間接互惠與合作演化的若干問題研究進(jìn)展

張艷玲 劉愛志 孫長銀

達(dá)爾文的進(jìn)化論認(rèn)為“物競天擇、適者生存”,說明競爭在進(jìn)化中起核心的作用[1].依據(jù)這一理論,在“弱肉強(qiáng)食”的生存斗爭中,適應(yīng)性強(qiáng)的個體勝出,適應(yīng)性差的個體被淘汰.從而在激烈的生存斗爭中,每個個體均會從自身利益出發(fā),變得利己自私、唯利是圖.然而,從細(xì)菌群落到蜂群蟻群,從狼群獅群圍捕獵物到群居的大猩猩,再到復(fù)雜而有序的人類社會,合作行為無處不在[1?4].顯然,幫助對手會降低自身的適應(yīng)度,從而削弱自身的競爭優(yōu)勢,合作的存在看似并不合理.面對廣泛存在的合作行為,達(dá)爾文本人也深感困惑,在其著作中相應(yīng)的解釋只是一筆帶過[5].

合作行為廣泛存在,同時在很多領(lǐng)域中又十分匱乏.研究促進(jìn)合作涌現(xiàn)的機(jī)制有以下三點(diǎn)益處:1)有助于解釋眾多產(chǎn)生原因未知的現(xiàn)象,例如,細(xì)胞的癌變[6]、語言的產(chǎn)生[7]和集群行為[8];2)有助于解決我們面臨的全球性問題,例如,“公地悲劇”[9]、環(huán)境惡化[10]和資源枯竭[11];3)有助于破解互聯(lián)網(wǎng)時代在虛擬世界中我們遇到的新問題,例如,網(wǎng)絡(luò)欺詐[12]等違法犯罪行為.由此可見,研究促進(jìn)合作演化的機(jī)制對人類發(fā)展有著重大的現(xiàn)實(shí)意義和時代緊迫感.

如何研究合作行為的演化?這是一個熱點(diǎn)問題,2005年Science雜志就指出“合作行為如何進(jìn)化”是21世紀(jì)最關(guān)鍵的25個科學(xué)問題之一[13].演化博弈論(Evolutionary game theory)為研究合作的演化提供一個有力的數(shù)學(xué)框架.Smith等首次將von Neumann開創(chuàng)的博弈論觀點(diǎn)(大腦在利益沖突時做出理性決定)擴(kuò)展為根據(jù)自然選擇而得出決定[14],這標(biāo)志著演化博弈論的開創(chuàng).近年來,國內(nèi)外越來越多的學(xué)者利用此理論研究促進(jìn)合作涌現(xiàn)的機(jī)制[15?37].其中最著名的是哈佛大學(xué)的Nowak教授,他對“綜合進(jìn)化論”(這一理論將突變、選擇和進(jìn)化的基本概念整合到一個數(shù)學(xué)框架中)的思想進(jìn)行了擴(kuò)展,將囚徒困境放到演化的群體中進(jìn)行研究.Nowak首次總結(jié)了促進(jìn)合作涌現(xiàn)的5大機(jī)制[38]:親緣選擇(Kin selection)、直接互惠(Direct selection)、間接互惠(Indirect selection)、網(wǎng)絡(luò)互惠(Network reciprocity)和群組選擇(Group selection).親緣選擇意味著,與誰的血緣關(guān)系越近,就越傾向與之合作;直接互惠意味著,今天我?guī)椭?明天你會幫助我;間接互惠意味著,今天我?guī)椭?明天會有他人幫助我;網(wǎng)絡(luò)互惠意味著,個體僅僅與鄰居進(jìn)行博弈,合作者團(tuán)簇最終勝出背叛者團(tuán)簇;群組選擇意味著,競爭既發(fā)生在個體之間,也發(fā)生在群組之間.除了這5大機(jī)制,最近的綜述還歸納出另外5種促進(jìn)合作演化的機(jī)制[39]:綠胡子選擇(Green beard selection)、強(qiáng)互惠性(Strong reciprocity)、有成本的示好(Costly signaling)、集合選擇(Set selection)和選擇性參與(Optional participation).綠胡子選擇意味著,相似性越高的個體之間越容易發(fā)生合作;強(qiáng)互惠性意味著,個體愿意犧牲自身利益懲罰背叛行為;有成本的示好意味著,個體愿意承擔(dān)成本吸引其他個體的關(guān)注;集合選擇意味著,個體僅僅與相同集合的個體進(jìn)行交互;選擇性參與意味著,個體有權(quán)利拒絕與特定個體進(jìn)行博弈.

1 關(guān)于間接互惠的概述

1.1 研究間接互惠的意義

間接互惠是促進(jìn)合作涌現(xiàn)的重要機(jī)制之一.相對于直接互惠,間接互惠不再要求相同的個體間重復(fù)相遇,同時利他個體能夠從第三方獲得收益,這可以很好地解釋陌生個體間的合作行為[40?46].大量的非親緣、非直接的間接互惠行為在人類社會和動物世界中廣泛存在.特別地,人類社會中語言的出現(xiàn)[7,47]、道德規(guī)范的形成[38]、社會的分工[39]以及人類大腦的發(fā)育[47]都與間接互惠密不可分.在經(jīng)濟(jì)全球化和進(jìn)入網(wǎng)絡(luò)時代的背景下,電子商務(wù)大大地增加了陌生個體間交易的頻率,陌生個體間的一次性交互逐步取代傳統(tǒng)的相識個體間的重復(fù)交互[37,48?52].此時的交易主要依賴于聲望和信任,從而局部信息條件下個體信任被利用的“道德風(fēng)險”不斷增大[45].因此,針對間接互惠如何促進(jìn)合作涌現(xiàn)的研究吸引了演化生物學(xué)家、經(jīng)濟(jì)學(xué)家和社會科學(xué)家等學(xué)者的極大興趣.

1.2 間接互惠的分類和研究方法

間接互惠包括 “上游互惠”(Upstream reciprocity)、“下游互惠”(Downstream reciprocity)和 “廣義互惠”(Generalized reciprocity)三種形式[45,53?57].如圖1所示,“上游互惠”指的是,B得到A的幫助后受到激勵,繼而幫助C;“下游互惠”指的是,C觀察到A曾經(jīng)幫助了B,因此幫助A,這是一種建立在聲望基礎(chǔ)上的間接互惠;“廣義互惠”指的是,D觀察到A幫助B,于是D幫助C.“上游互惠”并不能單獨(dú)促進(jìn)合作的涌現(xiàn),只有與直接互惠或者網(wǎng)絡(luò)互惠相結(jié)合才能促進(jìn)合作的涌現(xiàn)[56?57].“下游互惠”和“廣義互惠”均可單獨(dú)促進(jìn)合作的涌現(xiàn),不過前者是研究間接互惠的主流方向,而關(guān)于后者的相關(guān)研究還甚少.目前,針對間接互惠的研究方法主要有理論分析、蒙特卡羅仿真(Monte Carlo simulation)和實(shí)驗(yàn)驗(yàn)證(包括實(shí)驗(yàn)室實(shí)驗(yàn)、實(shí)地實(shí)驗(yàn)和在線實(shí)驗(yàn)).

圖1 間接互惠的三種形式Fig.1 Three kinds of indirect reciprocity

接下來的文章從以下三方面歸納總結(jié)關(guān)于“下游互惠”的研究:經(jīng)典的博弈模型、聲望評估準(zhǔn)則與行為準(zhǔn)則和基于八卦的聲望信息傳播.

2 經(jīng)典的博弈模型

在演化博弈論框架下研究間接互惠,需要將個體之間發(fā)生的交互行為抽象為博弈模型. 目前,常被用來研究間接互惠的博弈模型包括捐助博弈(Donation game)[43?44,58?72]、信任博弈(Trust game)[73?75]、獨(dú)裁者博弈(Dictator game)[76?82]和公共品博弈(Public goods game)[83?88].

1)捐助博弈,如圖2(a)所示.一方為捐助者A,另一方為接受者B:如果A給予B捐助,則A付出成本c且B得到收益b(b＞c);如果A不給予B捐助,則雙方均未獲得收益且沒有損失.

