間接互惠與合作演化的若干問題研究進展

張艷玲 劉愛志 孫長銀

達爾文的進化論認為“物競天擇、適者生存”,說明競爭在進化中起核心的作用[1].依據這一理論,在“弱肉強食”的生存斗爭中,適應性強的個體勝出,適應性差的個體被淘汰.從而在激烈的生存斗爭中,每個個體均會從自身利益出發,變得利己自私、唯利是圖.然而,從細菌群落到蜂群蟻群,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度,從而削弱自身的競爭優勢,合作的存在看似并不合理.面對廣泛存在的合作行為,達爾文本人也深感困惑,在其著作中相應的解釋只是一筆帶過[5].

合作行為廣泛存在,同時在很多領域中又十分匱乏.研究促進合作涌現的機制有以下三點益處:1)有助于解釋眾多產生原因未知的現象,例如,細胞的癌變[6]、語言的產生[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]、環境惡化[10]和資源枯竭[11];3)有助于破解互聯網時代在虛擬世界中我們遇到的新問題,例如,網絡欺詐[12]等違法犯罪行為.由此可見,研究促進合作演化的機制對人類發展有著重大的現實意義和時代緊迫感.

如何研究合作行為的演化?這是一個熱點問題,2005年Science雜志就指出“合作行為如何進化”是21世紀最關鍵的25個科學問題之一[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學框架.Smith等首次將von Neumann開創的博弈論觀點(大腦在利益沖突時做出理性決定)擴展為根據自然選擇而得出決定[14],這標志著演化博弈論的開創.近年來,國內外越來越多的學者利用此理論研究促進合作涌現的機制[15?37].其中最著名的是哈佛大學的Nowak教授,他對“綜合進化論”(這一理論將突變、選擇和進化的基本概念整合到一個數學框架中)的思想進行了擴展,將囚徒困境放到演化的群體中進行研究.Nowak首次總結了促進合作涌現的5大機制[38]:親緣選擇(Kin selection)、直接互惠(Direct selection)、間接互惠(Indirect selection)、網絡互惠(Network reciprocity)和群組選擇(Group selection).親緣選擇意味著,與誰的血緣關系越近,就越傾向與之合作;直接互惠意味著,今天我幫助你,明天你會幫助我;間接互惠意味著,今天我幫助你,明天會有他人幫助我;網絡互惠意味著,個體僅僅與鄰居進行博弈,合作者團簇最終勝出背叛者團簇;群組選擇意味著,競爭既發生在個體之間,也發生在群組之間.除了這5大機制,最近的綜述還歸納出另外5種促進合作演化的機制[39]:綠胡子選擇(Green beard selection)、強互惠性(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生合作;強互惠性意味著,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,個體愿意承擔成本吸引其他個體的關注;集合選擇意味著,個體僅僅與相同集合的個體進行交互;選擇性參與意味著,個體有權利拒絕與特定個體進行博弈.

1 關于間接互惠的概述

1.1 研究間接互惠的意義

間接互惠是促進合作涌現的重要機制之一.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[7,47]、道德規范的形成[38]、社會的分工[39]以及人類大腦的發育[47]都與間接互惠密不可分.在經濟全球化和進入網絡時代的背景下,電子商務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的相識個體間的重復交互[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“道德風險”不斷增大[45].因此,針對間接互惠如何促進合作涌現的研究吸引了演化生物學家、經濟學家和社會科學家等學者的極大興趣.

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曾經幫助了B,因此幫助A,這是一種建立在聲望基礎上的間接互惠;“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”并不能單獨促進合作的涌現,只有與直接互惠或者網絡互惠相結合才能促進合作的涌現[56?57].“下游互惠”和“廣義互惠”均可單獨促進合作的涌現,不過前者是研究間接互惠的主流方向,而關于后者的相關研究還甚少.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)和實驗驗證(包括實驗室實驗、實地實驗和在線實驗).

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關于“下游互惠”的研究:經典的博弈模型、聲望評估準則與行為準則和基于八卦的聲望信息傳播.

