strategic RA, say RA1. The asked pay-from RA1 try<\/p>\n<p>Although in this case RA1 does have reputational concerns, these are not sufficient to prevent RA1 from being lax and not giving GR to bad projects.<!--more--> Since by being honest RA1 is giving up I today, in exchange for having a higher chance of getting I in the next period, it is not optimal for RA1 to be honest, given that RA1 is impatient (i.e., ? &lt; 1 ). Hence, the optimal strategy of RA1 is to always lie, that is, x<sub>T ? 1<\/sub> = 1 .<\/p>\n<h2>5 Evidence of Proposition 4<\/h2>\n<p>Proof. Since p<sub>G<\/sub> = 1 , the reputation of RA1 (i.e., the strategic RA) will go to zero if it gives a GR to a bad project since now every good project succeeds and every bad project fails. So the expected pay-off from giving a GR to a bad project is I . This simplifies expressions (9) and (10) and allows us to derive RA1&#8217;s equilibrium strategy.<\/p>\n<p>Having fun with Equations (6) and you can (7) and you can listing one RA1 will always be lie into the episodes t = dos, 3 , this is rewritten just like the<\/p>\n<p>We look for an equilibrium of the game by examining RA1&#8217;s trade-off between lying and not lying. If the pay-off from lying is greater when x<sub>1<\/sub> = 1 , we have a pure-strategy equilibrium in which RA1 always lies; if the pay-off from not lying is greater when x<sub>1<\/sub> = 0 , we have a pure-strategy equilibrium in which RA1 never lies; otherwise we have a mixed-strategy equilibrium in which RA1 is indifferent between lying or not given some prior beliefs about its strategy, that is, 0 &lt; x<sub>1<\/sub> &lt; 1 .<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Remember that and you will , which is, are decreasing during the x step one Proof Proposition 1 There exists a unique x1 , where 0 ? x1 ? 1 , given that Vt(q1, q2) is an increasing function in q1 . Proof. When the strategic RA (RA1) gets a &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-39849","post","type-post","status-publish","format-standard","hentry","category-form","column","threecol"],"_links":{"self":[{"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=\/wp\/v2\/posts\/39849","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=39849"}],"version-history":[{"count":1,"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=\/wp\/v2\/posts\/39849\/revisions"}],"predecessor-version":[{"id":39850,"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=\/wp\/v2\/posts\/39849\/revisions\/39850"}],"wp:attachment":[{"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=39849"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=39849"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.princess-it.org\/pbl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=39849"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}