2)信任博弈,如圖2(b)所示.一方為投資者A,另一方為響應(yīng)者B:A將部分資金c(總額為R, 0≤c≤R)給予B,從而B獲得收益r×c(r＞1);隨后,B決定將其獲得的部分收益a(0≤a≤r×c)返還給A.最后,A獲得收益R?c+a,B獲得收益r×c?a.

3)獨(dú)裁者博弈,如圖2(c)所示.一方為獨(dú)裁者A,另一方為接受者B:A將部分資金c(總額為R, 0≤c≤R)分給B.無論A給了B多少,B只能接受,沒有拒絕的權(quán)利,從而B得到收益c,而A獲得其余收益R?c.

4)公共品博弈,如圖2(d)所示.博弈的成員同時向公共資源池進(jìn)行投資,投資總額乘以增益系數(shù)r(1＜r＜博弈人數(shù))后平均分配給所有博弈成員,每個成員的收益為所獲得的回報減去自身的投資額.

3 聲望評估準(zhǔn)則與行為準(zhǔn)則

3.1 常見的聲望評估準(zhǔn)則及其相關(guān)研究

聲望是間接互惠發(fā)揮作用的核心,然而聲望的建立首先面臨的問題是如何評價個體聲望的好與壞,即如何構(gòu)建聲望評估準(zhǔn)則.目前,被廣泛研究的評估準(zhǔn)則包括“一階評估”、“二階評估”和“三階評估”[43?44,59?71,85?101],如表1所示.

“一階評估”在評價個體聲望時僅考慮捐助者行為(是否給予幫助).經(jīng)典的“一階評估”是“形象分?jǐn)?shù)”:當(dāng)捐助者幫助接受者時,捐助者的形象分?jǐn)?shù)增加一分;當(dāng)捐助者拒絕幫助接受者時,捐助者的形象分?jǐn)?shù)減少一分.1998年,Nowak等首次利用“形象分?jǐn)?shù)”構(gòu)建了刻畫間接互惠的數(shù)學(xué)模型,如圖3所示.他們認(rèn)識到間接互惠在促進(jìn)合作演化方面的巨大作用[43]:當(dāng)玩家的聲望由多值“形象分?jǐn)?shù)”確定時,蒙特卡羅仿真表明合作行為在群體中以較高頻率涌現(xiàn).之后,這個結(jié)論被行為實(shí)驗(yàn)證實(shí)[63].與此同時,Nowak等理論分析了二值“形象分?jǐn)?shù)”[43?44].稍后的理論研究表明很多因素導(dǎo)致合作行為在采取二值“形象分?jǐn)?shù)”的群體中消失[64?66,96].這種現(xiàn)象是由于此準(zhǔn)則固有的困境:拒絕幫助形象差的玩家,雖然懲罰了他們,但同時也令自身形象變差[67,97?98].顯然,僅考慮捐助者行為的二值“形象分?jǐn)?shù)”會造成不公正的聲望評價.最近,理論工作揭示了多人博弈[68,99]、三值“形象分?jǐn)?shù)”(好、中性、壞)[69]或特定“一階評估”(觀察者根據(jù)捐贈者在以往多次行動中的表現(xiàn)確定其名聲)[70,100]可以克服這個困境,促進(jìn)合作行為的涌現(xiàn).

圖2 博弈模型及收益矩陣Fig.2 Games and their payoあmatrices

表1 聲望評估準(zhǔn)則Table 1 Reputation evaluation criterion

圖3 經(jīng)典的間接互惠模型Fig.3 Representative model about indirect reciprocity

“二階評估”也能彌補(bǔ)二值“形象分?jǐn)?shù)”固有的缺陷:在評價個體聲望時,不僅考慮捐助者的行為(是否給予捐助),還要考慮接受者的聲望(好、壞).典型的“二階評估”包括“溫和準(zhǔn)則”和“嚴(yán)苛準(zhǔn)則”,如表2所示.二者唯一的不同點(diǎn)在于,前者認(rèn)為拒絕幫助壞人會為捐助者帶來好的聲望,而后者認(rèn)為此行為會為捐助者帶來壞的聲望.學(xué)者在“二階評估”中引入懲罰策略(不僅給被懲罰者帶來損失,而且懲罰者也要承擔(dān)少量損失),發(fā)現(xiàn)對背叛者置之不理比懲罰背叛者更有利于合作的涌現(xiàn)[71].

在“二階評估”基礎(chǔ)上,額外考慮捐贈者的聲望,這種評估準(zhǔn)則被稱為“三階評估”[91?92].例如,名聲差的人通過幫助好名聲之人“收買”好名聲.學(xué)者考察所有可能的“三階評估”,假設(shè)群體最多擁有兩種策略,發(fā)現(xiàn)了8種評估準(zhǔn)則可以令合作行為具有演化穩(wěn)定性[93].這8種準(zhǔn)則如表3所示,具有一些共性:與好人合作(捐助)其名聲為好,而背叛好人(不捐助)則為壞,同時好人背叛壞人不會損壞名聲.值得一提的是,它們均不屬于“一階評估”,而其中兩種屬于“二階評估”,分別為“溫和準(zhǔn)則”和“嚴(yán)苛準(zhǔn)則”.學(xué)者在群體共存多種策略的假設(shè)下對這兩種準(zhǔn)則進(jìn)行研究[94].上述研究均假設(shè)群體共享相同評估準(zhǔn)則,而比較的是不同行為準(zhǔn)則的競爭.鑒于認(rèn)知差異會導(dǎo)致個體對于如何評估聲望的理解不同,學(xué)者也考慮了評估準(zhǔn)則因人而異的情形[95,101].

表2 典型的“二階評估”Table 2 Representative“second-order evaluation”

表3 8種促進(jìn)合作演化的聲望評估準(zhǔn)則Table 3 Eight reputation evaluation criterions which favor the evolution of cooperation

3.2 常見的行為準(zhǔn)則及其相關(guān)研究

關(guān)于間接互惠的早期研究假設(shè)個體僅幫助聲望好的個體,或者個體僅幫助形象分?jǐn)?shù)高于某一閾值的個體[43?44,64?68,96?99]. 這些最簡單的行為準(zhǔn)則(行為準(zhǔn)則是能否捐助的依據(jù))要求個體僅根據(jù)對手的聲望決定自己是否給予捐助.稍后,略微復(fù)雜的行為準(zhǔn)則,例如個體決定是否捐助時需要同時考慮自身和對手的聲望,受到關(guān)注[69?71,89?90,94?95,100?101]. 上述研究主要關(guān)注哪

種聲望評估準(zhǔn)則更有利于合作的演化.最近,學(xué)者們對較為復(fù)雜的行為準(zhǔn)則如何影響合作涌現(xiàn)進(jìn)行了探索[72,87,102].一些學(xué)者考察個體在決定是否捐助時對接受者的聲望有一定的容忍范圍(當(dāng)接受者的聲望在這個范圍內(nèi)則進(jìn)行捐助),通過仿真發(fā)現(xiàn),一定的聲望容忍度有助于合作的涌現(xiàn)[87,102].還有一些研究提出了一種基于向量的行為準(zhǔn)則(捐助者將自身聲望與接受者聲望進(jìn)行比較,當(dāng)至少滿足三種條件中的兩種時則進(jìn)行捐助,這三種條件包括聲望近似、聲望高于自己和聲望低于自己),通過仿真發(fā)現(xiàn),“捐贈者會為與自己聲望近似或者高于自己聲望的接受者進(jìn)行捐助”這種策略在較小的成本收益比下能夠成為占優(yōu)策略,同時促進(jìn)合作的演化[72].

4 基于八卦的聲望信息傳播

直接觀察和八卦(個體之間通過交流,共享彼此的聲望信息)是聲望信息傳播的兩種方式[45,103?104],如圖4所示.當(dāng)群體規(guī)模較小時,個體可以通過直接交互或者直接觀察獲得對方一手的聲望信息.然而隨著群體規(guī)模的擴(kuò)大,直接觀察到所有個體行為變得不大可能,必須通過與第三方交流來分享和傳播二手的聲望信息[104?105].可見在較大的群體中,八卦常常是聲望信息傳播的主要方式.