2 經典的博弈模型

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)獨裁者博弈,如圖2(c)所示.一方為獨裁者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行投資,投資總額乘以增益系數r(1＜r＜博弈人數)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 聲望評估準則與行為準則

3.1 常見的聲望評估準則及其相關研究

聲望是間接互惠發揮作用的核心,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,即如何構建聲望評估準則.目前,被廣泛研究的評估準則包括“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).經典的“一階評估”是“形象分數”:當捐助者幫助接受者時,捐助者的形象分數增加一分;當捐助者拒絕幫助接受者時,捐助者的形象分數減少一分.1998年,Nowak等首次利用“形象分數”構建了刻畫間接互惠的數學模型,如圖3所示.他們認識到間接互惠在促進合作演化方面的巨大作用[43]:當玩家的聲望由多值“形象分數”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.之后,這個結論被行為實驗證實[63].與此同時,Nowak等理論分析了二值“形象分數”[43?44].稍后的理論研究表明很多因素導致合作行為在采取二值“形象分數”的群體中消失[64?66,96].這種現象是由于此準則固有的困境: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“形象分數”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“形象分數”(好、中性、壞)[69]或特定“一階評估”(觀察者根據捐贈者在以往多次行動中的表現確定其名聲)[70,100]可以克服這個困境,促進合作行為的涌現.

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

表1 聲望評估準則Table 1 Reputation evaluation criterion

圖3 經典的間接互惠模型Fig.3 Representative model about indirect reciprocity

“二階評估”也能彌補二值“形象分數”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“溫和準則”和“嚴苛準則”,如表2所示.二者唯一的不同點在于,前者認為拒絕幫助壞人會為捐助者帶來好的聲望,而后者認為此行為會為捐助者帶來壞的聲望.學者在“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少量損失),發現對背叛者置之不理比懲罰背叛者更有利于合作的涌現[71].

在“二階評估”基礎上,額外考慮捐贈者的聲望,這種評估準則被稱為“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.學者考察所有可能的“三階評估”,假設群體最多擁有兩種策略,發現了8種評估準則可以令合作行為具有演化穩定性[93].這8種準則如表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“溫和準則”和“嚴苛準則”.學者在群體共存多種策略的假設下對這兩種準則進行研究[94].上述研究均假設群體共享相同評估準則,而比較的是不同行為準則的競爭.鑒于認知差異會導致個體對于如何評估聲望的理解不同,學者也考慮了評估準則因人而異的情形[95,101].

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

表3 8種促進合作演化的聲望評估準則Table 3 Eight reputation evaluation criterions which favor the evolution of cooperation

3.2 常見的行為準則及其相關研究

關于間接互惠的早期研究假設個體僅幫助聲望好的個體,或者個體僅幫助形象分數高于某一閾值的個體[43?44,64?68,96?99]. 這些最簡單的行為準則(行為準則是能否捐助的依據)要求個體僅根據對手的聲望決定自己是否給予捐助.稍后,略微復雜的行為準則,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,受到關注[69?71,89?90,94?95,100?101]. 上述研究主要關注哪

種聲望評估準則更有利于合作的演化.最近,學者們對較為復雜的行為準則如何影響合作涌現進行了探索[72,87,102].一些學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(當接受者的聲望在這個范圍內則進行捐助),通過仿真發現,一定的聲望容忍度有助于合作的涌現[87,102].還有一些研究提出了一種基于向量的行為準則(捐助者將自身聲望與接受者聲望進行比較,當至少滿足三種條件中的兩種時則進行捐助,這三種條件包括聲望近似、聲望高于自己和聲望低于自己),通過仿真發現,“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行捐助”這種策略在較小的成本收益比下能夠成為占優策略,同時促進合作的演化[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.當群體規模較小時,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.然而隨著群體規模的擴大,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 關于八卦的解析研究和仿真研究

