Empathy in One-Shot Prisoner Dilemma
aa r X i v : . [ c s . G T ] F e b Empathy in One-Shot Prisoner Dilemma
Giulia Rossi, Alain Tcheukam and Hamidou Tembine ∗ February 28, 2017
Abstract
Strategic decision making involves affective and cognitive functions likereasoning, cognitive and emotional empathy which may be subject to ageand gender differences. However, empathy-related changes in strategicdecision-making and their relation to age, gender and neuropsychologicalfunctions have not been studied widely. In this article, we study a one-shot prisoner dilemma from a psychological game theory viewpoint. Fortyseven participants (28 women and 19 men), aged 18 to 42 years, weretested with a empathy questionnaire and a one-shot prisoner dilemmaquestionnaire comprising a closiness option with the other participant.The percentage of cooperation and defection decisions was analyzed. Anew empathetic payoff model was calculated to fit the observations fromthe test whether multi-dimensional empathy levels matter in the outcome.A significant level of cooperation is observed in the experimental one-shot game. The collected data suggests that perspective taking, empathicconcern and fantasy scale are strongly correlated and have an importanteffect on cooperative decisions. However, their effect in the payoff is notadditive. Mixed scales as well as other non-classified subscales (25+8 outof 47) were observed from the data.
Keywords:
Empathy, other-regarding payoff, cooperation
Contents ∗ The authors are with Learning & Game Theory Laboratory, New York University AbuDhabi, Email: [email protected] Introduction
In recent years a growing field of behavioral game studies has started to emergefrom several academic perspective. Some of these approaches and disciplinessuch as neuroscience, social psychology, artificial intelligence have already pro-duced major collections and experiments on empathy. In the context of strategicinteraction, empathy may play a key role in the decision-making and the out-come of the game.
Widely known results in repeated games
For long-run interactions under suitable monitoring assumption it has beenshown that cooperative outcomes may emerge as time goes. This is known as“Folk Theorem” or general feasibility theorem (see [1, 2]). For example, theTit-For-Tat Strategy which consists to start the game by cooperating,Then dowhatever your other participant did on the previous iteration, leads to a partialcooperation between the players . While cooperation may emerge by means ofrepeated long-run interactions under observable plays, there is very little studyon how cooperation can be possible in one-shot games.
How about cooperative behavior in one-shot games?
Unfortunately, the Folk theorem result does not apply to one-shot games. Thisis because there is no previous iteration. There is no next iteration in one-shotgames. There is no opportunity to detect, learn or punish from experiences. Forthe same reasons, the existing reputation-based schemes do not apply directly.
Is cooperation possible outcome in experimental one-shotgames?
Experimental results have revealed a strong mismatch between the outcome ofthe experiments and the predicted outcome from classical game model. Is theobserved mismatch because of some important factors that are not consideredin the classical game formulation? Is it because the empathy of the players areneglected in the classical formulation?This work conducts a basic experiment on one-shot prisoner dilemma andestablishes correlation between players choices and their empathy levels. Theprisoner’s dilemma is a canonical example of a game analyzed in classical gametheory that shows why two individuals (without empathy consideration) mightnot cooperate, even if it appears that it is in their best interests to do so in termsof collective decision. It was originally framed by Flood and Dresher working atRAND. In 1950, Tucker gave the name and interpretation of prisoner’s dilemmato Flood and Dresher’s model of cooperation and conflict, resulting in the mostwell-known game theoretic academic example.2 ontribution
The contribution of this work can be summarized as follows. We investigate howplayers behave and react in experimental one-shot Prisoner Dilemma in relationto their levels of empathy. The experiment is conducted with several voluntaryparticipants from different countries, cultures and educational backgrounds. Foreach participant to the project the Interpersonal Reactivity Index (IRI) whichis a multi-dimensional empathy measure, is used. In contrast to the classicalempathy scale studied in game theory literature that are limited to perspectivetaking, this work goes one-step further by investigating the effect of three otherempathy subscales: empathy concern, fantasy scale and personal distress. Theexperiment reveals a strong mixture of the empathy scales across the popu-lation. In addition, each participant responds to a questionnaire that mimicsone-shot Prisoner Dilemma situation and specific reaction time and closinessto the other participant. We observe that empathic concern as well as fantasyscale dimensions may affect positively other-regarding payoff. In contrast to theclassical prisoner dilemma in which Defection is known as a dominating strat-egy, the experimental game exhibits a significant level of cooperation in thepopulation (see Section 4). In particular, Defection not a dominating strategyanymore when players’ psychology is involved. Based on these observations anempathetic payoff model in Section 4, that better captures the preferences ofthe decision-makers, is proposed. With this empathetic payoff, the outcome ofthe game captures more the observed cooperation level in the one-shot prisonerdilemma. The experiment reveals not only positive affect of empathy but also adispositional negative affect (spiteful or malicious) of empathy in the decision-making of some of the participants. Spitefulness is observed at the personaldistress scale in the population. Person distress scale is negatively correlatedwith perspective taking scale. Taken together, these findings suggest that theempathy types of the participants play a key role in their payoffs and in theirdecision in one-shot prisoner dilemma. It also reduces the gap between gametheory and game practice by closing-the-loop between model and observations.It provides an experimental evidence that strengthens the model of empatheticpayoff and its possible engineering applications [45].
Stucture
The rest of the article is organized as follows. The next section presents somebackground and literature overview on empathy. Section 3 presents the exper-imental study about the impact of individual psychology on human decisionmaking in one-shot prisoner dilemma. The analysis of the results of the ex-periment are presented in Section 4. An explanation of the results is given inSection 5. Section 6 concludes the paper.3
Background on Empathy
From the field of relational care to the field of economy, the concept of empathyseems to have an ubiquitously position. Empathy is not only an important andlongstanding issue, but a commonly used term in everyday life and situations.Even if it is easily approached and used, this concept has until nowadays differentdefinitions and meanings. Born in the aesthetic and philosophical field, it cameto be an important operative concept in behavioral game theory, where oncemore it is used as an instrument to create relations between decision-makers.The public opinion and the world scientific scenario, however, are not alwaysgiving the correct attention to what is implying an empathetic reaction withthe others: be empathetic is not something simple as well as is not somethinggiven once to the personality of persons. It depends on the context of relationsand on the social interaction dimension where people are involved as players,consumers, or agents.