4.1 關(guān)于八卦的解析研究和仿真研究

一些學(xué)者通過解析和仿真的方式對于八卦如何影響合作的涌現(xiàn)進(jìn)行研究.此時的模型通常假設(shè)觀察者以一定的概率q了解玩家的聲望(通過概率的形式簡單模擬了聲望的局部傳播).針對“形象分?jǐn)?shù)”,Nowak等給出了簡單的數(shù)學(xué)關(guān)系:當(dāng)q高于成本收益比c/b時,合作可以涌現(xiàn)[43?44].在“二階評估”下,類似的條件在兩個調(diào)查中獲得[106?107],這兩個調(diào)查最大區(qū)別在于,當(dāng)觀察者未看到交互過程時,捐贈者的名聲保持不變或者設(shè)定為未知.若將交互劃分為公開和私下兩種(觀察者一直看到公開交互而以概率q看到私下交互),類似的條件仍然滿足[108].上述研究均假設(shè)q為常數(shù),針對q隨時間推移而增大的情形(觀察者越來越可能了解其余個體的聲望),也有學(xué)者進(jìn)行了理論分析[109].

圖4 聲望信息傳播的兩種方式Fig.4 Two ways of reputation dispersal

八卦在傳播聲望信息過程中可能受到噪聲的干擾和謊言的入侵,導(dǎo)致不公正的聲望評價.噪聲一方面來源于不完整的觀察給出不公正的聲望,另一方面來源于在聲望傳播過程中無意地誤導(dǎo)他人;而謊言則是故意傳播虛假的聲望信息而對他人進(jìn)行誤導(dǎo).一項(xiàng)研究在聲望傳播中引入欺騙策略(傳播虛假聲望信息),發(fā)現(xiàn)這種策略在沒有其他機(jī)制的情形下導(dǎo)致群體合作演化的失敗[110].另兩項(xiàng)研究表明:當(dāng)群體中沒有虛假信息傳播時,八卦數(shù)量的增加有助于促進(jìn)合作的演化;而存在噪聲干擾和謊言所導(dǎo)致的不公正評價時,中等數(shù)量的八卦最有利于促進(jìn)合作的演化[111?112].這兩項(xiàng)研究是基于累加的八卦信息進(jìn)行決策,而最近的研究發(fā)現(xiàn)基于最新的八卦信息作出決策更能促進(jìn)合作的演化[113].上述關(guān)于八卦的模型均沒有加入聲望傳播所需的成本(例如時間的消耗).當(dāng)考慮這種成本時,結(jié)果表明間接互惠不再促進(jìn)合作的演化[114].

4.2 關(guān)于八卦的實(shí)驗(yàn)研究

另一部分學(xué)者通過行為實(shí)驗(yàn)的方法對八卦進(jìn)行研究,主要發(fā)現(xiàn)如下.即使個體能夠通過直接交互或者直接觀察獲取他人的一手聲望信息,實(shí)驗(yàn)發(fā)現(xiàn)個體也會傾向于基于八卦信息做出判斷[115?117].八卦所傳播的聲望信息有助于個體甄別合作對象從而避免被欺騙,并有效提高群體的合作水平[88,103,118].當(dāng)八卦將個體的聲望傳播到未來會與其發(fā)生交互的個體時,八卦可以促使個體更加關(guān)注自身聲望并促進(jìn)慷慨行為的產(chǎn)生[82,119?121].八卦按照傳播主題可以被劃分為傳播好名聲和傳播壞名聲兩種,傳播好名聲的八卦更能夠促進(jìn)合作的涌現(xiàn)[115].社會網(wǎng)絡(luò)結(jié)構(gòu)允許個體可以在不同時間從多個來源獲取彼此的聲望信息,這有助于減少信息傳播中可能出現(xiàn)的誤差[122?123].“道德威懾”通過拆穿謊言后的懲罰機(jī)制維護(hù)八卦的可信性,從而促進(jìn)合作的涌現(xiàn)[124].當(dāng)聲望被視為可以買賣的物品時,由于人類具有認(rèn)知和辨別能力以及欺騙者為了購買聲望會付出一定的收益而降低適應(yīng)度,因此,虛假的聲望對合作水平的影響并不明顯[125?126].

5 總結(jié)

合作行為在很多領(lǐng)域中十分匱乏,因此,研究促進(jìn)合作演化的機(jī)制對人類發(fā)展有著重大的現(xiàn)實(shí)意義和時代緊迫感.2005年Science雜志就指出“合作行為如何進(jìn)化”是21世紀(jì)最關(guān)鍵的25個科學(xué)問題之一.在演化博弈論的框架下,研究人員已提出一些促進(jìn)合作演化的機(jī)制,其中間接互惠是促進(jìn)合作演化的最重要機(jī)制之一,并已吸引了演化生物學(xué)家、經(jīng)濟(jì)學(xué)家和社會學(xué)家等學(xué)者的極大興趣.它包括“上游互惠”、“下游互惠”和“廣義互惠”三種方式:“上游互惠”并不能單獨(dú)促進(jìn)合作的涌現(xiàn),只有與直接互惠或者網(wǎng)絡(luò)互惠相結(jié)合才能促進(jìn)合作的涌現(xiàn);“下游互惠”和“廣義互惠”均可單獨(dú)促進(jìn)合作的涌現(xiàn),不過前者是研究間接互惠的主流方向,而關(guān)于后者的相關(guān)研究還甚少.本文關(guān)注的是以聲望為核心的“下游互惠”,具體而言,個體通過幫助他人建立自己在群體中的好聲望,從而期待未來獲得他人的幫助.

本文從三個方面對關(guān)于“下游互惠”的研究進(jìn)行總結(jié).首先,回顧了在演化博弈論框架下研究間接互惠的博弈模型:捐助博弈、信任博弈、獨(dú)裁者博弈和公共品博弈.其次,回顧了被廣泛研究的三類聲望評估準(zhǔn)則:“一階評估”、“二階評估”和“三階評估”.相關(guān)研究假設(shè)采用比較簡單的行為準(zhǔn)則,而聚焦于哪種聲望評估準(zhǔn)則能夠促進(jìn)合作的演化.同時回顧了關(guān)于較為復(fù)雜的行為準(zhǔn)則如何促進(jìn)合作演化的一些研究.再次,回顧了利用解析方法和仿真方法對八卦如何促進(jìn)合作演化進(jìn)行的研究.解析研究一般假設(shè)個體以一定的概率獲得彼此的聲望信息,這個概率通常為常值,個別研究假設(shè)其可隨時間變化.仿真研究假設(shè)更加復(fù)雜的模型,例如八卦不再如實(shí)傳遞信息,而是融入了噪聲和謊言.同時也回顧了利用行為實(shí)驗(yàn)對八卦進(jìn)行的研究,內(nèi)容十分寬泛.

6 未來展望

基于聲望的間接互惠具有廣闊的研究前景,其未來可能的研究方向有復(fù)雜網(wǎng)絡(luò)上的間接互惠、聲望傳播系統(tǒng)的魯棒性、聲望共享系統(tǒng)的建立和間接互惠在P2P網(wǎng)絡(luò)中的應(yīng)用.

