问题：﻿恋爱中有哪些博弈？ 刚上完博弈论，老师在课堂上提出了这样一个问题：恋爱中有哪些博弈？作为男方/女方该如何决策才能达到两者最优？ 相关问题:到底为什么有钱，长得帅，长得高，和…
话题：﻿恋爱、恋爱心理
回答：﻿首先简单解释为什么写这个答案.我参考的是算法是立足于.恋爱中有哪些博弈？-尼克余的回答而这个回答是"针对"恋爱中有哪些博弈？-施徐国的回答看了@施徐国的结论后,我对【男人的幸福感普遍偏高（>0.94）】这个结论抱有怀疑.因为这个意味着每个男人最后的伴侣的expectedvalue都是他的前60outof1000.这个概率从直觉上不是很大,也应该确实不是很大.于是就自己算了一下,结果却是跟他的很不相符.联系施后看了code,编程的思路我认为很有意思,确实大大简化了计算,但是我的matlab没法算他的程序.然后有几个地方我也觉得应该不对.尔后缺乏进一步联系.而且code这种东西不是author本人很难完全理解全部思路.尤其是本意不是写给别人看的所以没有很多comments.所以我在这里也不对他的回答做更多评论.重点应该是希望大家也算一下,看一下结果到底是什么.这也是我最后写这个答案的目的.而原因是反复验证过几次认为我的计算过程没问题了,在尼克余的建议下发布出来.然后解释我的具体步骤先使用GaleShapleyStableMarriageAlgorithm得出parings,然后再算happiness/popularity.用的方法都是mean,也就是我理解的施的算法,最后plot.所有的algos都经过sanitycheck,用circulantmatrix和https://inst.eecs.berkeley.edu/~cs70/sp15/notes/n4.pdf所给的n=4example试了都没问题.算出来n=1000的情况malehappiness=505.2860,femalehappiness=491.4000(rangefrom0to1000).而直观上图看上去和施的femalehappinessvspopularity没区别(noticemyplotisformaletho)又开了10次重复实验,得到了malehappinessmeanS和femalehappinessmeanS如下(row1=male,row2=female):Columns1through8508.1640499.6980504.2450493.6790486.7670489.2750515.6580514.1140495.4850494.8700500.6960492.6250506.2670499.0770504.7940512.2420Columns9through10508.3880502.8860504.7410497.5080应该来说在N=10,n=1000中我还没明显看出男人比女人更容易幸福.而且从pattern来看我也怀疑最后difference会是statisticallysignificant.*下划线部分是最开始的描述,但是因为我发现了反例所以确实这点上没问题.因此作废,详见分割线后补充部分也就是说是存在男性比女性更容易幸福但是很微弱(0.2%)老实说我期望男性幸福期望会更高,比如0.6什么的.而且居然存在femalehappinessmean>male的情况,让我理解不能.也就是说男女一样幸福,这个微弱优势不具备任何统计意义,可以无视所以我也对我自己的结论抱有怀疑,但是excel自己对表查check过几次后我认为我自己写的程序是没问题的,如果有问题只可能是我引用的algo出错了,除了circulantmatrix(1,1000)和pdf上example我没去验证其他例子.那就只好姑且相信.希望有人有兴趣的话reproduce一下.这个问题很有意思.同时有鉴于此希望大家不要用我和施的code,而自己另外算,最好是能用R资源的stablematching算一次最有说服力.我本人实在不想再在R上算了.我也不敢说我的一定是对的,施的一定是错的.这里提出来.如果我的是错的我立刻修改免得误人子弟.----------------------------------------------------------------------------------------------------思考了一下meanoffemalehappiness>meanofmalehappiness没问题.例子来源于我在施底下的回复.抱歉我回复时就是英文写的,因为我不习惯用中文思考逻辑和解释问题而针对的那位同学恰好懂英语,更懒得修该,大家将就看吧.thinkaboutmalepreference[123;123;132]whilewehavefemalepreference:[123;213;312]themaleoptimalone,whichistheoutputisobviously(1,1)(2,2)(3,3)check:man1ishappybecausehe'sgothisdreamgirlman2isokbecausealthohelikesgirl1better,girl1wouldgowithman1,andhissecondchoicelikeshimmost.(12)(21)containsroguecouple(1,1)man3isokforthesamereason.butiflookathappiness,apparentlygirlsarehappierthanboysbecuasetheyallgotwhattheylikemostbutboysdidn't.