Definition of Empathy
We present historical definitions and concepts of empathy. Rather than havingto choose which of the ’definitions’ of empathy is correct, this work suggestsa better appreciation for it as a multidimensional phenomenon at least allowsa perspective and the ability to specify which aspect of empathy the experi-mentalist and the theorist are referring to when making particular particularinvestigation in behavioral games. • Philosophy: From philosophical perspective, Empathy derives from theGreek word ´ ǫµπ ´ αθǫiα (empatheia), which literally means physical affec-tion. In particular, it is composed by ´ ǫv (en) “in, at” and π ´ αθoς (pathos),“passion” or “suffering”. The work in [3] has introduced the term Ein-fuhlung to aesthetic philosophical field in his main book “On the opticalSense of Form: A contribution to Aesthetics” and many other authors (see[4] and the references therein), have introduced the concept to feeling andquasi-perceptual acts. • Psychology: From a psychological perspective, it corresponds to a cogni-tive awareness of the emotions, feelings and thoughts of the other persons.In this sense, the term primary significance is that of “an intellectualgrasping of the affects of another, with the result of a mimic expression ofthe same feelings” [5]. • Sociology: From a sociological perspective, empathy corresponds to anability to be aware of the internal lives of the others. It is related tothe existence of language as a sort of personal awareness of us as selves[6]. Regarding a neuroscientific perspective, empathy has been studiedas a “two empathic sub-processes, explicitly considering those states andsharing other’s internal states” [7]. These two cognitive processes areexhaustively represented in the Figure 1.4igure 1: Cognitive and emotional empathy are the bases of Empathy. Theyare related to cognitive and affective Theory of Mind as suggested in [21].Empathy lies in the structures that include the anterior insula cortex andthe dorsal anterior cingulate cortex. In particular, empathy for others painis considered being located in anterior insula cortex [8, 10]. These areas arestudied in relation to empathy and empathy concerns of collective actions(CA) [9]. Oxytocin (OT), an “evolutionarily ancient molecule that is akey part of the mammalian attachment system”, is considered in thesestudies as a sort of variable to be manipulated to increase or decrease CAin human beings.Furthermore, empathy must be analyzed in relation to the concepts of com-passion and sympathy. Compassion, from Latin ecclesiastical compati (sufferwith), literally means have feelings together. Nowadays it is associated with thecapacity of feeling the other’s worries, even tough it doesn’t imply an automaticaction. Sympathy, from the Greek σuµπ ´ aθǫia , literally means fellow feelings.Its meaning lies in the capacity of understanding the internal feelings of theother with the intentional desire of changing his/her worries. As per indicationin [11], “the object of sympathy is the other person’s well being. The object ofempathy is understanding”. It has been difficult to distinguish empathy fromsympathy because they both involve the emotional state of one person to thestate of another. This problem was increased by the fact that the mapping ofthe terms has recently reversed: what is now commonly called empathy wasreferred to before the middle of the twentieth century as sympathy [12]. At theend, the concept of empathy must be understood also in relation to Theory ofMind. Theory of Mind, also described as ToM, is the capability to understandof others as mental beings, with personal mental states, for example feelings,motives and thoughts. It is one of the most important developments in earlychildhood social cognition and it is influencing children life at home as well as atschool. Its development from birth to 5 years of age is now described in researchliterature with the possibility to understand how infants and children behave inexperimental and natural situations [13].5 ifferent types of empathy We are not restricting ourselves to the positive part of empathy. Empathy mayhave a dark or at least costly side specially when the environment is strategicand interactive as it is the case in games. Can empathy be bad for the self?Empathy can be used, for example, by a other player attacker to identify theweak nodes in the network. Can empathy be bad for others? Empathetic usersmay use their ability to destroy the opponents. In strategic interaction betweenpeople, empathy may be used to derive antipathetic response (distress at seeingothers’ pleasure, or pleasure at seeing others distress). In both cases, it willinfluence the dynamics of the self and other regarding preferences.The ability of empathy to generate moral behavior and determine cooper-ation is limited by three common occurrences: over-arousal, habituation andbias. • Empathic over-arousal is an involuntary process that occurs when an ob-server’s empathic distress becomes so painful and intolerable that it istransformed into an in tense feeling of personal distress, which may movethe person out of the empathic mode entirely [14, 15] . • Generally speaking, in a classical relation victim-observer, the greater isthe victim’s distress, the greater is the observer’s empathic distress. If aperson is exposed repeatedly to distress over time, the person’s empathicdistress may diminish to the point where the person becomes indifferentto the distress of others. This is called habituation. This diminishedempathic distress and corresponding indifference is very common in thosewho, for example, abuse and kill animals. • Humans evolved in small groups. These groups sometimes competed forscarce resources: in this way is not surprising that evolutionary psycholo-gists have identified kin selection has a moral motivator with evolutionaryroots. The forms of familiarity bias include in-group bias and similaritybiases. In-group bias is simply the tendency to favour one’s own group.This is not one group in particular, but whatever group we are able to as-sociate with at a particular time. In-group bias is working on self-esteemof the members. On the opposite side of these biases, we have out-groupones, where people out of the groups are considered in a negative way,with a different (and, for the most of the time) and worst treatment (e. g,racial inequality). The similarity bias derives from psychological heuris-tic pertaining to how people make judgments based on similarity. Morespecifically, similarity biases are used to account for how people makejudgments based on the similarity between current situations and othersituations or prototypes of those situations. The goal of these biases is tomaximize productivity through favorable experience while not repeatingunfavourable experiences (adaptive behaviour).6 mpathy main integrative theories
During the 1970s, in the public psychological scenario empathy was conceivedas a procedure with affective and cognitive implications. The work in [16] intro-duced the first multidimensional model of empathy in the psychological litera-ture, where affective and cognitive procedures were working together. Accordingto her, although empathy is defined as a shared emotion between two persons,it depends on cognitive factors. In her integrative-affective model, the affectiveempathy reaction derives from three components factors, hereinafter described.The first is represented by the cognitive ability to discriminate affective cues inothers, the second by the cognitive skills that are involved in assuming the per-spective and role of the others and the third factor is, at the end, described bythe emotional responsiveness, the affective ability to experience emotions. Bythe other hand, one of the most comprehensive perspectives on empathy and itsrelation to the moral development is provided in [17]. The author consideredempathy as a biologically based disposition for altruistic behavior [17]. He con-ceives of empathy as being due to various modes of arousal, which allows us torespond empathically in light of a variety of distress cues from another person.The author mentions mimicry, classical conditioning, and direct association asfast acting and automatic mechanisms producing an empathic response. Theauthor lists mediated association and role taking in relation to more cognitivelydemanding modes, mediates by language and proposed some of the limitationsin our natural capacity to empathize or sympathize with others, particularlywhat he refers to as ’here and now’ biases. In other words, the main tendencyaccording to [17], is to empathize more with persons that are in some senseperceived to be closer to us. The authors in [18] defined empathy as a sharedemotional experience occurring when one person (comes to feel a similar emotionto another (the object) as a result of perceiving the other’s state. This processresults from the representations of the emotions activated when the subject paysattention to the emotional state of the object. The neural mechanism assumesthat brain areas have processing domains based on their cellular compositionand connectivity.The main theories that we will discuss further are related to the use wewill have of empathy concept in game theory analysis. Broadly speaking, weare approaching empathy as made up of two components, an affective and acognitive one. The affective (or emotional) component develops from infants andits structure may be summarized in this progressive intertwinement, a.) emotionrecognition, b.) empathic concern, c.) personal distress and d.) emotionalcontagion. The cognitive component of empathy develops during the progressivedevelopment of the person from his her childhood. It is based on the theory ofmind, imagination (of emotional future outcomes) and on perspective taking.According to [19] two main approaches have been used to study empathy:the first one focuses on cognitive empathy or the ability to take the perspectiveof another person and to infer his mental state (Theory of Mind). The secondone emphasizes emotional or affective empathy [20] defined as an observer’semotional response to another person’s emotional state. The Table 1 below7motional Empathy Cognitive EmpathySimulation System Mentalizing systemTheory of MindEmotional contagion, personal distress perspective takingEmpathic concern, emotion recognition imagination of emotional future outcomesCore structure Core structureDevelopment DevelopmentTable 1: Principal features of affective and cognitive empathy.highlights some of principal features of affective and cognitive empathy [21].A model of empathy-altruism was developed in [22]. Through the lines ofthis model, the author simply assumes that empathy feelings for another personcreate an altruistic motivation to increase that person’s welfare. In particular,the work in [23] found out how the participants in a social dilemma experimentallocated some of their resource to a person for whom they felt empathy. Theauthor developed also the model of empathy-joy [22]. This hypothesis underlineshow a prosocial act is not completely explained only by empathy but, also, bythe positive emotion of joy a helper expects as a result of helping another personin need. In connection with this theory, empathy relies on an automatic processthat generates, immediately, other types of behavior useful to predict the other-regarding actions. In relation to one-trial prisoner’s dilemma [24] underlinedhow empathy-altruism should increase cooperation (that, then, will emerge inthe situation).The model of empathic brain proposed in [25] proposes a modulate modelof empathy, where different factors occur in its development. These factors arefour, in particular related to four different situations so described, i) one is inaffective state, ii) this state is isomorphic to another person’s affective state,iii) this state is elicited by the observation or imagination of another person’saffective state, iv) one knows that the other person is the source of one’s ownaffective state. Condition (a) is particularly important as it helps to differen-tiate empathy from mentalizing. Mentalizing is the ability to represent others’mental states without emotional involvement. In particular, the two authorsare underlying the epistemological value of empathy, by one side related to pro-vide information about future actions between people and, by the other side, tofunction as “origin of the motivation for cooperative and prosocial behavior”.The model we provide is based on both these theories and, in particular, itwill take into account the distinction between empathy itself and the corticalrepresentations of the emotions. By a developmental point of view, empathy isstudied also in relation with prosocial behavior. Two theoretical studies [26, 27]are fundamental in this sense. In particular, the author considers that the de-velopment of a vicarious affective reaction to another distress is beginning frominfancy. Individual patterns of behavior that responses to the distress are, also,tailored to the needs of the other. According to [28] although an empathic basisto altruistic behavior entails a net cost to the actor, cooperation and altruism8equire behavior tailored to the feelings and needs of others.