一些學者通過解析和仿真的方式對于八卦如何影響合作的涌現進行研究.此時的模型通常假設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“形象分數”,Nowak等給出了簡單的數學關系:當q高于成本收益比c/b時,合作可以涌現[43?44].在“二階評估”下,類似的條件在兩個調查中獲得[106?107],這兩個調查最大區別在于,當觀察者未看到交互過程時,捐贈者的名聲保持不變或者設定為未知.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q為常數,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),也有學者進行了理論分析[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他人;而謊言則是故意傳播虛假的聲望信息而對他人進行誤導.一項研究在聲望傳播中引入欺騙策略(傳播虛假聲望信息),發現這種策略在沒有其他機制的情形下導致群體合作演化的失敗[110].另兩項研究表明:當群體中沒有虛假信息傳播時,八卦數量的增加有助于促進合作的演化;而存在噪聲干擾和謊言所導致的不公正評價時,中等數量的八卦最有利于促進合作的演化[111?112].這兩項研究是基于累加的八卦信息進行決策,而最近的研究發現基于最新的八卦信息作出決策更能促進合作的演化[113].上述關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).當考慮這種成本時,結果表明間接互惠不再促進合作的演化[114].

4.2 關于八卦的實驗研究

另一部分學者通過行為實驗的方法對八卦進行研究,主要發現如下.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,實驗發現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].當八卦將個體的聲望傳播到未來會與其發生交互的個體時,八卦可以促使個體更加關注自身聲望并促進慷慨行為的產生[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合作的涌現[115].社會網絡結構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的誤差[122?123].“道德威懾”通過拆穿謊言后的懲罰機制維護八卦的可信性,從而促進合作的涌現[124].當聲望被視為可以買賣的物品時,由于人類具有認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

合作行為在很多領域中十分匱乏,因此,研究促進合作演化的機制對人類發展有著重大的現實意義和時代緊迫感.2005年Science雜志就指出“合作行為如何進化”是21世紀最關鍵的25個科學問題之一.在演化博弈論的框架下,研究人員已提出一些促進合作演化的機制,其中間接互惠是促進合作演化的最重要機制之一,并已吸引了演化生物學家、經濟學家和社會學家等學者的極大興趣.它包括“上游互惠”、“下游互惠”和“廣義互惠”三種方式:“上游互惠”并不能單獨促進合作的涌現,只有與直接互惠或者網絡互惠相結合才能促進合作的涌現;“下游互惠”和“廣義互惠”均可單獨促進合作的涌現,不過前者是研究間接互惠的主流方向,而關于后者的相關研究還甚少.本文關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于“下游互惠”的研究進行總結.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則:“一階評估”、“二階評估”和“三階評估”.相關研究假設采用比較簡單的行為準則,而聚焦于哪種聲望評估準則能夠促進合作的演化.同時回顧了關于較為復雜的行為準則如何促進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合作演化進行的研究.解析研究一般假設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,個別研究假設其可隨時間變化.仿真研究假設更加復雜的模型,例如八卦不再如實傳遞信息,而是融入了噪聲和謊言.同時也回顧了利用行為實驗對八卦進行的研究,內容十分寬泛.

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雜網絡上的間接互惠、聲望傳播系統的魯棒性、聲望共享系統的建立和間接互惠在P2P網絡中的應用.

6.1 復雜網絡上的間接互惠

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,絕大多數現實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雜網絡實現的.在演化博弈論框架下,未涉及間接互惠的靜態復雜網絡和動態復雜網絡已被廣泛研究[130?142],而只有較少研究關注復雜網絡上的間接互惠[143?147].文獻[143]發現在社會網絡中,根據聲望選擇交互伙伴這種行為有助于促進合作的演化.文獻[144?145]假設小世界網絡和無標度網絡等復雜網絡可以重構(斷邊重連),發現聲望共享“聯盟”的存在有助于促進群體合作.文獻[146?147]假設直接互惠和間接互惠同時存在于網絡上,發現間接互惠有助于刻畫現實社會的無標度網絡的形成.

雖然科研人員已經對于復雜網絡上的間接互惠進行了一些初步的探索,但是還有很多問題需要進一步研究.例如,上述研究均認為聲望是通過觀察獲得的公共信息(即聲望全局可知),然而在現實社會中,聲望多數情況下是通過八卦進行傳播的,由此可見,靜態或動態復雜網絡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 聲望傳播系統的魯棒性

八卦是大規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他人;而謊言則是故意傳播虛假的聲望信息而對他人進行誤導.一項研究在聲望傳播中引入欺騙策略(傳播虛假聲望信息),發現這種策略在沒有其他機制的情形下導致群體合作演化的失敗[110].另兩項研究表明:當群體中沒有虛假信息傳播時,八卦數量的增加有助于促進合作的演化;而存在噪聲干擾和謊言所導致的不公正評價時,中等數量的八卦最有利于促進合作的演化[111?112].這兩項研究是基于累加的八卦信息進行決策,而最近的研究發現基于最新的八卦信息作出決策更能促進合作的演化[113].

科研人員已經對于加入噪聲和謊言的八卦進行了初步的探索,但已研究的模型還有很多可以改進的地方,相應的結果并不全面.在未來的研究中,我們需要建立更加合適的模型,結合現實生活提出能夠抵抗噪聲干擾和謊言入侵的八卦,令聲望傳播系統具有魯棒性,進而發現能夠促進合作演化且強抗干擾的機制.

6.3 聲望共享系統的建立

以往關于間接互惠的絕大多數研究均沒有考慮個體間聲望共享所需的成本.但在實際中,人們在評價和分享他人聲望的過程中需要耗費時間和精力.例如,在網絡購物平臺中,人們需要花費時間和精力去評價所購買的產品或者服務.近期的一項研究表明,當考慮聲望共享所需成本時,間接互惠無法促進合作的涌現[114].

隨著經濟全球化和網絡時代的到來,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聲望呢?目前的研究還沒有給出一個滿意的答復.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且促進合作涌現的有效機制.

6.4 間接互惠在P2P網絡中的應用

近年來,P2P(Peer to peer)網絡應用廣泛,因此對其研究發展快速.在P2P網絡中,參與者共享自身所擁有的一部分硬件資源(存儲能力、網絡連接能力和打印機等),這些共享資源通過網絡提供服務和內容,能被其他對等節點(Peer)直接訪問而無需經過中間實體.在此網絡中的參與者既是資源、服務和內容的提供者(Server),又是資源、服務和內容的獲取者(Client).合作是確保所有參與者獲得所需服務的關鍵,出于惡意和自私的非合作行為往往導致參與者獲得較少服務甚至一無所獲.消除非合作行為的有效機制包括信任機制和激勵機制.信任機制指的是根據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[151]、Beta聲望系統[152]、Eigentrust聲望系統[148]和Powertrust聲望系統[153].激勵機制包括金錢激勵和非金錢激勵[154?157].

鑒于 P2P網絡中個人利益和集體利益相沖突,經典博弈理論已被廣泛用來研究此類網絡[154,157?160].不過經典博弈理論假設參與者完全理性且擁有全局信息.這些假設并不現實,同時經典博弈理論不能描述參與者策略的動態演化過程及策略在整個系統中的傳播過程.近來,可以克服上述缺點的演化博弈論被用來研究P2P網絡[155,161?165].文獻[161]假設P2P網絡是混合均勻且有無限節點,并利用復制動力學研究三種激勵機制的穩定性.文獻[162]同樣利用復制動力學發現一種延拓的模仿動力學可以改進整個網絡路徑選擇的效率,從而避免路徑上的過載或長延遲.文獻[163]假設P2P網絡具有有限節點,分別在混合均勻網絡和同型結構網絡上研究一種激勵機制(Reciprocation-based incentive mechanism).文獻[164]將關于同類激勵機制的研究推廣到異型結構的P2P網絡.文獻[155,165]假設P2P網絡具有有限節點,利用計算機仿真調查兩種信任機制.上述研究是針對一般性的P2P網絡,還有一些研究利用演化博弈論分析特殊的P2P網絡,例如基于P2P的無線傳感網絡[166?169]和基于P2P的車輛自組織網絡[170].

科研人員已利用演化博弈論對P2P網絡進行了一些探索,本文主體部分總結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用到關于P2P網絡的研究中.大體思路有以下4點:

1)聲望評估準則可視作信任機制.將“一階評估”、“二階評估”或“三階評估”作為信任機制集合,尋找能夠令P2P網絡中合作行為穩定的信任機制.

2)行為準則可視為激勵機制.將已研究過的行為準則構成激勵機制集合,尋找能夠令P2P網絡高效、有序運行的激勵機制.

3)在P2P網絡的聲望傳播過程中融入八卦,研究八卦對于網絡穩定性的影響.

4)可以將深度學習方法[171]與間接互惠機制結合,來研究網絡控制問題[172?174].

致謝

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

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