至于为什么,前因后果在这里:(施的评论区里面的)[GengYoung关于问题一，maleoptimality是可以证明的，对于n>2依然成立。关于问题二，maleoptimality的定义是在所有可能的稳定的配对中（即不存在rougecouple)，不存在一个配对使得任意一个男性的配偶比当前配对的配偶处在这个男性preferencelist的更高位。可以证明通过proposeandreject算法取得的配对中，propose的一方一定是optimal的。以上两点的证明，参见https://inst.eecs.berkeley.edu/~cs70/sp15/notes/n4.pdf][woeMr回复GengYoungIgaveitsomethoughtsandyouwereusingrightstufftoprovesomethingunrelatedandthelogicfailstowork.thefirstpartiscorrect,andfurtherattheendofthepdfitprovedthat[Ifapairingismaleoptimal,thenitisalsofemalepessimal].BUTIMHO,ithasnothingtodowiththestatisticsshownhere.theoretically,[theoutputofthealgorithmismaleoptimal]onlysaysamongallSTABLEpairings,onlythisonewecanhaveallgentshavetheiroptimalladies,whichmightsuggestthemeanofhappinessisthehighestamongallstablepairings.Andit'sfemalepessimalatthesametime,soIwouldclaimthemeanoffemalehappinesswouldbethelowest(Ididn'tproveit,butlet'ssayitistrue,otherwisethewholediscussionwillbepointlesssincewewouldhavethingsevenmoreunrelatedthanitisnow).BUT,itdoesnotsuggestthehighestmeanofmalehappinesswouldnecessarilybegreaterthanlowestmeanoffemalehappiness.letTbethesetofallstablepairings.mbeafunctionmeasuresmeanmalehappinessofApairingandfbeafunctionmeasuresmeanoffemalehappinessforApairing.Youwouldneedtoprovehigh(m(T))>low(f(T))whichisnotdonebythenote.Ifthatiswhatyouclaimed,it'suptoyoutoproveit'strue.Iamoverworkingsocan'tcookanimmediateexample.Butyoucanlookatmyanswerforproofthatitcouldhappen,assumingthealgoIdownloadedfrommathworksiscorrect,whichIdidnotrejectbecauseofsomesanitychecks.AlsoIrecommendyoutoreplymeundermyanswersothatwedon'thavetobotherthisveryrespondent.andalmostforgot,thatwasaverygoodnote,thanksforsharing.P.S.Iflanguagebothersyou,EnglishisactuallymypreferredlanguagewhenitcomestomathandapparentlyyoucanreadinEnglishandwearediscussingaboutanEnglishsourcesoIwouldlikehaveitthisway.plztellmeifyoudontfeelliketoandfeelfreetowritebackinChineseifyouwill.04:44恋爱中有哪些博弈？-施徐国的回答woeMr回复GengYoungactuallyImightjusthaveanexampleathand.thinkaboutmalepreference[123;123;132]whilewehavefemalepreference:[123;213;312]themaleoptimalone,whichistheoutputisobviously(1,1)(2,2)(3,3)check:man1ishappybecausehe'sgothisdreamgirlman2isokbecausealthohelikesgirl1better,girl1wouldgowithman1,andhissecondchoicelikeshimmost.(12)(21)containsroguecouple(1,1)man3isokforthesamereason.butiflookathappiness,apparentlygirlsarehappierthanboysbecuasetheyallgotwhattheylikemostbutboysdidn't04:58]