How to measure empathy?
We overview empathy measurement in psychology and present existing modelsof empathy’s effect in game theory.
Empathy measures in Psychology
Psychologists used to study both situational and dispositional empathy con-cepts. Situational empathy, i.e., empathic reactions in a specific situations,is measured by asking subjects about their experiences immediately after theywere exposed to a particular situation, by studying the “facial, gestural, and vo-cal indices of empathy-related responding” [46] or by various physiological mea-sures such as the measurement of heart rate or skin conductance. Dispositionalempathy, understood as a person’s stable character trait, has been measuredeither by relying on the reports of others (particularly in case of children) or,most often (in researching empathy in adults), by relying on the administrationof various questionnaires associated with specific empathy scales. • Measuring empathic ability: The work in [47] proposes to test empathicability by measuring the degree of correspondence between a person A anda person B’s ratings of each other on six personality traits-such as self-confidence, superior-inferior, selfish-unselfish, friendly-unfriendly, leader-follower, and sense of humor-after a short time of interacting with eachother. More specifically, empathic ability is measured through a question-naire that asked both persons, i) to rate themselves on those personalitytraits, ii) to rate the other as they see them, iii) to estimate from theirperspective of how the other would rate himself and to rate themselvesaccording to how they think the other would rate them. Person’s A em-pathic ability is then determined by the degree to which A’s answers to(iii) and (iv) corresponds to B’s answer to (i) and (ii). The less A’s an-swers diverge from B’s, the higher one judges A’s empathic ability andaccuracy. The test aims to measure the level of empathy thanks to thedimension of role-taking. • Empathy Test: The authors in [48] created the so-called Empathy Test,that was used in industry in the 1950s. The main purpose of the test is tomeasure person’s ability to ”anticipate” certain typical reactions, feelingsand behaviour of other people. This test consists of three sections, whichrequire persons to rank the popularity of 15 types of music, the nationalcirculation of 15 magazines and the prevalence of 10 types of annoyancefor a particular group of people. • Measure of cognitive empathy: The authors in [49] is a cognitive empathyscale that consists of 64 questions selected from a variety of psycholog-ical personality tests such as the Minnesota Multiphasic Personality In-ventory (MMPI) and the California Personality Inventory (CPI). Hogan9hose those questions in response to which he found two groups of people-who were independently identified as either low-empathy or high-empathyindividuals-as showing significant differences in their answers. • Measure of emotional empathy: EETS, Emotional Empathy TendencyScale, has been developed in [50]. The questionnaire consists of 33 itemsdivided into seven subcategories testing for “susceptibility to emotionalcontagion”, ”appreciation of the feelings of unfamiliar and distant oth-ers,“extreme emotional responsiveness”, “tendency to be moved by others’positive emotional experiences”, “tendency to be moved by others’ nega-tive emotional experience”, “sympathetic tendency”, and “willingness tobe in contact with others who have problems”. This questionnaire empha-sizes the original definition of the empathy construct in its seven subscalesthat together show high split-half reliability, indicating the presence of asingle underlying factor thought to reflect affective or emotional empa-thy. The authors in [51] suggested more recently, however, that ratherthan measuring empathy per se, the scale more accurately reflects generalemotional arousability. In response, a revised version of the measure, theBalanced Emotional Empathy Scale [52] intercepts respondent’s reactionsto others’ mental states [55]. • Multidimensional measure of empathy: The Interpersonal Reactivity In-dex has been developed in [56] as an instrument whose aim was to measureindividual differences in empathy. The test is made of 28 items belongingto cognitive and emotional domain, and, in particular, they are belong-ing to four different domains. These are represented by four differentsubscales, Perspective Taking, Empathic Concern, Fantasy and PersonalDistress, each of which includes seven item answered on a 5-point scaleranging from 0 (Does not describes me very well) to 4 (Describes me verywell). The Perspective Taking subscale measures the capability to adoptthe views of the others spontaneously. The Empathic Concern subscalemeasures a tendency to experience the feelings of others and to feel sym-pathy and compassion for the unfortunate people. • Self-report empathy measure: Regarding the dimension of self-report em-pathy measures, we consider important to be mentioned the Scale ofEthnocultural Empathy [57], the Jefferson Scale of Physician Empathy[58], the Nursing Empathy Scale [59], the Autism Quotient [60] and theJapanese Adolescent Empathy Scale [61]. Although these instrumentswere designed for use with specific groups, aspects of these scales may besuitable for assessing a general capacity for empathic responding. • Measuring deficit in theory of mind: The Autism Quotient [60] was de-veloped to measure Autism spectrum disorder symptoms. The authorsviewed a deficit in theory of mind as the characteristic symptom of thisdisease [62] and a number of items from this measure relate to broaddeficits in social processing (e.g., “I find it difficult to work out people’s10ntentions.”). Thus, any measure of empathy should exhibit a negativecorrelation with this measure. The magnitude of this relation, however,will necessarily be attenuated by the other aspects of the Autism Quo-tient, which measure unrelated constructs (e.g., attentional focus and localprocessing biases). Additional self-report measures of social interchangeappearing in the neuropsychological literature contain items tapping em-pathic responding including the Disexecutive Questionnaire [63] and ameasure of emotion comprehension developed in [64]. These scales focuson the respondent’s ability to identify the emotional states expressed byanother (e.g., “I recognize when others are feeling sad”.). Current theo-retical notions of empathy emphasize the requirement for understandingof another’s emotions to form an empathic response [65]. Only a smallnumber of items on current measures of empathy, however, assess this abil-ity. Table 2 summarizes the Empathy scales measurement in Psychologyoverviewed above.