6.1 復(fù)雜網(wǎng)絡(luò)上的間接互惠

目前,大部分理論研究均是在混合均勻群體中獲得的[127?129].然而,絕大多數(shù)現(xiàn)實(shí)社會中的群體并非混合均勻的,個體之間的交互和聲望傳播都是利用復(fù)雜網(wǎng)絡(luò)實(shí)現(xiàn)的.在演化博弈論框架下,未涉及間接互惠的靜態(tài)復(fù)雜網(wǎng)絡(luò)和動態(tài)復(fù)雜網(wǎng)絡(luò)已被廣泛研究[130?142],而只有較少研究關(guān)注復(fù)雜網(wǎng)絡(luò)上的間接互惠[143?147].文獻(xiàn)[143]發(fā)現(xiàn)在社會網(wǎng)絡(luò)中,根據(jù)聲望選擇交互伙伴這種行為有助于促進(jìn)合作的演化.文獻(xiàn)[144?145]假設(shè)小世界網(wǎng)絡(luò)和無標(biāo)度網(wǎng)絡(luò)等復(fù)雜網(wǎng)絡(luò)可以重構(gòu)(斷邊重連),發(fā)現(xiàn)聲望共享“聯(lián)盟”的存在有助于促進(jìn)群體合作.文獻(xiàn)[146?147]假設(shè)直接互惠和間接互惠同時存在于網(wǎng)絡(luò)上,發(fā)現(xiàn)間接互惠有助于刻畫現(xiàn)實(shí)社會的無標(biāo)度網(wǎng)絡(luò)的形成.

雖然科研人員已經(jīng)對于復(fù)雜網(wǎng)絡(luò)上的間接互惠進(jìn)行了一些初步的探索,但是還有很多問題需要進(jìn)一步研究.例如,上述研究均認(rèn)為聲望是通過觀察獲得的公共信息(即聲望全局可知),然而在現(xiàn)實(shí)社會中,聲望多數(shù)情況下是通過八卦進(jìn)行傳播的,由此可見,靜態(tài)或動態(tài)復(fù)雜網(wǎng)絡(luò)上八卦這種聲望傳播方式如何影響合作的演化是一個值得深入研究的方向.

6.2 聲望傳播系統(tǒng)的魯棒性

八卦是大規(guī)模群體中聲望傳播的主要方式,它在傳播聲望信息過程中可能受到噪聲的干擾和謊言的入侵,從而導(dǎo)致不公正的聲望評價.噪聲一方面來源于不完整的觀察給出不公正的聲望,另一方面來源于在聲望傳播過程中無意地誤導(dǎo)他人;而謊言則是故意傳播虛假的聲望信息而對他人進(jìn)行誤導(dǎo).一項(xiàng)研究在聲望傳播中引入欺騙策略(傳播虛假聲望信息),發(fā)現(xiàn)這種策略在沒有其他機(jī)制的情形下導(dǎo)致群體合作演化的失敗[110].另兩項(xiàng)研究表明:當(dāng)群體中沒有虛假信息傳播時,八卦數(shù)量的增加有助于促進(jìn)合作的演化;而存在噪聲干擾和謊言所導(dǎo)致的不公正評價時,中等數(shù)量的八卦最有利于促進(jìn)合作的演化[111?112].這兩項(xiàng)研究是基于累加的八卦信息進(jìn)行決策,而最近的研究發(fā)現(xiàn)基于最新的八卦信息作出決策更能促進(jìn)合作的演化[113].

科研人員已經(jīng)對于加入噪聲和謊言的八卦進(jìn)行了初步的探索,但已研究的模型還有很多可以改進(jìn)的地方,相應(yīng)的結(jié)果并不全面.在未來的研究中,我們需要建立更加合適的模型,結(jié)合現(xiàn)實(shí)生活提出能夠抵抗噪聲干擾和謊言入侵的八卦,令聲望傳播系統(tǒng)具有魯棒性,進(jìn)而發(fā)現(xiàn)能夠促進(jìn)合作演化且強(qiáng)抗干擾的機(jī)制.

6.3 聲望共享系統(tǒng)的建立

以往關(guān)于間接互惠的絕大多數(shù)研究均沒有考慮個體間聲望共享所需的成本.但在實(shí)際中,人們在評價和分享他人聲望的過程中需要耗費(fèi)時間和精力.例如,在網(wǎng)絡(luò)購物平臺中,人們需要花費(fèi)時間和精力去評價所購買的產(chǎn)品或者服務(wù).近期的一項(xiàng)研究表明,當(dāng)考慮聲望共享所需成本時,間接互惠無法促進(jìn)合作的涌現(xiàn)[114].

隨著經(jīng)濟(jì)全球化和網(wǎng)絡(luò)時代的到來,陌生個體間的交易日益頻繁.為什么人們會不計成本、不厭其煩地和陌生人分享他人的真實(shí)聲望呢?目前的研究還沒有給出一個滿意的答復(fù).因此,我們需要針對考慮聲望共享所需成本的模型,提出能夠建立聲望共享系統(tǒng)且促進(jìn)合作涌現(xiàn)的有效機(jī)制.

6.4 間接互惠在P2P網(wǎng)絡(luò)中的應(yīng)用

近年來,P2P(Peer to peer)網(wǎng)絡(luò)應(yīng)用廣泛,因此對其研究發(fā)展快速.在P2P網(wǎng)絡(luò)中,參與者共享自身所擁有的一部分硬件資源(存儲能力、網(wǎng)絡(luò)連接能力和打印機(jī)等),這些共享資源通過網(wǎng)絡(luò)提供服務(wù)和內(nèi)容,能被其他對等節(jié)點(diǎn)(Peer)直接訪問而無需經(jīng)過中間實(shí)體.在此網(wǎng)絡(luò)中的參與者既是資源、服務(wù)和內(nèi)容的提供者(Server),又是資源、服務(wù)和內(nèi)容的獲取者(Client).合作是確保所有參與者獲得所需服務(wù)的關(guān)鍵,出于惡意和自私的非合作行為往往導(dǎo)致參與者獲得較少服務(wù)甚至一無所獲.消除非合作行為的有效機(jī)制包括信任機(jī)制和激勵機(jī)制.信任機(jī)制指的是根據(jù)參與者的交互歷史計算他的可信任值[148?153],例如,eBay聲望系統(tǒng)[151]、Beta聲望系統(tǒng)[152]、Eigentrust聲望系統(tǒng)[148]和Powertrust聲望系統(tǒng)[153].激勵機(jī)制包括金錢激勵和非金錢激勵[154?157].

鑒于 P2P網(wǎng)絡(luò)中個人利益和集體利益相沖突,經(jīng)典博弈理論已被廣泛用來研究此類網(wǎng)絡(luò)[154,157?160].不過經(jīng)典博弈理論假設(shè)參與者完全理性且擁有全局信息.這些假設(shè)并不現(xiàn)實(shí),同時經(jīng)典博弈理論不能描述參與者策略的動態(tài)演化過程及策略在整個系統(tǒng)中的傳播過程.近來,可以克服上述缺點(diǎn)的演化博弈論被用來研究P2P網(wǎng)絡(luò)[155,161?165].文獻(xiàn)[161]假設(shè)P2P網(wǎng)絡(luò)是混合均勻且有無限節(jié)點(diǎn),并利用復(fù)制動力學(xué)研究三種激勵機(jī)制的穩(wěn)定性.文獻(xiàn)[162]同樣利用復(fù)制動力學(xué)發(fā)現(xiàn)一種延拓的模仿動力學(xué)可以改進(jìn)整個網(wǎng)絡(luò)路徑選擇的效率,從而避免路徑上的過載或長延遲.文獻(xiàn)[163]假設(shè)P2P網(wǎng)絡(luò)具有有限節(jié)點(diǎn),分別在混合均勻網(wǎng)絡(luò)和同型結(jié)構(gòu)網(wǎng)絡(luò)上研究一種激勵機(jī)制(Reciprocation-based incentive mechanism).文獻(xiàn)[164]將關(guān)于同類激勵機(jī)制的研究推廣到異型結(jié)構(gòu)的P2P網(wǎng)絡(luò).文獻(xiàn)[155,165]假設(shè)P2P網(wǎng)絡(luò)具有有限節(jié)點(diǎn),利用計算機(jī)仿真調(diào)查兩種信任機(jī)制.上述研究是針對一般性的P2P網(wǎng)絡(luò),還有一些研究利用演化博弈論分析特殊的P2P網(wǎng)絡(luò),例如基于P2P的無線傳感網(wǎng)絡(luò)[166?169]和基于P2P的車輛自組織網(wǎng)絡(luò)[170].

科研人員已利用演化博弈論對P2P網(wǎng)絡(luò)進(jìn)行了一些探索,本文主體部分總結(jié)了在演化博弈論框架下對于間接互惠的研究成果,一個自然的想法是將這些研究思路應(yīng)用到關(guān)于P2P網(wǎng)絡(luò)的研究中.大體思路有以下4點(diǎn):

1)聲望評估準(zhǔn)則可視作信任機(jī)制.將“一階評估”、“二階評估”或“三階評估”作為信任機(jī)制集合,尋找能夠令P2P網(wǎng)絡(luò)中合作行為穩(wěn)定的信任機(jī)制.

2)行為準(zhǔn)則可視為激勵機(jī)制.將已研究過的行為準(zhǔn)則構(gòu)成激勵機(jī)制集合,尋找能夠令P2P網(wǎng)絡(luò)高效、有序運(yùn)行的激勵機(jī)制.

3)在P2P網(wǎng)絡(luò)的聲望傳播過程中融入八卦,研究八卦對于網(wǎng)絡(luò)穩(wěn)定性的影響.

4)可以將深度學(xué)習(xí)方法[171]與間接互惠機(jī)制結(jié)合,來研究網(wǎng)絡(luò)控制問題[172?174].

致謝

對北京科技大學(xué)自動化學(xué)院劉劍、孟祥鈺、古鵬飛和王雷等同學(xué)給予的幫助表示感謝!

1 Darwin C.On the origin of species by means of natural selection.Science,1963,71(6):354?357

2 McDonald D B.Cooperation among animals:an evolutionary perspective.Lee Alan Dugatkin.The Quarterly Review of Biology,1998,73(3):387?388

3 Nowak M A,Sigmund K.Evolutionary dynamics of biological games.Science,2004,303(5659):793?799

4 Clutton-Brock T.Cooperation between non-kin in animal societies.Nature,2009,462(7269):51?57

5 Darwin C.The Works of Charles Darwin,Volume 15:On the Origin of Species 1859.New York:New York University Press,2010.69?83

6 Axelrod R,Axelrod D E,Pienta K J.Evolution of cooperation among tumor cells.Proceedings of the National Academy of Sciences of the United States of America,2006, 103(36):13474?13479

7 Smith E A.Communication and collective action:language and the evolution of human cooperation.Evolution and Human Behavior,2010,31(4):231?245

8 Tuyls K,Parsons S.What evolutionary game theory tells us about multiagent learning.Arti fi cial Intelligence,2007, 171(7):406?416

9 Hardin G.The tragedy of the commons.Science,1968, 162(3859):1243?1248

10 Milinski M,Sommerfeld R D,Krambeck H J,Reed F A, Marotzke J.The collective-risk social dilemma and the prevention of simulated dangerous climate change.Proceedings of the National Academy of Sciences of the United States of America,2008,105(7):2291?2294

11 Requejo R J,Camacho J.Evolution of cooperation mediated by limiting resources:connecting resource based models and evolutionary game theory.Journal of Theoretical Biology, 2011,272(1):35?41

12 Zhang Y,He J H.Research on the mobile net business knowledge sharing strategy of fraud evade.Applied Mechanics and Materials,2014,631?632:1171?1173

13 Pennisi E.How did cooperative behavior evolve?Science, 2005,309(5731):93

14 Smith J M,Price G R.The logic of animal con fl ict.Nature, 1973,246(5427):15?18

15 Fu F.Evolutionary Games and Evolution of Cooperation [Ph.D.dissertation],Peking University,China,2009.

16 Chen X J.Evolutionary Dynamics of Cooperation in Complex Networks[Ph.D.dissertation],Peking University, China,2010.

17 Wu B.Evolutionary Game Dynamics in Finite Populations [Ph.D.dissertation],Peking University,China,2011.

18 Wang J.Evolutionary Game Dynamics in Populations [Ph.D.dissertation],Peking University,China,2011.

19 Zhang C Y.Cooperation in Evolutionary Games on Networks of Agents[Ph.D.dissertation],Peking University, China,2012.

20 Zhang J L.Cooperation Mechanisms in Evolutionary Games [Ph.D.dissertation],Peking University,China,2013.

21 Wu T.Evolutionary Cooperation Dynamics[Ph.D.dissertation],Peking University,China,2013.

22 Yang Z H.Evolutionary Games and Evolutionary Cooperation Dynamics in Complex Networks[Ph.D.dissertation], Xidian University,China,2014.

23 Zhang Y L.Two Theoretical Methods upon the Evolution of Cooperation in Finite Populations and the Applications [Ph.D.dissertation],Peking University,China,2015.

24 Cong R.Coevolutionary Games on Complex Networks [Ph.D.dissertation],Xidian University,China,2014.

25 Du J M.Evolutionary Game Dynamics in Complex Systems [Ph.D.dissertation],Xidian University,China,2016.

26 Li K.Evolutionary Dynamics in Collective Behavior[Ph.D. dissertation],Peking University,China,2016.

27 Wang Long,Fu Feng,Chen Xiao-Jie,Wang Jing,Li Zhuo-Zheng,Xie Guang-Ming,Chu Tian-Guang.Evolutionary games on complex networks.CAAI Transactions on Intelligent Systems,2007,2(2):1?10 (王龍,伏鋒,陳小杰,王靖,李卓政,謝廣明,楚天廣.復(fù)雜網(wǎng)絡(luò)上的演化博弈.智能系統(tǒng)學(xué)報,2007,2(2):1?10)

28 Wang Long,Fu Feng,Chen Xiao-Jie,Wang Jing,Wu Bin,Chu Tian-Guang,Xie Guang-Ming.Collective decisionmaking over complex networks.CAAI Transactions on Intelligent Systems,2008,3(2):95?108 (王龍,伏鋒,陳小杰,王靖,武斌,楚天廣,謝廣明.復(fù)雜網(wǎng)絡(luò)上的群體決策.智能系統(tǒng)學(xué)報,2008,3(2):95?108)

29 Wang Long,Wang Jing,Wu Bin.Quantum games:new methodologies and strategies.CAAI Transactions on Intelligent Systems,2008,3(4):294?304 (王龍,王靖,武斌.量子博弈:新方法與新策略.智能系統(tǒng)學(xué)報, 2008,3(4):294?304)

30 Wang Long,Wu Te,Zhang Yan-Ling.Feedback mechanism in coevolutionary games.Control Theory&Applications, 2014,31(7):823?836 (王龍,吳特,張艷玲.共演化博弈中的反饋機(jī)制.控制理論與應(yīng)用, 2014,31(7):823?836)

31 Boccabella A,Natalini R,Pareschi L.On a continuous mixed strategies model for evolutionary game theory.Kinetic&Related Models,2011,4(1):187?213

32 Salimi Sartakhti J,Manshaei M H,Sadeghi M.MMP-TIMP interactions in cancer invasion: an evolutionary gametheoretical framework.Journal of Theoretical Biology,2017, 412:17?26

33 Perc M,Jordan J J,Rand D G,Wang Z,Boccaletti S,Szolnoki A.Statistical physics of human cooperation.Physics Reports,2017,687:1?51

34 Wang Z,Jusup M,Wang R W,Shi L,Iwasa Y,Moreno Y,Kurths J.Onymity promotes cooperation in social dilemma experiments.Science Advances,2017,3(3):Article No.e1601444

35 Allen B,Lippner G,Chen Y T,Fotouhi B,Momeni N,Yau S T,Nowak M A.Evolutionary dynamics on any population structure.Nature,2017,544(7649):227?230

36 Taylor C,Nowak M A.Transforming the dilemma.Evolution,2007,61(10):2281?2292

37 Rand D G,Nowak M A.Human cooperation.Trends in Cognitive Sciences,2013,17(8):413?425

38 Nowak M A.Five rules for the evolution of cooperation.Science,2006,314(5805):1560?1563

39 Zaggl M A.Eleven mechanisms for the evolution of cooperation.Journal of Institutional Economics,2014,10(2): 197?230

40 Boyd R,Richerson P J.The evolution of indirect reciprocity.Social Networks,1989,11(3):213?236

41 Wedekind C.Give and ye shall be recognized.Science,1998, 280(5372):2070?2071

42 Ferri′ere R.Evolutionary biology:help and you shall be helped.Nature,1998,393(6685):517?519

43 Nowak M A,Sigmund K.Evolution of indirect reciprocity by image scoring.Nature,1998,393(6685):573?577

44 Nowak M A,Sigmund K.The dynamics of indirect reciprocity.Journal of Theoretical Biology,1998,194(4): 561?574

45 Nowak M A,Sigmund K.Evolution of indirect reciprocity.Nature,2005,437(6685):1291?1298

46 Wedekind C,Braithwaite A V A.The long-term bene fi ts of human generosity in indirect reciprocity.Current Biology, 2002,12(12):1012?1015

47 Gardenfors P.Games,Actions and Social Software.Berlin: Springer-Verlag,2012.164?183

48 Resnick P,Kuwabara K,Zeckhauser R,Zeckhauser R,Friedman E.Reputation systems.Communications of the ACM, 2000,43(12):45?48

49 Bolton G E,Katok E,Ockenfels A.How eあective are electronic reputation mechanisms?An experimental investigation.Management Science,2004,50(11):1587?1602

50 Resnick P,Zeckhauser R,Swanson J R,Lockwood K.The value of reputation on eBay:a controlled experiment.Experimental Economics,2006,9(2):79?101

51 Geunes J,Ak?cali E,Pardalos P M,Romeijn H E,Shen Z J M.Applications of Supply Chain Management and E-Commerce Research.Boston: Springer-Verlag,2005. 195?216

52 Lucking-Reiley D,Bryan D,Prasad N,Reeves D.Pennies from eBay:the determinants of price in online auctions.The Journal of Industrial Economics,2007,55(2):223?233

53 Greiner B,Levati M V.Indirect reciprocity in cyclical networks:an experimental study.Journal of Economic Psychology,2003,26(5):711?731

54 Pfeiあer T,Rutte C,Killingback T,Taborsky M,Bonhoeffer S.Evolution of cooperation by generalized reciprocity.Proceedings of the Royal Society B,2005,272(1568): 1115?1120

55 Chiong R,Kirley M.Promotion of cooperation in social dilemma games via generalised indirect reciprocity.Connection Science,2015,27(4):417?433

56 Nowak M A,Roch S.Upstream reciprocity and the evolution of gratitude.Proceedings of the Royal Society B,2007, 274(1610):605?610

57 Iwagami A,Masuda N.Upstream reciprocity in heterogeneous networks.Journal of Theoretical Biology,2010, 265(3):297?305

58 Roberts G.Partner choice drives the evolution of cooperation via indirect reciprocity.PLoS One,2015,10(6):Article No.e0129442

59 Swakman V,Molleman L,Ule A,Egas M.Reputation-based cooperation:empirical evidence for behavioral strategies.Evolution and Human Behavior,2016,37(3):230?235

60 dos Santos M,Plac′? S,Wedekind C.Stochasticity in economic losses increases the value of reputation in indirect reciprocity.Scienti fi c Reports,2015,5:Article No.18182

61 Berger U,Gr¨une A.On the stability of cooperation under indirect reciprocity with fi rst-order information.Games and Economic Behavior,2016,98:19?33

62 Tian L L,Li M C,Wang Z.Cooperation enhanced by indirect reciprocity in spatial prisoner′s dilemma games for social P2P systems.Physica A:Statistical Mechanics and its Applications,2016,462:1252?1260

63 Wedekind C,Milinski M.Cooperation through image scoring in humans.Science,2000,288(5467):850?852

64 LeimarO,HammersteinP.Evolution ofcooperation through indirect reciprocity.Proceedings of the Royal Society B,2001,268(1468):745?753

65 Milinski M,Semmann D,Bakker T C M,Krambeck H J. Cooperation through indirect reciprocity:image scoring or standing strategy?Proceedings of the Royal Society B, 2001,268(1484):2495?2501

66 Panchanathan K,Boyd R.A tale of two defectors:the importance of standing for evolution of indirect reciprocity.Journal of Theoretical Biology,2003,224(1):115?126

67 Fehr E,G¨achter S.Altruistic punishment in humans.Nature,2002,415(6868):137?140

68 Suzuki S,Akiyama E.Evolution of indirect reciprocity in groups of various sizes and comparison with direct reciprocity.Journal of Theoretical Biology,2007,245(3): 539?552

69 Tanabe S,Suzuki H,Masuda N.Indirect reciprocity with trinary reputations.Journal of Theoretical Biology,2013, 317:338?347

70 Berger U.Learning to cooperate via indirect reciprocity.Games and Economic Behavior,2011,72(1):30?37

71 Ohtsuki H,Iwasa Y,Nowak M A.Indirect reciprocity provides only a narrow margin of eきciency for costly punishment.Nature,2009,457(7225):79?82

72 Whitaker R M,Colombo G B,Allen S M,Dunbar R I M. A dominant social comparison heuristic unites alternative mechanisms for the evolution of indirect reciprocity.Scienti fi c Reports,2016,6:Article No.31459

73 Esp′?n A M,Exadaktylos F,Neyse L.Heterogeneous motives in the trust game:a tale of two roles.Frontiers in Psychology,2016,7:Article No.728

74 Burks S V,Carpenter J P,Verhoogen E.Playing both roles in the trust game.Journal of Economic Behavior&Organization,2003,51(2):195?216

75 Wu J H,Balliet D,Van Lange P A M.Gossip versus punishment:the eきciency of reputation to promote and maintain cooperation.Scienti fi c Reports,2016,6:Article No.23919

76 Eckel C C,Grossman P J.Altruism in anonymous dictator games.Games and Economic Behavior,1996,16(2): 181?191

77 Bardsley N.Dictator game giving:altruism or artefact?Experimental Economics,2008,11(2):122?133

78 Engel C.Dictator games:a meta study.Experimental Economics,2011,14(4):583?610

79 Deng X Y,Liu Q,Sadiq R,Deng Y.Impact of roles assignation on heterogeneous populations in evolutionary dictator game.Scienti fi c Reports,2014,4:Article No.6937

80 Schank J C,Smaldino P E,Miller M L.Evolution of fairness in the dictator game by multilevel selection.Journal of Theoretical Biology,2015,382:64?73

81 Strang S,Grote X,Kuss K,Park S Q,Weber B.Generalized negative reciprocity in the dictator game-how to interrupt the chain of unfairness.Scienti fi c Reports,2016,6:Article No.22316

82 Piazza J,Bering J M.Concerns about reputation via gossip promote generous allocations in an economic game.Evolution and Human Behavior,2008,29(3):172?178

83 Milinski M,Semmann D,Krambeck H J.Reputation helps solve the‘tragedy of the commons’.Nature,2002, 415(6870):424?426

84 Hauert C,De Monte S,Hofbauer J,Sigmund K.Replicator dynamics for optional public good games.Journal of Theoretical Biology,2002,218(2):187?194

85 Brandt H,Hauert C,Sigmund K.Punishment and reputation in spatial public goods games.Proceedings of the Royal Society B,2003,270(1519):1099?1104

86 Hauert C.Replicator dynamics of reward&reputation in public goods games.Journal of Theoretical Biology,2010, 267(1):22?28

87 Li A M,Wu T,Cong R,Wang L.One step memory of group reputation is optimal to promote cooperation in public goods games.EPL,2013,103(3):Article No.30007

88 Feinberg M,Willer R,Schultz M.Gossip and ostracism promote cooperation in groups.Psychological Science,2014, 25(3):656?664

89 Sigmund K.Moral assessment in indirect reciprocity.Journal of Theoretical Biology,2012,299:25?30

90 Fehr E,Fischbacher U.Social norms and human cooperation.Trends in Cognitive Sciences,2004,8(4):185?190

91 Ohtsuki H,Iwasa Y.How should we de fi ne goodness?—reputation dynamics in indirect reciprocity.Journal of Theoretical Biology,2004,231(1):107?120

92 Brandt H,Sigmund K.The logic of reprobation:assessment and action rules for indirect reciprocation.Journal of Theoretical Biology,2004,231(4):475?486

93 Ohtsuki H,Iwasa Y.The leading eight:social norms that can maintain cooperation by indirect reciprocity.Journal of Theoretical Biology,2006,239(4):435?444

94 Ohtsuki H,Iwasa Y.Global analyses of evolutionary dynamics and exhaustive search for social norms that maintain cooperation by reputation.Journal of Theoretical Biology, 2007,244(3):518?531

95 Pacheco J M,Santos F C,Chalub F A C C.Stern-judging: a simple,successful norm which promotes cooperation under indirect reciprocity.PLoS Computational Biology,2007, 2(12):Article No.e178

96 Ohtsuki H.Reactive strategies in indirect reciprocity.Journal of Theoretical Biology,2004,227(3):299?314

97 Dawes R M,Messick D M.Social dilemmas.International Journal of Psychology,2000,35(2):111?116

98 Fehr E,Fischbacher U.The nature of human altruism.Nature,2003,425(6960):785?791

99 Suzuki S,Akiyama E.Three-person game facilitates indirect reciprocity under image scoring.Journal of Theoretical Biology,2007,249(1):93?100

100 Berger U,Gr¨une A.Evolutionary Stability of Indirect Reciprocity by Image Scoring,Department of Economics Working Papers,WU Vienna University of Economics and Business,Vienna,2014.1?22

101 Uchida S,Sigmund K.The competition of assessment rules for indirect reciprocity.Journal of Theoretical Biology,2010, 263(1):13?19

102 Ding H,Cao L,Ren Y Z,Choo K K R,Shi B Y.Reputationbased investment helps to optimize group behaviors in spatial lattice networks.PLoS One,2016,11(9):Article No.e0162781

103 Dunbar R I M.Gossip in evolutionary perspective.Review of General Psychology,2004,8(2):100?110

104 Foster E K.Research on gossip:taxonomy,methods,and future directions.Review of General Psychology,2004,8(2): 78?99

105 Anderson C,Shirako A.Are individuals′reputations related to their history of behavior?Journal of Personality and Social Psychology,2008,94(2):320?333

106 Uchida S.Eあect of private information on indirect reciprocity.Physical Review E,2010,82(2):Article No.036111

107 Nakamura M,Masuda N.Indirect reciprocity under incomplete observation.PLoS Computational Biology,2011,7(7): Article No.e1002113

108 Ohtsuki H,Iwasa Y,Nowak M A.Reputation eあects in public and private interactions.PLoS Computational Biology, 2015,11(11):Article No.e1004527

109 Brandt H,Sigmund K.Indirect reciprocity,image scoring, and moral hazard.Proceedings of the National Academy of Sciences of the United States of America,2005,102(7): 2666?2670

110 Sz′amad′o S,Szalai F,Scheuring I.Deception undermines the stability of cooperation in games of indirect reciprocity.PLoS One,2016,11(1):Article No.e0147623

111 Nakamaru M,Kawata M.Evolution of rumours that discriminate lying defectors.Evolutionary Ecology Research, 2004,6(2):261?283

112 Seki M,Nakamaru M.A model for gossip-mediated evolution of altruism with various types of false information by speakers and assessment by listeners.Journal of Theoretical Biology,2016,407:90?105

113 Franks H,Griきths N.Robust reputation in decentralized markets.Computational Intelligence,2015,31(4):569?592

114 Suzuki S,Kimura H.Indirect reciprocity is sensitive to costs of information transfer.Scienti fi c Reports,2013,3:Article No.1435

115 Sommerfeld R D,Krambeck H J,Semmann D,Milinski M. Gossip as an alternative for direct observation in games of indirect reciprocity.Proceedings of the National Academy of Sciences of the United States of America,2007,104(44): 17435?17440

116 Sommerfeld R D,Krambeck H J,Milinski M.Multiple gossip statements and their eあect on reputation and trustworthiness.Proceedings of the Royal Society B,2008, 275(1650):2529?2536

117 Lorenz J,Rauhut H,Schweitzer F,Helbing D.How social in fl uence can undermine the wisdom of crowd eあect.Proceedings of the National Academy of Sciences of the United States of America,2011,108(22):9020?9025

118 Giardini F,Norling E.Multi-Agent-Based Simulation XV. Switzerland:Springer-Verlag,2014.104?118

119 Wu J H,Balliet D,Van Lange P A M.Reputation management:why and how gossip enhances generosity.Evolution and Human Behavior,2016,37(3):193?201

120 Wu J H,Balliet D,Van Lange P A M.When does gossip promote generosity?Indirect reciprocity under the shadow of the future.Social Psychological and Personality Science, 2015,6(8):923?930

121 Wu J H,Balliet D,Van Lange P A M.Reputation,gossip, and human cooperation.Social and Personality Psychology Compass,2016,10(6):350?364

122 Hess N H,Hagen E H.Psychological adaptations for assessing gossip veracity.Human Nature,2006,17(3):337?354

123 Giardini F,Vilone D.Evolution of gossip-based indirect reciprocity on a bipartite network.Scienti fi c Reports,2016, 6:Article No.37931

124 Giardini F.Deterrence and transmission as mechanisms ensuring reliability of gossip.Cognitive Processing,2012, 13(S2):465?475

125 Pfeiあer T,Tran L,Krumme C,Rand D G.The value of reputation.Journal of the Royal Society Interface,2012,9(76): 2791?2797

126 Antonioni A,S′anchez A,Tomassini M.Cooperation survives and cheating pays in a dynamic network structure with unreliable reputation.Scienti fi c Reports,2016,6:Article No.27160

127 Zhang Y L,Fu F,Wu T,Xie G M,Wang L.A tale of two contribution mechanisms for nonlinear public goods.Scienti fi c Reports,2013,3:Article No.2021

128 Zhang Y L,Wu T,Cheng X J,Xie G M,Wang L.Mixed strategy under generalized public goods games.Journal of Theoretical Biology2013,334:52?60

129 Zhang Y L,Fu F,Wu T,Xie G M,Wang L.Inertia in strategy switching transforms the strategy evolution.Physical Review E,2011,84(6):Article No.066103

130 Lieberman E,Hauert C,Nowak M A.Evolutionary dynamics on graphs.Nature,2005,433(7023):312?316

131 Ohtsuki H,Hauert C,Lieberman E,Nowak M A.A simple rule for the evolution of cooperation on graphs and social networks.Nature,2006,441(7092):502?505

132 Nowak M A,Tarnita C E,Antal T.Evolutionary dynamics in structured populations.Philosophical Transactions of the Royal Society of London,2009,365(1537):19?30

133 Hauert C,Imhof L A.Evolutionary games in deme structured, fi nite populations.Journal of Theoretical Biology, 2012,299:106?112

134 Vilone D,Giardini F,Paolucci M.Partner selection supports reputation-based cooperation in a Public Goods Game.Social Science Electronic Publishing,2014.

135 Eあerson C,Lalive R,Fehr E.The coevolution of cultural groups and ingroup favoritism.Science,2008,321(5897): 1844?1849

136 Perc M,Szolnoki A.Coevolutionary games— a mini review.Biosystems,2010,99(2):109?125

137 Fehl K,Van der Post D J,Semmann D.Co-evolution of behaviour and social network structure promotes human cooperation.Ecology Letters,2011,14(6):546?551

138 Wang J,Suri S,Watts D J.Cooperation and assortativity with dynamic partner updating.Proceedings of the National Academy of Sciences of the United States of America,2012, 109(36):14363?14368

139 Jordan J J,Rand D G,Arbesman S,Fowler J H,Christakis N A.Contagion of cooperation in static and fl uid social networks.PLoS One,2013,8(6):Article No.e66199

140 Zhang Y L,Liu A Z,Sun C Y.Impact of migration on the multi-strategy selection in fi nite group-structured populations.Scienti fi c Reports,2016,6:Article No.35114

141 Zhang Y L,Su Q,Sun C Y.Intermediate-range migration furnishes a narrow margin of eきciency in the two-strategy competition.PLoS One,2016,11(5):Article No.e0155787

142 Zhang Y L,Fu F,Chen X J,Xie G M,Wang L.Cooperation in group-structured populations with two layers of interactions.Scienti fi c Reports,2015,5:Article No.17446

143 Fu F,Hauert C,Nowak M A,Wang L.Reputation-based partner choice promotes cooperation in social networks.Physical Review E,2008,78(2):Article No.026117

144 Peleteiro A,Burguillo J C,Chong S Y.Exploring indirect reciprocity in complex networks using coalitions and rewiring.In:Proceedings of the 2014 International Conference on Autonomous Agents and Multi-agent Systems. Paris,France:ACM,2014.669?676

145 Ding H,Huang J Y,Chen Y F,Ren Y Z.Don′t speak to strangers: the suspicious strategy can help to improve cooperation in spatial donation game.In:Proceedings of the 2015 IEEE International Conference on Computer and Information Technology;Ubiquitous Computing and Communications;Dependable,Autonomic and Secure Computing;Pervasive Intelligence and Computing (CIT/IUCC/DASC/PICOM).Liverpool,Britain:IEEE, 2015.1954?1959

146 Phelps S.Emergence of social networks via direct and indirect reciprocity.Autonomous Agents and Multi-Agent Systems,2013,27(3):355?374

147 Han X,Shen Z S,Wang W X,Lai Y C,Grebogi C.Reconstructing direct and indirect interactions in networked public goods game.Scienti fi c Reports,2016,6:Article No.30241

148 Kamvar S D,Schlosser M T,Garcia-Molina H.The eigentrust algorithm for reputation management in P2P networks.In:Proceedings of the 12th International Conference on World Wide Web.Budapest,Hungary:ACM,2003. 640?651

149 Xiong L,Liu L.PeerTrust:supporting reputation-based trust for peer-to-peer electronic communities.IEEE Transactions on Knowledge and Data Engineering,2004,16(7): 843?857

150 Yu Y L,Li K Q,Jin Y W,Zhang Y.A trust management model for service-oriented distributed networks.Concurrency and Computation:Practice and Experience,2013, 25(14):2098?2111

151 Resnick P,Zeckhauser R.Trust among strangers in internet transactions:empirical analysis of eBay′s reputation system.The Economics of the Internet and E-Commerce.Amsterdam:Emerald Group Publishing Limited,2002.127?157

152 J?sang A,Ismail R.The beta reputation system.In:Proceedings of the 15th Bled Electronic Commerce Conference e-Reality:Constructing the e-Economy.Bled,Slovenia, 2002.2502?2511

153 Zhou R F,Hwang K.PowerTrust:a robust and scalable reputation system for trusted peer-to-peer computing.IEEE Transactions on Parallel and Distributed Systems,2007, 18(4):460?473

154 Buragohain C,Agrawal D,Suri S.A game theoretic framework for incentives in P2P systems.In:Proceedings of the 3rd International Conference on Peer-To-Peer Computing. Washington DC,USA:IEEE,2003.48?56

155 Feldman M,Lai K,Stoica I,Chuang J.Robust incentive techniques for peer-to-peer networks.In:Proceedings of the 5th ACM Conference on Electronic Commerce.New York, USA:ACM,2004.102?111

156 Liu Y,Xiong N,Park J H,Yang C,Xu K.Fair incentive mechanism with pyramidal structure for peer-to-peer networks.IET Communications,2010,4(1):1?12

157 Ma R T B,Lee S C M,Lui J C S,Yau D K Y.Incentive and service diあerentiation in P2P networks:a game theoretic approach.IEEE/ACM Transactions on Networking, 2006,14(5):978?991

158 Gupta R,Somani A K.Game theory as a tool to strategize as well as predict peers′behavior in peer-to-peer networks. In:Proceedings of the 11th International Conference on Parallel and Distributed Systems.Fukuoka,Japan:IEEE,2005. 244?249

159 Mortazavi B,Kesidis G.Cumulative reputation systems for peer-to-peer content distribution.In:Proceedings of the 40th Annual Conference on Information Sciences and Systems.Princeton NJ,USA:IEEE,2006.1546?1552

160 Mejia M,Pe?na N,Mu?noz J L,Esparza O,Alzate M A.A game theoretic trust model for on-line distributed evolution of cooperation inMANETs.Journal of Network and Computer Applications,2011,34(1):39?51

161 Zhao B Q,Lui J C S,Chiu D M.Analysis of adaptive incentive protocols for P2P networks.In:Proceedings of the 2009 IEEE INFOCOM.Rio de Janeiro,Brazil:IEEE,2009. 325?333

162 Zuo F,Zhang W.An evolutionary game-based mechanism for routing P2P network fl ow among sel fi sh peers.Journal of Networks,2014,9(1):10?17

163 Wang Y F,Nakao A,Vasilakos A V,Ma J H.P2P soft security:on evolutionary dynamics of P2P incentive mechanism.Computer Communications,2011,34(3):241?249

164 Cui G H,Li M C,Wang Z,Ren J K,Jiao D,Ma J H. Analysis and evaluation of incentive mechanisms in P2P networks:a spatial evolutionary game theory perspective.Concurrency and Computation:Practice and Experience, 2015,27(12):3044?3064

165 Lu K,Wang J L,Li M C.An Eigentrust dynamic evolutionary model in P2P fi le-sharing systems.Peer-to-Peer Networking and Applications,2016,9(3):599?612

166 Chen Z D,Qiu Y H,Liu J J,Xu L.Incentive mechanism for sel fi sh nodes in wireless sensor networks based on evolutionary game.Computers&Mathematics with Applications,2011,62(9):3378?3388

167 Zhu J,Jiang D D,Yuan Y H,Fang W L.An evolutionary game theory-based channel access mechanism for wireless multimedia sensor network with rate-adaptive applications.Multimedia Tools and Applications,2016,75(22): 14329?14349

168 Zhao S S,Zhu Q,Zhu H B.Evolutionary game theoretical approach to dynamic spectrum sharing.Journal of Computational Information Systems,2012,8(10):4225?4232

169 Jiang C X,Chen Y,Gao Y,Liu K J R.Joint spectrum sensing and access evolutionary game in cognitive radio networks.IEEE Transactions on Wireless Communications, 2013,12(5):2470?2483

170 Wu D,Liu H,Bi Y R,Zhu H S.Evolutionary game theoretic modeling and repetition of media distributed shared in P2P-based VANET.International Journal of Distributed Sensor Networks,2014,4(6):Article No.718639

171 Zhang Hui,Wang Kun-Feng,Wang Fei-Yue.Advances and perspectives on applications of deep learning in visual object detection.Acta Automatica Sinica,2017,43(8):1289?1305

(張慧,王坤峰,王飛躍.深度學(xué)習(xí)在目標(biāo)視覺檢測中的應(yīng)用進(jìn)展與展望.自動化學(xué)報,2017,43(8):1289?1305)

172 You Ke-You,Xie Li-Hua.Survey of recent progress in networked control systems.Acta Automatica Sinica,2013, 39(2):101?118

(游科友,謝立華.網(wǎng)絡(luò)控制系統(tǒng)的最新研究綜述.自動化學(xué)報, 2013,39(2):101?118) 173 Wang Li-Yuan,Guo Ge,Zhuang Yan.Transmission power allocation for networked control systems.Acta Automatica Sinica,2017,43(8):1350?1357

(王麗媛,郭戈,莊嚴(yán).網(wǎng)絡(luò)控制系統(tǒng)發(fā)送功率分配問題研究.自動化學(xué)報,2017,43(8):1350?1357)

174 Hu Yan-Yan,Jin Zeng-Wang,Xue Xiao-Ling,Sun Chang-Yin.Fault diagnosis for networked systems by asynchronous IMM fusion fi ltering.Acta Automatica Sinica,2017,43(8): 1329?1338

(胡艷艷,金增旺,薛曉玲,孫長銀.基于異步IMM融合濾波的網(wǎng)絡(luò)化系統(tǒng)故障診斷.自動化學(xué)報,2017,43(8):1329?1338)