Empathy Models in Game Theory
In this subsection, we review some fundamental aspect of behavioral game the-ory. By a game theoretic approach, empathy and emotive intelligence are con-sidered essential for the development of the games themselves between players.In particular, empathy is essential for the strategic evolution of the games andfoundational of Nash Equilibrium [29, 30]. In other words, empathy itself is theinstrument that let the dynamic process between n-players happen as well asthe understanding and evaluation of their preferences and beliefs. Cooperativebehavior patterns must be considered an important sample of close relationsbetween individuals, based on confidding and disclosure. Relations like helpingand assistance behavior, as well as mutual confiding, mutual communicationand self disclosure are of cooperative behavior. To understand the possible roleof friendship in cooperation or defection between n-players in one-shot prisonerdilemma, it’s essential to reflect on how the evolutionary line of our specie hasthe possibility to create close relationship only between persons who are con-sidering themselves keen in terms of genes. The same kind of attitude is alsoinfluencing communal relationship.The cooperative behaviour in one shot Pris-oner Dilemma between friends, in particular, lead to the activation of the socalled cooperative-parithetic system, that is activated only when there is theperception that the last goal may be reached through a sort of collaborationbetween the players of the group itself. Empathy has been approached in differ-ent ways regarding game theory field. The author in [31] underlines how homoeconomicus must be empathetic to some degree, even if in a different meaningfrom the concept used in [32, 33]. In particular, in relation to game theory, heintroduces the concept of empathy in connection to the study of interpersonalcomparison of utility in games.More specifically, the model of empathy - altruism developed in [22] whoseassumption is that empathy feelings for another person create an altruistic moti-vation to increase that person’s welfare. Furthermore, the work of [34] is related11TEMS SCALE CORE CONCEPT AUTHORSEmpathy Ability 24 0-4 LikertScale Imaginative trans-posing of oneselfinto the thinking ofanother Dymond (1949)Empathy Test 40 RankingMultipleChoice Cognitive role-taking Kerr & Speroff(1954)Empathy Scale 64 0-4 LikertScale Apprehension ofanother’s conditionor state of mind byan intellectual orimaginati ve pointof view Hogan (1969)EETS - EmotionalEmpathy TendencyScale 33 -4 to 4 LikertScale Emotional Empa-thy Mehrabian & Ep-stein (1972)IRI- InterpersonalReactivity Index 28 0-4 LikertScale Reactions of one in-dividual to the ob-served experiencesof another Davis (1980)Ethnocultural Em-pathy Scale 31 Culturally SpecificEmpathy Patterns Wang, Davidson,Yakushko,Savoy, Tan, Bleier(2003)Jefferson Scale ofPhysician Empathy 5 0 - 5 LikertScale Patient oriented vstechnology orientedempathy in physi-cians Kane, Gotto, Man-gione, West , Hojat,(2001)Nursing EmpathyScale 12 0-7 LikertScale Nurses empathicbehaviour in thecontext of inter-action with theclient Reynolds (2000)Autism Quotient 50 0-4 LikertScale Autism SpectrumDisorder symptoms Baron-Cohen,Wheelwright,Skinner, Martin,Cubley (2001)Japanese Ado-lescent EmpathyScale 30 Likert Scale Empathy to feel ornot to feel posi-tive and negativefeelings towards theothers Hashimoto, Shiomi(2002)Table 2: Empathy measurement in psychology12o how the participants in a social dilemma experiment allocate some of theirresource to a person for whom they felt empathy. In the context of one trial pris-oner’s dilemma the authors underlined how empathy altruism should increasecooperation (that, then, will emerge in the situation). Secondly, the model ofempathy joy developed in [35]. This hypothesis underlines how a prosocial act isnot completely explained only by empathy but, also, by the positive emotion ofjoy a helper expects as a result of helping (or, better, of having a beneficial im-pact on) another person in need. In connection with this theory, empathy relieson an automatic process that generates, immediately, other types of behaviouruseful to predict the other regarding actions [79, 80].The works in [36, 37] proposed the exploration of more psychological andprocess-oriented models as a more productive framework in comparison withthe classical ones in game theory (fairness, impure altruism, reciprocity). Atthe light of this perspective, many concepts related to human behaviour are in-troduced to explain choice in game theory approach. Empathy as an operativeconcept must be understood as different from biases affecting belief formationand biases affecting utility. Empathy is operating through both beliefs and util-ity formation. Hence, in the presence of empathy, “beliefs and utility becomeintricately linked” [38]. Regarding empathy as a process of beliefs formation,the author proposed to analyze two mechanisms, imagine-self and imagine-other.Imagine self-players are able to imagine themselves in other people’s shoes, inother words they try to imagine themselves in similar circumstances. ”Imagineother” is when a person tries to imagine how another person is feeling. Theauthors underlined how empathy refers to people’s capability to infer what oth-ers think or feel, the so-called mind reading. They underlined, at the sametime, how empathy itself may have also any consequences on each player evalu-ation. The main contribution of the authors lies in a critique analysis of altru-istic behaviour in game theory. With three toy games, they demonstrated howempathy-altruism is not always linked with imagine-other dimension (and theso-called beliefs formation), since players may use only imagine-self dimension.The authors in [41] criticize a common concept of given empathy presentin public good experiment and, at the end, they demonstrate how empathymay be linked more to the context and social interaction itself in game theoryexperimental researches. The work [42] states that a disposition for empathydoes not influence the behaviour related to different games (towards them acentral role is played by Theory of Mind). Regarding this position, the sameauthors are underlying that also individual differences related to empathy do notshape social preferences. On the contrary, many other studies conducted showhow empathy may influence the structure of the games themselves. The workin [43] study the Ultimatum Game in an evolutionary concept and underline,in their study, how empathy can lead to the evolution of fairness. The work in[44] studied the correlation between empathy, anticipated guilt and pro socialbehaviour; in this study he found out that empathy affects pro-social behaviourin a more complex way than the one represented by the model of social choices.Recently, the concept of empathy has been introduced in mean-field-typegames in [45, 66, 67, 68] in relation to cognitively plausible explanation mod-13ls of choices in wireless medium access channel and mobile devices strategicinteraction. The main results of this applied research that lie in an operativeand real world use of empathy concept, are represented by the enforcement ofmean-field equilibrium payoff equity and fairness itself between players.
Participants
The population of participants includes 47 persons between 18 and 42 yearsold. The population is composed of 19 men and 28 women chosen from differenteducational backgrounds, cultures and nationalities (see Table 3). The names ofthe participants are not revealed. Different numbers are generated and assignedto the participants. Gender Number Frequency %Men 19 40.42Women 28 59.58Total 47Table 3: Composition: gender and frequency of the participantsAll the subjects were asked to perform two different tests: an IRI test (In-terpersonal Reactivity Index [69]) and a questionnaire that is mimicking, withan empathic and moral emphasis, a prisoner dilemma situation.
Empathy questionnaire
The IRI is a 28-item, 5-point Likert-type scale that evaluates four dimensions ofempathy: Perspective-Taking, Fantasy, Empathic Concern, and Personal Dis-tress. Each of these four subscales counts 7 items. The Perspective-Takingsubscale measures empathy in the form of individual’s tendency to adopt, in aspontaneous way, the other’s points of view. The Fantasy subscale of the IRIevaluates the subject’s ability to put themselves into the feelings and behavioursof fictional characters in books, movies, or plays. The Empathic Concern sub-scale assesses individual’s feelings of concern, warmth, and sympathy towardothers. The Personal Distress subscale measures self-oriented anxiety and dis-tress feelings regarding the distress experienced by others. As pointed out byBaron-Cohen and colleagues [70], however, the Fantasy and Personal Distresssubscales of this measure contain items that may more properly assess imagi-nation (e.g., “I daydream and fantasize with some regularity about things thatmight happen to me”) and emotional self-control (e.g., “in emergency situa-tions I feel apprehensive and ill at ease”), respectively, than theoretically-derivednotions of empathy. Indeed, the Personal Distress subscale appears to assessfeelings of anxiety, discomfort, and a loss of control in negative environments.Factor analytic and validity studies suggest that the Personal Distress subscale14ay not assess a central component of empathy [71]. Instead, Personal Distressmay be more related to the personality trait of neuroticism, while the most ro-bust components of empathy appear to be represented in the Empathic Concernand Perspective Taking subscales [72]IRI Davis Scale has been chosen for its relation to the measurement of in-dividual differences in empathy construct and, secondly, for its relation withmeasures of social functioning and the so-called psychological superior functions[73]. Table 4 summarizes the first questionnaire on multidimensional empathymeasure.
Game questionnaire
The second questionnaire is about a prisoner dilemma game. Each of the 47participants is asked to answer with a yes or no to 4 questions (see Table 5), eachrelated to the level of cooperation - cooperation (CC), cooperation - defection(CD), defection - cooperation (DC), and defection-defection (DD). A virtualother participant is represented in each interaction leading to 94 decision-makersin the whole process. The set of choices of each participant is { C, D } where D is also referred to N for non-cooperation. Data collection
Regarding the approach to the test, the whole population had a complete com-prehension and adherence to the tasks. Only 2 questions have been left out bya participant in the IRI test. In total we have a 99,63% of responsiveness in allthe questions. In the next section, we analyze the results of the second ques-tionnaire and study the impact of the four IRI scales on the decision making ofthe population.
The analysis is divided into three steps. In the first step, the population isclassified based on the result of the IRI scale. In the second step we analyzethe result of the cooperation. Lastly, the level of cooperation is studied on thebasis of classification of the population in the IRI scale.
IRI scale and population classification
The first step of the analysis concerns the results of women and men populationrespectively at the IRI scale. We depict the characteristic of each individualwho participated to the test in table 6. Table 7 represents the number of peoplebelonging to each sub-scale and those who do not.The classification of the population based on different empathy subscales ispresented in Table 7. The result shows that 14 people belong to a pure IRI scalewhile 25 people has a mixed IRI characteristics and 8 people do not belong to15able 4: IRI subscales. Extension of the empathy measure of Davis 1980,Yarnold et al.1996 and Vitaglione et al. 2003. The star sign (*) denotes anopposite (reversed) counting/scoring.Abridged item Women (59.58%) Men(40.42%)PT EC FS PD PT EC FS PD(1) Daydream and fantasize (FS)(2) Concerned with unfortunates (EC) 0.6(3) Can’t see others’ views ∗ (PT)(4) Not sorry for others ∗ (EC)(5) Get involved in novels (FS) 0.8(6) Not-at-ease in emergencies (PD) 0.7(7) Not caught-up in movies ∗ (FS)(8) Look at all sides in a fight (PT) 0.9124 0.2444(9) Feel protective of others (EC) 0.3(10) Feel helpless when emotional (PD)(11) Imagine friend’s perspective (PT) 0.8393 0.824(12) Don’t get involved in books ∗ (FS)(13) Remain calm if other’s hurt ∗ (PD)(14) Others’ problems none mine ∗ (EC)(15) If I’m right I won’t argue ∗ (PT)(16) Feel like movie character (FS)(17) Tense emotions scare me (PD)(18) Don’t feel pity for others ∗ (EC)(19) Effective in emergencies ∗ (PD)(20) Touched by things I see (EC) -0.3452(21) Two sides to every question (PT)(22) Soft-hearted person (EC)(23) Feel like leading character (FS)(44) Lose control in emergencies (PD)(25) Put myself in others’ shoes (PT)(26) Image novels were about me (FS)(27) Other’s problems destroy me (PD)(28) Put myself in other’s place (PT) 0.4216layer ICooperate DefectPlayer II Cooperate ( A, A ) (
B, C )Defect (
C, B ) (
D, D )Table 5: Payoff matrix for standard prisoner’s dilemma (without empathy con-sideration). The following inequalities must hold:
A > D > B > C [74].
Scale Type Women ID Men ID
PT 1,3, 4,10, 16,19,26,27 12EC 15 -FS 11,25 8PD - 18PT + EC 7,8,20 -PT + PD - 4,15PT + FS 6,12,24 -EC + FS 17 14EC + PD 2 -PT + EC + FS 9,18,21 5,19PT + EC + PD 23 6,11PT + FS + PD - 17EC + FS + PD 5 -PT + EC + FS + PD 13,14,22 9None of the scale 28 1,2,3,7,10,13,16Table 6: IRI scale and participant identificationany IRI scale. In the next section we study the level of cooperation based onthe classification of the population in the IRI scale.
Cooperation study: Prisoner Dilemma
The analysis is based on the IRI test results and on the prisoner’s dilemma testresults. The result of the prisoner’s dilemma suggested that the 35,71 % ofthe women population and the 36,84 % of men population have fully confessed.The results are depicted in Table 8, 9 and 10. Notice that 53,57 % of thewomen population and 31,57 % of the men population have partially confessed.When considering the whole population, 23,40% of them has partially confessed.Hence, it is necessary to classified them looking at the cooperation level withinthe population of those who partially confessed.A more refined version of cooperation among the women population who17 cale Type Women Men Total Freq
PT 8 1 9 19,14%EC 1 - 1 2,12 %FS 2 1 3 6,38%PD - 1 1 2,12 %PT + EC 3 - 3 6,38%PT + PD - 2 2 4,25%PT + FS 3 - 3 6,38%EC + FS 1 1 2 4,25%EC + PD 1 - 1 2,12 %PT + EC + FS 3 2 5 10,63%PT + EC + PD 1 2 3 6,38%PT + FS + PD - 1 1 2,12 %EC + FS + PD 1 - 1 2,12 %PT + EC + FS + PD 3 1 4 8,51%None of the scale 1 7 8 17,02%Participants 28 19 47Table 7: IRI scale and population distributionpartially confessed (15 out of 28) is given in Table 11. We want to computethe level of cooperation within that population and hence we care about allthe answer of the participants at the questionnaire. Then we derive the levelof cooperation in that population by computing the marginal probability ofconfess in the population. More precisely, we consider two random variables X = { c , d } and Y = { c , d } for player 1 and player 2 respectively where c i stands for cooperation of player i and d i defection. We then compute themarginal probability of cooperation of the player 1 given that the player 2 canconfess or defect. p ( c ) = X y ∈{ c ,d } p ( X = c , Y = y ) . Cooperation results (Women)
Decision positively partially denyResult 10 out of 28 15 out of 28 3 out of 28Frequency 35,71% 53,57% 10,71%Table 8: Cooperation results: Women18 ooperation results (Men)
Decision positively partially denyResult 7 out of 19 6 out of 19 6 out of 19Frequency 36,84 % 31,57% 31,57%Table 9: Cooperation results: Men
Cooperation results (Entire population)
Decision positively partially denyResult 17 out of 47 21 out of 47 9 out of 47Frequency 36,17 % 44,68% 19,14%Table 10: Cooperation results: Entire PopulationWe use the sample statistics to compute the probability of player 1 to cooperatethrough the number of occurrences of c . The result of the marginal probabilityof cooperation is equals to 0 ,
51. Hence in average, 7 people out the 15 can beclassified as positively confessed.Player ICooperate DefectPlayer II Cooperate 10 1Defect 5 13Table 11: Women population: Partially confess (decision making). p ( c ) = 0 . p ( c ) = 0 ,
46. Hence in average, 2 people out the 6 canbe classified as positively confessed.When considering the whole population, the fraction of people who partiallyconfess is 21/47 and the marginal probability of cooperation is equals to p ( c ) =0 ,
5. Hence in average, 10 people out of the 21 can be classified as positivelyconfessed.
Cooperation vs IRI scale
In this subsection, we are interested in computing the level of cooperation ineach IRI ’pure’ subscale. For this aim, we consider the subpopulation belongingto each scale. We then use the answer of cooperation in the prisoner dilemmagame for computing the probability of cooperation.
PT vs Cooperation p ( c ) = 0 . . Player ICooperate DefectPlayer II Cooperate 15 3Defect 6 18Table 13: Population: Partially confess (decision making). p ( c ) = 0 . Women
Coop \ PT A B C D Ep(c) 0 % 0.5 % 0.75% 0.66% 100%
Men
Cooperation \ PT A B C D Ep(c) 0 % 0 % 0% 66,66% 0%
Women + Men
Coop \ PT A B C D Ep(c) 0 % 0,5 % 75% 66% 100%The Pearson correlation coefficient between the level of cooperation and thePT scale is r W omen = 0 . p < .
01) for Women, r men = 1 ( p < .
01) formen and r population = 0 . p < .
01) for the population belonging to the PTscale. The interpretation is that there is a positive correlation for Women. Thefact that only one man was PT and had positively cooperate leads to a strongpositive correlation. The overall population of PT positively cooperates.
PD vs CooperationMen (18)
Cooperation \ PD A B C D Ep(c) 0 % 0 % 0 % 0% 0%There is only one man who is PD in the IRI scale and the probability of hislevel of cooperation was zero since he only denied.
EC vs Cooperation: WomenWomen (15)
Cooperation \ EC A B C D Ep(c) 0 % 0 % 100 % 0% 0%There is only one woman EC in the IRI scale and the probability of hislevel of cooperation is 1 since she positively confessed. Therefore the Pearsoncorrelation coefficient is one. 20
S vs CooperationWomen (11,25)
Coop \ FS A B C D Ep(c) 0 % 0 % 0 % 100% 0%
Men (8)
Coop \ FS A B C D Ep(c) 0 % 0 % 0% 0% 66,66%
Women + Men
Coop. \ FS A B C D Ep(c) 0 % 0 % 0% 100% 66,66%The Pearson correlation coefficient between the level of cooperation and theFS scale is r W omen = 1 ( p < .
01) for Women, r men = 1 ( p < .
01) for men and r population = 0 . p < .
01) for the population belonging to the FS scale. Thestrong positive correlation between FS and cooperation is due to the fact thattwo people had positively confessed and one had partially confessed. awful bad average good excellent3131416920 Empathy Scale Quality: Perspective Taking (PT) T o t a l S c o r e o f A n s w e r s WomenMen wful bad average good excellent010 Empathy Scale Quality: Personal Distress (PD) T o t a l S c o r e o f A n s w e r s WomenMenawful bad average good excellent20310 Empathy Scale Quality: Empathic Concern (EC) T o t a l S c o r e o f A n s w e r s WomenMen wful bad average good excellent136210 Empathy Scale Quality: Fantasy Scale (FS) T o t a l S c o r e o f A n s w e r s WomenMen
Cooperation vs IRI mixed scale
In this section we analyze the correlation between the mixed scale of length twoand we also compute the level of cooperation in each sub-population. • Case
PT + EC : the sub-population is composed of only women. ThePearson correlation coefficient between PT and EC is r W omen = r population = 0 , p < . . The probability of cooperation was p(c) = 0,5. • Case
PT + FS : the sub-population is composed of only women. ThePearson correlation coefficient between PT and FS is r W omen = r population = 0 , p < . . The probability of cooperation was p(c) = 0,62. • Case
EC + FS : the sub-population is composed of women and men. ThePearson correlation coefficient between EC and FS is r W omen = = 0 , p < . r Men = = 0 , p < . , r population = 0 , p < .
01) forwomen, men and the global population respectively. The probability ofcooperation was p(c) = 0,75. • Case
PT + PD : the sub-population is composed of only men. ThePearson correlation coefficient between PT and PD is r Men = r population = 0 , p < . . The probability of cooperation was p(c) = 0,6. • Case
EC + PD : the sub-population is composed of only women. ThePearson correlation coefficient between PT and FS is r W omen = r population = − , p < . . The probability of cooperation was p(c) = 0,5.The result of level of cooperation corresponding to the mixed IRI scale ofTable 14 is given in Table 15. We can observe that a high level of cooperationassociated to a high correlation coefficient correspond to the Empathy-Altruism23earson correlation PT EC FS PDPT - -0,3462FS - - - -PD - - - -Table 14: subscale correlationbehaviour (namely PT + FS and EC + FS ). A high level of cooperation as-sociated to a low correlation coefficient corresponds to Empathy-Spitefulness(namely PT + PD, EC + PD). Cooperation levelPT + EC 50%PT + FS 62,5%PT + PD 66,66 %EC + FS 75%EC + PD 50%Table 15: Level of cooperation at mixed scales
The effect of empathy on decisions
In this section we study the effect of individual scales on the degree of cooper-ation. For this aim we will compare the result of a pure scale with the groupof individual who do not belong to any IRI sub-scale. The motivation of thisplacebo test is that people who do not belongs to any scale can be a valuablesample for assessing the impact of an IRI scale like PT, EC and FS on user’sdecision making.Since our dataset is not too large, we rely on the nonparametric linear re-gression using the Theil’s method [76, 77, 78] for computing the slope medianvalue, given a dependent variable set { y } and an independent variable { x } .The dataset of the independent variable { x } is represented by an IRI scaleand it is obtained in the following way: (i) we first select the scale we wantto study ( let say PT scale). The cardinality of the dataset is then given bythe number of people belonging to that scale (see Table 6). Next the value x i associate to the individual i is computed by choosing the value (let say A)with the highest choice within the questionnaire { A, B, C, D, E } . Based on thechoice’s result, an integer value is assigned to { x i } following { A = 1 , B = 2 , C =3 , D = 4 , E = 5 } .The dataset of the dependable variable { y } is represented by the result ofthe cooperation. An individual i will be assigned a value y i = 1 if he has fullycooperated, y i = 0 . y i = 0 if he has denies.24ased on the above definition we can now study the effect of the PT scaleon the level of cooperation. There are 9 individual belonging to the pure PTscale (see Table 16 ). PT level: pure PT individual x 2 3 3 4 4 4 4 4 5y 0.5 0.5 1 0 0.5 1 1 1 1
Median slope: β P T = . Table 16:
PT: nonparametric linear regression dataset
The result of the Theil’s slope median is given by β P T = . , where β P T is the median slope value of the set {− . , − . , − . , − . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , , , , . , , , . , , , , . , } For the placebo test, the dataset for the individual belonging to “None ofthe scale” is given by the Table 17
PT level: None of the scale individual x 1 2 2 2 2 2 4 4y 0 0 0 0.5 0.5 1 0.5 1
Median slope: β non of the scale = . Table 17:
PT level: nonparametric linear regression dataset (none ofthe scale)
The result of the Theil’s slope median is given by β non of the scale = . , where β non of the scale is the median slope value of the set {− . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , , , . , . , . , . , , . , , , } Result interpretation: the angular coefficient β measures the effect of theindependent variable x on the dependent variable y . The more is the value of theangular coefficient, the better is the effect of the independent variable x on thevariable y . The results we get are β P T = 0 . β non of the scale = 0 . β P T < β non of the scale . Since we are studying the effect of the PT scale onthe level of cooperation and based on the following result, we cannot concludesthat the only factor which increases the level of cooperation is given by the PTcomponent. 25imilarly, we are interested in studying the influence of Fantasy scale compo-nent on the level of cooperation and we follow and apply the approach mentionedabove on the FS component.The result of the Theil’s slope median is given by β F S = . , where β F S is the median slope value (see Table 18 ) of the set {− . , . , . } FS level: pure FS individual x 4 4 5y 0.5 1 1
Median slope: β F S = . Table 18:
FS: nonparametric linear regression dataset
In the case of individual belonging to “None of the scale”, the result of theTheil’s slope median is given by β non of the scale = 0 . β non of the scale is the median slope (see Table 19 ) value of the set {− . , − . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , , , , , , , , , } FS level: Non of the scale individual x 1 1 1 1 2 2 2 3y 0 0 0.5 0.5 0 0.5 1 1
Median slope: β non of the scale = . Table 19:
FS level: nonparametric linear regression dataset (none ofthe scale)
The dataset of the component EC and PD is to small to perform the non-parametric linear regression on it.
Explanation
Game without empathy
We consider the one-shot game given by Table 20. Pareto efficiency, or Paretooptimality, is an action profile in which it is not possible to make any one playerbetter off without making at least one player worse off. A Nash equilibrium isa situation in which no player can improve her payoff by unilateral deviation.The action profile (
D, D ) is the unique Nash equilibrium, and D is a dominantstrategy choice for each player. But ( C, C ) Pareto-dominates (
D, D ) . The threechoice pairs (
C, C ), (
C, D ) , and ( D, C ) are all Pareto optimal, but (
C, C ) is themost socially efficient choice pair.The classical game model fails to explain the experimental observation:26layer ICooperate DefectPlayer II Cooperate (-6,-6) ( − , , − Game with empathy consideration
As observed from the data, a significant level of cooperation appears in theexperimental game. This suggests a new modelling and design of the classicalgame and better understanding the behavior of the participants. We proposea a new payoff matrix that takes into consideration the effect of empathy inthe outcome. Denote by λ the degree of empathy of the prisoner 1 has overthe prisoner 2 and by λ the vice versa. The payoff of the classical prisonerdilemma game (see Table 20) changes and now depends on the level of empathy λ and λ of the prisoners (see Table 21). Now we are interested in finding allthe possible equilibria of the new game based on the value of λ and λ . P IC DP II C ( − − λ , − − λ ) ( − , − λ )D ( − λ , − − − λ , − − λ ) Table 21: Payoff matrix of the prisoner dilemma with empathy consideration.Equilibrium analysis of Table 21 • CC is an equilibrium if λ ≥ ; λ ≥ • CN is an equilibrium if λ ≥ ; λ ≤ • NC is an equilibrium if λ ≤ ; λ ≥ • NN is an equilibrium if λ ≤ ; λ ≤ Since empathy can be positive, negative or null, we analyze the outcome of thegame with different signs of the parameters λ and λ .27 nalysis 1: λ , λ ≥ λ and λ as two random variableswith a distribution across the population. We generalized the outcome of thegame based on their values. • case 1: (medium-medium) : if λ , λ ∈ (cid:2) , (cid:3) then we have 3 equi-libria: CC, NN, and the mixed equilibria p C +(1 − p ) N or p C +(1 − p ) N with p = − λ λ ) and p = − λ λ ) . • case 2 (high - high): if λ , λ ∈ (cid:2) , (cid:3) then CC is the unique equilib-rium. • case 3 a (high - low): if λ ∈ (cid:2) , (cid:3) and λ ∈ (cid:2) , (cid:3) then CN is theunique equilibrium. • case 3 b (low - high): if λ ∈ (cid:2) , (cid:3) and λ ∈ (cid:2) , (cid:3) then NC is theunique equilibrium. • case 4 a (medium - low): if λ ∈ (cid:2) , (cid:3) and λ ∈ (cid:2) , (cid:3) then NNis the unique equilibrium. • case 4 b ( low - medium ): if λ ∈ (cid:2) , (cid:3) and λ ∈ (cid:2) , (cid:3) then NNis the unique equilibrium. • case 5 a ( λ high ): if λ > then C is a dominating strategy (un-conditional cooperation) for player 1. • case 5 b ( λ high ): if λ > then C is a dominating strategy (uncon-ditional cooperation). for player 2. • case 6 a ( λ low ): if λ ∈ (cid:2) , (cid:3) then N is a dominating strategy(unconditional non-cooperation) for player 1. • case 6 b ( λ low ): if λ ∈ (cid:2) , (cid:3) then N is a dominating strategy(unconditional non-cooperation) for player 2. Analysis 2: λ , λ < • if λ , λ < Analysis 3: λ > , λ < • if λ < • if λ > then CN is an equilibrium. • if λ < then NN is an equilibrium. Analysis 4: λ < , λ > • if λ < if λ > and λ ∈ (cid:2) − , (cid:3) then NC is an equilibrium. • if λ < then NN is an equilibrium.Figure 2 summarizes the outcome of the two-player game. −1/114 0 1/114 2/3 1−1/11401/1142/31 C C C CC CCN λ λ highmediummedium NCNNCNN N negative N NN cc NNNNNNN NN N Nhighlow low C NNpC + (1−p)
Figure 2: Equilibrium of the game with Empathy considerationThe proposed empathetic payoff better captures the preferences of the play-ers as a negligible proportion of cooperators are obtained analytically in thenew game. Thus, if one quantity accurately the empathy’s effect in the payoff,then the resulting game is more adapted to the results of experiment. By doingthis iteratively over several experiments and model adjustment we obtain bet-ter game theoretic models for real life interaction. We believe that the genericapproach developed here can be extended to other class of games as indicatedin [45, 75].
We have proposed a basic experiment on the role of empathy in one-shot Pris-oner Dilemma. We analyzed multidimensional components of empathy usingIRI scale. The experiment on the field conducted at NYUAD, Learning andGame Theory Lab, was composed of population of 47 persons (28 women and19 men). The experimental game provided interesting data. A non-negligibleproportion of the participants (35,71% of women and 36,84% of the men popula-tion) have fully confessed. Considering the whole population, 36,17% have fullyconfessed and the 19,14% have fully denied. In terms of partial confession be-haviors, 0.46% of the women population and 0,54% of the men population havepartially confessed. Considering the whole population, 0,45% have partiallyconfessed in this reproduction of Prisoner Dilemma game. Regarding the distri-bution of women and men population at the Interpersonal Reactivity Index, the29igure 3: Empathy scale distribution across the population of participantsexperimental results reveal that the dominated strategies of the classical gametheory are not dominated any more when users’s psychology is involved, and asignificant level of cooperation is observed among the users who are positivelypartially empathetic.The next future lines of our work would be based on a possible creationand implementation of a new model of empathy measurement that may takeinto account a multi-faceted presence of different variables (general attitude torisk, a general estimation of the different heuristics present in the person, howis internalized individually the model Imagine Self/Imagine other that leads toreciprocity, individual attitude to fairness). Our aim is to make of this modela possible and valid model of measurement related to every day life situationswhere empathy is playing a key role not only in engineering field but, also, insocial, economic and institutional area.Everyday life seems to be really different and far from laboratory situations,where all the concepts are built around a crystalized idea of what it is or it shouldbe. The evolutionary lines are then taken into account in our research as animportant way to get data from a longitudinal perspective. The dissatisfaction30or a simple instrument of testing empathy leads us to rethink, first of all,our next step in empathy measurement. It would take into account two lines,essentially:1. a combined series of instrument of measurement, that will consider a mul-tidimensional level of empathy.2. a possibility to test and retest the variable in different moments and ways(construct validity, test and retest the person about the same cluster, e.g affective empathy).3. A feedback from verbal and not verbal communication analysis software.It would be interesting to investigate (i) if there is any relationship betweenage and strategic decision making, (ii) How the altruism and spitefulness evolvewith increasing age. Furthermore, gender difference (if any) should be investi-gated in a bigger population and in games with distribution-dependent payoffs[39, 40, 53, 54].
Compliance with Ethical Standards
Conflict of interest: The authors declare that they have no conflict of interest.Ethical approval: All procedures performed in studies involving human par-ticipants were in accordance with the ethical standards of the institutionaland/or national research committee and with the 1964 Helsinki declaration andits later amendments or comparable ethical standards.Informed consent: Informed consent was obtained from all individual par-ticipants included in the study.
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Below we provide statistical data from the experimental game conducted in theLaboratory.Tables 22 23 24 25 report the data for women in the four IRI scales (PT,EC,FS,PD).Tables 26, 27, 28,29 focus on men statistical data for the four IRI scales(PT,EC,FS,PD). 37 iography
Giulia Rossi received her Master degree with summa cum laude in ClinicalPsychology in 2009 from the University of Padova. She worked as independentresearcher in the analysis and prevention of psychopathological diseases and inthe intercultural expression of mental diseases. Her research interests includebehavioral game theory, social norms and the epistemic foundations of mean-field-type game theory. She is currently a research associate in the Learning &Game Theory Laboratory at New York University Abu Dhabi.
Alain Tcheukam received his PhD in 2013 in Computer Science and Engi-neering at the IMT Institute for Advanced Studies Lucca. His research interestsinclude crowd flows, smart cities and mean-field-type optimization. He receivedthe Federbim Valsecchi award 2015 for his contribution in design, modelling andanalysis of smarter cities, and a best paper award 2016 from the InternationalConference on Electrical Energy and Networks. He is currently a postdoctoralresearcher with Learning & Game Theory Laboratory at New York UniversityAbu Dhabi.
Hamidou Tembine (S’06-M’10-SM’13) received his M.S. degree in Ap-plied Mathematics from Ecole Polytechnique and his Ph.D. degree in ComputerScience from University of Avignon. His current research interests include evo-lutionary games, mean field stochastic games and applications. In 2014, Tem-bine received the IEEE ComSoc Outstanding Young Researcher Award for hispromising research activities for the benefit of the society. He was the recipientof 7 best paper awards in the applications of game theory. Tembine is a prolificresearcher and holds several scientific publications including magazines, letters,journals and conferences. He is author of the book on ”distributed strategiclearning for engineers” (published by CRC Press, Taylor & Francis 2012), andco-author of the book ”Game Theory and Learning in Wireless Networks” (El-sevier Academic Press). Tembine has been co-organizer of several scientificmeetings on game theory in networking, wireless communications and smartenergy systems. He is a senior member of IEEE.38 omen positively confess
PT A B C D EWoman 3 0 3 0 4 0Woman 5 0 3 3 1 0Woman 6 0 1 2 3 1Woman 11 0 2 4 1 0Woman 15 0 5 2 0 0Woman 16 1 2 1 3 0Woman 17 0 3 3 0 1Woman 19 1 1 0 1 4Woman 24 2 1 2 2 0Woman 27 0 2 3 1 0Who is PT 3,6, 16, 19,24, 27Not PT 5,11,15,17Unclear
Women partially confess
PT A B C D EWoman 2 1 3 3 0 0Woman 4 1 1 2 2 1Woman 7 2 0 0 0 5Woman 8 2 0 2 3 0Woman 9 0 2 3 2 0Woman 10 0 3 2 2 0Woman 12 0 1 5 1 0Woman 14 0 1 4 2 0Woman 18 0 2 0 1 4Woman 20 1 1 1 1 3Woman 21 1 1 1 4 0Woman 22 0 0 7 0 0Woman 23 0 2 3 1 1Woman 25 1 3 1 0 2Woman 26 0 1 3 1 1Who is PT 4,7,8,9,10,12,14,18,20,21,22,23,26Not PT 2, 25Unclear
Woman Deny
PT A B C D EWoman 1 0 1 2 4 0Woman 13 0 1 2 2 2Woman 28 3 1 1 2 0Who is PT 1,13Not PT 28UnclearTable 22:
PT: Woman Result (positively, partially and deny tables) oman positively confess EC A B C D EWoman 3 2 3 1 1 0Woman 5 2 1 0 4 0Woman 6 0 4 1 1 1Woman 11 0 4 1 1 1Woman 15 3 0 2 2 0Woman 16 3 1 2 1 0Woman 17 2 1 1 3 0Woman 19 3 1 1 1 1Woman 24 0 4 1 1 1Woman 27 2 2 2 1 0Who is EC 5,15,17Not EC 3,6,11,16,19,24,27Unclear
Woman partially confess
EC A B C D EWoman 2 1 2 0 3 1Woman 4 1 2 4 0 0Woman 7 1 2 0 1 3Woman 8 3 0 1 3 0Woman 9 1 2 0 4 0Woman 10 3 1 1 2 0Woman 12 0 4 2 1 0Woman 14 0 0 4 3 0Woman 18 1 0 2 1 3Woman 20 3 0 0 1 3Woman 21 2 1 0 3 1Woman 22 1 2 0 4 0Woman 23 0 2 2 3 0Woman 25 4 0 1 1 1Woman 26 2 1 2 0 2Who is EC 2,9,18,14,7,20,21,8,22,23Not EC 4,10,12,25,26Unclear
Woman Deny
EC A B C D EWoman 1 1 1 4 1 0Woman 13 0 2 2 3 0Woman 28 2 1 2 0 2Who is EC 13Not EC 1,28UnclearTable 23:
EC: Woman Result (positively, partially and deny tables) oman positively confess FS A B C D EWoman 3 4 1 2 0 0Woman 5 3 0 3 1 0Woman 6 0 2 4 1 0Woman 11 0 2 1 4 0Woman 15 3 2 2 0 0Woman 16 1 5 0 1 0Woman 17 2 1 2 2 0Woman 19 2 3 0 1 1Woman 24 0 1 5 1 0Woman 27 2 0 3 2 0Who is FS 11,5,6,17,24,3Not FS 3,15,16,19Unclear
Woman partially confess
FS A B C D EWoman 2 2 1 1 1 2Woman 4 1 4 1 0 1Woman 7 0 3 1 3 0Woman 8 1 1 3 1 1Woman 9 2 0 0 5 0Woman 10 1 6 0 0 0Woman 12 0 1 4 2 0Woman 14 0 0 2 4 1Woman 18 1 1 2 2 1Woman 20 2 1 1 1 2Woman 21 1 1 3 2 0Woman 22 1 1 2 3 0Woman 23 0 0 1 1 5Woman 25 1 1 2 2 1Woman 26 0 4 3 0 0Who is FS 9,12,14,18,21,22,23,25Not FS 4,10,26Unclear
Woman Deny
FS A B C D EWoman 1 2 3 1 1 0Woman 13 0 0 0 3 4Woman 28 4 0 0 2 1Who is FS 1,28Not FS 13UnclearTable 24:
FS: Women’s Result (positively, partially and deny tables) oman positively confess PD A B C D EWoman 3 1 2 2 2 0Woman 5 3 0 0 4 0Woman 6 2 3 0 4 0Woman 11 0 4 3 0 0Woman 15 0 4 2 1 0Woman 16 1 2 3 1 0Woman 17 3 3 1 0 0Woman 19 4 1 0 1 1Woman 24 1 2 3 1 0Woman 27 2 3 2 0 0Who is PD 3,6,11,15,16,17,4,27,24Not PD 5Unclear
Woman partially confess
PD A B C D EWoman 2 3 0 1 1 2Woman 4 1 1 4 0 1Woman 7 1 2 1 2 1Woman 8 3 1 2 1 0Woman 9 0 4 3 0 0Woman 10 4 2 1 0 0Woman 12 0 4 2 1 0Woman 14 0 1 5 1 0Woman 18 2 2 1 2 0Woman 20 1 2 3 0 1Woman 21 1 5 0 1 0Woman 22 0 3 2 1 1Woman 23 0 0 5 2 0Woman 25 2 4 0 0 1Woman 26 2 3 1 0 1Who is PD 23, 2, 14, 22Not PD 4, 8, 9, 10, 12, 18, 20, 21, 25, 26Unclear
Woman Deny
PD A B C D EWoman 1 2 1 1 1 1Woman 13 0 0 3 4 0Woman 28 3 1 0 1 2Who is PD 1,28Not PD 13UnclearTable 25:
PD: Women Result (positively, partially and deny tables) en positively confess PT A B C D EMan 1 0 3 2 1 1Man 4 0 2 1 1 3Man 8 0 2 4 1 0Man 10 0 1 2 4 1Man 11 3 0 1 1 2Man 12 1 1 2 3 0Man 19 0 1 1 4 1Who is PT 4,10,12,11,19Not PT 1,8Unclear
Men partially confess
PT A B C D EMan 3 0 3 1 3 0Man 5 0 3 3 0 0Man 6 1 0 1 4 1Man 7 3 3 0 0 1Man 13 2 5 0 0 0Man 14 4 0 1 0 2Who is PT 7,13,14Not PT 5,6Unclear
Men Deny
PT A B C D EMan 2 0 3 2 0 2Man 9 0 1 3 3 0Man 15 0 2 1 4 0Man 16 0 4 3 0 0Man 17 0 3 3 1 0Man 18 0 4 3 0 0Who is PT 9,15,17Not PT 2,16,18UnclearTable 26:
PT: Men’s Result (positively, partially and deny tables) en positively confess EC A B C D EMan 1 3 3 0 1 0Man 4 3 0 2 1 1Man 8 0 4 3 0 0Man 10 0 2 4 0 1Man 11 1 0 1 4 1Man 12 3 1 1 2 0Man 19 1 0 1 4 1Who is EC 10,11,19Not EC 1,8,12,4Unclear
Men partially confess
EC A B C D EMan 3 0 5 2 0 0Man 5 1 1 3 0 2Man 6 1 1 0 4 1Man 7 1 2 4 0 0Man 13 0 5 2 0 0Man 14 0 1 4 2 0Who is EC 5,6,14Not EC 3,7,13Unclear
Men Deny
Man EC A B C D EMan 2 2 2 0 2 1Man 9 0 3 1 3 0Man 15 1 3 3 0 0Man 16 3 1 3 0 0Man 17 0 3 4 0 0Man 18 3 2 1 1 0Who is EC 9Not EC 2,15,16,17,18Unclear Table 27:
EC: Men’s Result group 3 en positively confess FS A B C D EMan 1 1 3 1 0 2Man 4 1 2 1 0 1Man 8 1 1 1 1 3Man 10 0 2 3 2 0Man 11 3 1 0 0 3Man 12 0 2 4 1 0Man 19 0 2 0 4 1Who is FS 8,10,19Not FS 1, 4,11,12Unclear
Men partially confess
FS A Man B C D EMan 3 2 5 0 0 0Man 5 0 0 4 1 2Man 6 4 3 0 0 0Man 7 4 3 0 0 0Man 13 5 1 1 0 0Man 14 0 1 6 0 0Who is FS 3,6,7,13Not FS 5,14Unclear
Men Deny
FS A B C D EMan 2 3 1 0 3 0Man 9 0 2 4 1 0Man 15 0 3 2 1 1Man 16 1 3 2 1 0Man 17 1 1 4 1 0Man 18 0 4 3 0 0Who is FS 9, 17Not FS 2,15,16,18UnclearTable 28:
FS: Men’s Result (positively, partially and deny tables) en positively confess PD A B C D EMan 1 2 2 0 3 0Man 4 2 0 2 0 3Man 8 0 3 2 2 0Man 10 0 3 3 1 0Man 11 1 1 1 0 4Man 12 3 2 2 0 0Man 19 2 1 2 1 1Who is PD 4,10,11Not PD 1,8,10,12,19Unclear
Men partially confess
PD A B C D EMan 3 0 5 2 0 0Man 5 0 4 1 2 0Man 6 1 0 4 2 0Man 7 4 1 0 0 2Woman 13 1 3 3 0 0Woman 14 0 4 1 1 1Who is PD 6Not PD 3,5,7,13,14Unclear
Men Deny
PD A B C D EMan 2 4 1 0 1 1Man 9 1 2 3 1 0Man 15 1 2 0 4 0Man 16 0 7 0 0 0Man 17 2 0 1 4 0Man 18 0 2 4 1 0Who is PD 9,15,17,18Not PD 2,16UnclearTable 29: