情緒在最後通諜賽局中的影響及預測 - 政大學術集成

全文

(1)國立政治大學經濟學研究所博士學位論文 National Chengchi University (NCCU) Graduate Institute of Economics Studies Doctoral Dissertation 指導教授:陳樹衡博士 Advisor：Dr. Chen, 治 Shu-Heng. 立. 政. 大. ‧ 國. 學. 情緒在最後通牒賽局中的影響及預測. ‧. Emotions and Economic Decision Making in. y. Nat. er. io. sit. Ultimatum Game Experiments: An Approach based. n. al on Artificial Emotional Agents v i n Ch engchi U. 研究生：林家仰 By Lin, Chia-Yang 中華民國 103 年 7 月 July, 2014.

(2) 誌謝 Economic is the oldest of the arts, the newest of the sciences! 首先誠摯的感謝指導教授陳樹衡博士，老師悉心的教導使我得以一窺情緒在實驗經濟學和智慧型代理人基等應用領域的深奧，不時的討論並指點我正確的方向，使我在這些年中獲益匪淺。老師對學問的嚴謹更是我輩學習的典範。. 政治大. 本論文的完成另外亦得感謝各位口試老師的協助。因為有你們的幫忙，使得. 立. 本論文能夠更完整而嚴謹。. ‧ 國. 學. 博士班的日子，在實驗室和研究中心裡有許多共同的心情點滴，不論學術上. ‧. 的討論，甚或言不及義的閒扯，都是生活的印記。來自眾位學長姐、同學及學弟. y. Nat. 妹的共同砥礪，你/妳們的陪伴讓研究生活變得絢麗多彩。感謝中擎、秉聰學長. 能在我迷惘時為我解惑，你們助我順利走過這幾年。. n. al. Ch. engchi. er. io. sit. 和嘉玲學姐不厭其煩的指導我研究中的缺失，也感謝業榮、瑩芳博士的幫忙，總. i n U. v. 最後，謹以此文獻給我摯愛的雙親，若沒有你們的體諒、包容，相信這幾年的生活將是很不一樣的光景，感謝你們。.

(3) 摘要關於情緒和決策的相關討論，在近期實驗經濟學的研究上，一直是非常熱絡的課題。在各種研究的方法中，最後通牒賽局一直是文獻上一種最廣為使用來探究情緒和決策之間關係的實驗方法。本研究利用最後通牒賽局實驗的結果，建構出一套人工情緒模型，來反推並探究受試者互動過程中，內生產生的情緒對決策的影響。在不受外力干擾下，我們假設受試者的情緒在最後通牒賽局中，可能在兩個情況下被觸發，其一是當提案被接受或拒絕時，以及，當提案的數字和心中. 政治大. 設想有落差時都可能產生情緒。同時在我們的最後通牒賽局中，也設計使用金錢. 立. 和巧克力進行實驗，以嘗試了解貨幣與非貨幣在決策中，是否帶來差異性的情緒. ‧ 國. 學. 刺激。我們的研究採用智慧型代理人基模型，並透過蒙地卡羅模擬，來測試不同參數下我們設定的人工情緒是否能對決策產生影響。借由模擬的方式，不僅讓我. ‧. 們可以借此檢驗情決策行為受情緒改變的顯著程度，更能進一步的觀察不同的交. y. Nat. n. er. io. al. sit. 易媒介和受試者性別差異帶來的行為改變。. Ch. engchi. i n U. v.

(4) Abstract The ultimatum game has been frequently used as an economic laboratorial environment to study the significance of emotions in economic decision making. While in the ultimatum game literature it has been often argued that respondents may react emotionally to the unfair offers made by the proposer, in this article we make the first attempt to propose a model of the artificial emotional agent to examine the empirical relevance of the emotional behavioral model using data from the ultimatum. 政治大 between the proposer and the 立. game experiments. The artificial-agent approach allows us to hypothesize each kind of possible interaction. respondent that may be. emotionally cueing. In this article, we build our artificial agents with two possible. ‧ 國. 學. emotionally cueing mechanisms: one is called the nay-based emotion and the other is. ‧. called the reference-based emotion. Both emotions can be quantified with different. sit. y. Nat. behavioral parameters. Using Monte Carlo simulation, we are able to examine how. io. er. strongly these two emotions can affect how proposer announces his/her offers and why responder considers accepting or rejecting the offer. The artificial agent approach. al. n. v i n is applied to a fine analysis by C taking into account theUexchange medium, i.e., money hengchi and chocolate, as well as gender. Hence, not only can we examine generally the significance of emotions in decision making, but also can have a fine look at the difference caused by the exchange medium and gender.. Keywords: artificial emotion; medium; gender; ultimatum game.

(5) Table of Content Chapter 1. Introduction ................................................................................................ 1. 1.1. Background ................................................................................................ 1. 1.2. Research Features ...................................................................................... 3. 1.3. Overview .................................................................................................... 8. Chapter 2. Related Research ........................................................................................ 9. 2.1. Ultimatum game......................................................................................... 9. 2.2. Emotion .................................................................................................... 12. 立. 政治大. ‧. ‧ 國. 學. sit. y. Nat. er. Emotions in ultimatum game ....................................................... 13. io. 2.2.1. al. n. v i n Emotion in C AI............................................................................... 16 hengchi U. 2.2.2. Chapter 3. Emotion Index Model .............................................................................. 17. 3.1. Proposer ................................................................................................... 17. 3.2. Responder ................................................................................................ 25. 3.2.1. Uni-variant model ........................................................................ 25. i.

(6) 3.2.2. Bi-variant model .......................................................................... 26. Chapter 4. Experiment design and procedures .......................................................... 28. 4.1. Ultimatum game....................................................................................... 28. 4.2. Monte Carlo simulation ........................................................................... 30. Chapter 5. Ultimatum game experiment results ........................................................ 33. Chapter 6. Simulation results..................................................................................... 40. 6.1. Proposer ................................................................................................... 41. 立. ‧ 國. ‧. Money and Chocolate: Gender .................................................... 43. y. sit er. io. Responder ................................................................................................ 48. al. n. 6.2. Money and Chocolate: General ................................................... 41. Nat. 6.1.2. 學. 6.1.1. 政治大. Ch. engchi. i n U. v. 6.2.1. Money and Chocolate: General ................................................... 48. 6.2.2. Money and Chocolate: Gender .................................................... 51. Chapter 7. Conclusions and future research .............................................................. 54. 7.1. Conclusions .............................................................................................. 54. 7.2. Future research ......................................................................................... 55 ii.

(7) Appendix A.. Relative difference: design and test ................................................. 69. Appendix B.. List of one-shot ultimatum game results .......................................... 71. Appendix C.. Results of Ultimatum game ............................................................. 73. Appendix D.. Ultimatum Game 最後通諜遊戲指導語 ........................................ 77. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. iii. i n U. v.

(8) List of Figues Figure 1. The variety of Ultimatum game researches ................................ 10. Figure 2. Reference-Based Emotion Index, Equation ( 2 ) ........................ 22. Figure 3. Acceptance rate as a function of experience. Note: The numbers. above the bars give the number of observations for that bar (Cooper & Dutcher, 2011) ...................................................................................... 37. Figure 4. 政治大. Acceptance rate as a function of experience in our experiments.. 立. (M) means the money treatment and (C) means the chocolate treatment.. ‧ 國. 學. .............................................................................................................. 37. er. al. n. Figure 8. sit. Money Experiments: All subiects (proposers) ........................... 40. io Figure 7. y. Nat. Figure 6. ‧. Figure 5 Offer Rates through Time .............................................................. 38. i n U. v. Chocolate Experiments: All subjects (proposers)....................... 41. Ch. engchi. Reference-Based Emotion: Money and Chocolate Experiments. (proposer) ............................................................................................. 42. Figure 9. Money Experiments: Male and Female (proposer) .................... 43. Figure 10. Chocolate Experiments: Male and Female (proposer) ............. 44. iv.

(9) Figure 11. The Nay-Based Emotion X in the Money Experiments and. Chocolate Experiments: Male proposer ............................................... 45. Figure 12. The Reference-Based Emotion Y in the Money Experiments. and Chocolate Experiments: Male ....................................................... 45. Figure 13. The Nay-Based Emotion X in the Money Experiments and. Chocolate Experiments: Female proposer ........................................... 46. 政治大 and Chocolate Experiments: Female proposer .................................... 46 立. The Reference-Based Emotion Y in the Money Experiments. Figure 15. 學. ‧ 國. Figure 14. The Reference-Based Emotion Y (C2) in the Money. Experiments (Left) and the Chocolate Experiments (Right): proposer47. ‧ The reference based emotion in the money experiment:. sit. y. Nat. Figure 16. er. io. responder .............................................................................................. 48. al. n. v i n C h based emotionUin the reference engchi. Figure 17. The. chocolate experiment:. responder .............................................................................................. 49. Figure 18. Money experiment: all subjects (responders) ......................... 49. Figure 19. Chocolate experiment: all subjects (responders) ...................... 50. Figure 20. Money Experiments: Male and Female (uni-variant, responder). .............................................................................................................. 51. v.

(10) Figure 21. Chocolate Experiments: Male and Female (uni-variant,. responder) ............................................................................................ 52. Figure 22. Money Experiments: Male and Female (bi-variant, responder). .............................................................................................................. 53. Figure 23. Chocolate Experiments: Male and Female (bi-variant, responder). .............................................................................................................. 53. 政治大. Figure 24 Individualized preference in Money experiment: responder ....... 56. 立. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. vi. i n U. v.

(11) List of Tables Table 1. Four classification of emotions (Pfister & Böhm, 2008) ............. 13. Table 2. Range for Emotional Parameters and the Reference.................... 21. Table 3. Subjects: Gender and the Role-to-Play ........................................ 29. Table 4. Monte Carlo Simulation: One Specific Runs ............................... 31. Table 5. Descriptive Statistics of the Ultimatum Game: Proposers ........... 34. Table 6. Descriptive Statistics of the Ultimatum Game: Responders ........ 34. 立. 政治大. ‧ 國. 學. Stastics test in defferent Medium and gender : proposer ............. 35. Table 8. Stastics test in defferent Medium and gender : responder ......... 35. io. sit. y. Nat. Average Offer Rates in Money and Chocolate Experiments ....... 35. n. al. er. Table 9. ‧. Table 7. Ch. engchi. vii. i n U. v.

(12) Chapter 1 Introduction 1.1 Background In this research, we address the idea of how to conceptualize emotions embedding in decision making. The study of emotions in the context of decision making, beginning. 政治大 Feldman, 1986; Toda, 1980), has received increasing attention over the past decade 立. more than thirty years ago (Bell, 1982; Loomes & Sugden, 1982; Pamela Johnston &. (Berezin, 2010; Haselhuhn & Mellers, 2005; Heilman et al., 2010; Kaufman, 2006;. ‧ 國. 學. Mussel et al., 2014; Rick & Loewenstein, 2008; Xiao & Houser, 2007). There is, however,. ‧. little consensus in the literature on what is actually meant by emotion or affect. This. sit. y. Nat. research tries to contribute to a more precise and useful conceptualization of emotion. io. er. concerning the emotion-decision making relationship. Although recent economic models of human decision making have recognized the role of emotion as an important biasing. al. n. v i n C h on decisions has factor, the impact of incidental emotion remained poorly explored. Given engchi U. that people are often not conscious of being influenced by the incidental emotional state, decisions based on an incidental emotion can become the basis for future decisions and we should pay attention on this enduring impact of transient emotions on decision making (Andrade & Ariely, 2009).. The modern economy model of decision making is based upon the assessing of utility system. When neoclassical economists constructed the “utility”, they refer to the desirability of an outcome, and decision making is represented as a choice of maximizing 1.

(13) aggregate outcome. Mainstream economists assume that choices reflect relative prices and preferences and, for rational subjects, the preferences are consistent at any point in time. However, if we back to the early age which the concept of utility was proposed (Bentham, 1789) and developed (Mill, 1863), we would find out emotion played the conspicuous part in the theory. Roughly, they proposed that people ought to desire those things that net sum of positive over negative emotion, where positive utility is defined as the tendency to bring happiness, and negative utility is defined as the tendency to bring pain (Loewenstein, 2000; Read, 2007).. 政治大. Since the emotion-utility was hard to measure, after 19 centuries, economists. 立. considered the order preference not happiness to construct their model(Arrow, 1958; Von. ‧ 國. 學. Neumann & Morgenstern, 1947). That’s why most economists viewed detailed accounts of such emotions as outside the scope of their discipline (Elster, 1998). Fortunately, in the. ‧. last three decades, the advent of “behavior economics” brought the emotions back to our. y. Nat. n. al. er. io. processes.. sit. former, and economists consider emotions and emotionality in the analyses of economic. Ch. engchi. i n U. v. Here are some examples that economists integrated emotion into economics. Robert Frank (1987, 1988, 2011) investigates the strategic role of emotions. Paul DiMaggio (2002) has made a call for“endogenizing animal spirits” to analysis uncertainty and risk. Pixely (2002, 2004, 2009) has written on emotions in economy and finance. Berezin (2009, 2010) reviewed this topic and made a call for more research by economic sociologists into the link between emotions and economic action. Now, emotions have become a major area of scientific study in economics (Civai et al., 2010; Pillutla & Murnighan, 1996; Sanfey et al., 2003), which have traditionally been linked to rational 2.

(14) thinking and choices (Von Neumann & Morgenstern, 2007).. As we mention, although, that emotion has long been recognized in the literature with moderate research progresses, this research differ from existing studies in four aspects and we will illustrate our contributions more specifically in the following： . Emotions were endogenously generated. . Focus on both proposers and responders in ultimatum game. . Two different mediums in ultimatum game. . Artificial emotions. 立. 政治大. ‧ 國. 學 ‧. 1.2 Research Features n. al. Ch. engchi. er. io. Emotions were endogenously generated. sit. y. Nat. . i n U. v. Importantly, Bandelj (2009) argues that current literature recognizes the importance of emotions but unexamined the roles of emotions in economic interaction between actors. She proposes a different perspective which focuses on emotional embeddedness and examines how emotions matter in economic interactions. Emotional embeddedness research concerns with a premise that emotions result from and are influenced by interactions between economic actors during the economic process. Following this line of inquiry, we start to pay attention to emotion embeddedness in decision making process. In our experiment environment, we do not apply an external device to arouse subjects’ 3.

(15) emotions, and if later on emotions do begin to play a role, it should be endogenously generated.. . Focus on both proposers and responders in ultimatum game. Usually, decision making problems could be viewed as choices among alternatives, and the traditional economic theories have told us that the rational subject should be free from the paradox of choice (Schwartz, 2004). However, empirical studies have provided evidences for human’s boundary-rationality and decision conflict during interpersonal. 政治大 (Muramatsu & Hanoch, 2005). 立 We consider ultimatum game. situations in which emotional functions of humans can violate economical rationality (Güth et al., 1982) to. ‧ 國. 學. implement the decision-making environment and to retrieve the embeddedness emotion. The ultimatum game has been frequently, may be the most, used as an economic. ‧. laboratorial environment to study the significance of emotions in economic decision. sit. y. Nat. making. Basically, two players are required to join ultimatum game. One player announces. n. al. er. io. a sharing proposal, and the other one must chose to accept or reject an offer of a monetary. i n U. v. division with the game partner. Although players may consider both strategic aspects and. Ch. engchi. equity aspects of the situation, as pointed out by Camerer (2003), whether to accept an ultimatum offer requires no strategic thinking since it is simply a choice. Hence, player’s emotions rather than game-theoretic reasoning seem to be the culprit responsible for the failure of the prediction.. We notice that there also exists a pile of literature addressing emotional arousal through emotional embeddedness in ultimatum game. Pillutla and Murnighan (1996) studied how the feeling of unfair offers can be attenuated or alleviated through. 4.

(16) information availability. Xiao and Houser (2005) considered the relationship between emotion releasing and communication channels. However, most of these studies (Bosman et al., 2001; Knight, 2012; Ma et al., 2012) focus on the perspective of responders and, mainly, the topics along with responders’ reactions to unfair offers. Our research not only target on responders, we try to contribute a deep look at the role of emotions in proposers’ decisions.. . Two different mediums in ultimatum game. 政治大 know whether the medium立 of exchange can actually trigger or induce emotions differently In this vein, if emotions do play a role in the ultimatum game, then it is interesting to. ‧ 國. 學. and, as a consequence, lead to different bargaining behavior. This is one of the main research questions of this paper. Bowles et al. (1997) hinted us:. ‧. sit. y. Nat. Economic theory typically assumes that behavioral responses should. io. er. be independent of the medium of exchange. It shouldn’t matter very much whether players in an ultimatum game are dividing a pot of ten. al. n. v i n dollars or ten candy C bars that can be exchanged h e n g c h i U for a dollar each.. Daily experience, however, contrasts with this assumption….. To test the importance of the medium of exchange in influencing ultimatum behavior, the game can be played with different mediums, including cash, food, service time and symbolic items (p. 440). Although it is quite intuitive to see how people will do in decision making when facing multiple choices, past researches were seldom designed for this aim in the ultimate game. In fact, only some earlier studies using non-money mediums and have shown this 5.

(17) possibility. For example, in their study of the children behavior in ultimatum games, Murnighan and Saxon (1998) found:. The fact that our respondents tended to accept offers of one M&M more often than offers of one penny suggests that respondents evaluated them quite differently. Their emotional reactions when the game switched to M&Ms were quite clear: they were much more physically active and smiled more when they knew that the currency had changed to M&Ms. Thus, future research might investigate. 政治大. whether immediately disposable, attractive commodities like M&Ms. 立. lead people to act as if anything is clearly better than nothing. (p. 440). ‧ 國. 學. Also, in their ultimatum games involving smokers, Takahashi (2007) also find that. ‧. smokers avoided inequity in the ultimatum game more dramatically for money than for. er. io. sit. y. Nat. cigarettes.. With these initial evidence, this research attempts to address whether money and. n. al. chocolate will trigger. i n C hobservably differently. emotions engchi U. v. Roughly, both money and. chocolate are people favorite items, but there exists the difference between monetary and non-monetary. We already learned that informal non-monetary sanctions, comparing to monetary sanction, may lose effectiveness over time (Masclet et al., 2003; Noussair & Tucker, 2005). However, it is just the beginning that economists are trying to understand the reasons non-monetary affect economic outcomes.. Comparing subjects’ behavior. under money and chocolate would help us to find out the relationship and influence of monetary and non-monetary mediums.. 6.

(18) . Artificial emotions. Finally, the way which we study emotions or measure emotions is different from the usual psychological or neuropsychological approach employed in this research area, exemplified by Sanfey et al. (2003), a pioneering study in this field. We do not offer any psychological or neurobiological measure of emotions, neither by skin conductance responses nor by fMRI (functional magnetic resonance imaging). The way which we approach the issue is inspired from a separate literature on artificial agents(Chen, 2012).. 政治大 first attempt to propose a model 立 of the artificial emotional agent to examine the empirical. Different from other emotion research in ultimatum game, in this article, we make the. ‧ 國. 學. relevance of the emotional behavioral model using data from the ultimatum game experiments. The artificial-agent approach allows us to hypothesize each kind of possible. ‧. interaction between the proposer and the respondent that may be emotionally cueing. We. sit. y. Nat. build our artificial agents with two possible emotionally cueing mechanisms: one is called. n. al. er. io. the nay-based emotion and the other is called the reference-based emotion. Both emotions. i n U. v. can be quantified with different behavioral parameters. Using Monte Carlo simulation, we. Ch. engchi. are able to examine how strongly these two emotions can affect responder’s decision on accepting or rejecting the offer. The artificial agent approach is applied to a fine analysis by taking into account the exchange media, i.e., money and chocolate, as well as gender. Hence, not only can we examine generally the significance of emotions in decision making, but also can have a fine look at the difference caused by the exchange medium and gender.. 7.

(19) 1.3 Overview The rest of the thesis is organized as follows. The related research background is given in Chapter 2. Among it, the ultimatum game is outlined first as in Section 2.1. Then Section 2.2 gives a brief survey of the emotion researches involving in ultimatum game and applying emotion theories in AI area. In Chapter 3, we explain how to model and calculate the” emotion index”. Then we describe the basic information that how ultimatum game experiments are conducted in Section 4.1. Section 4.2 is an instruction of. 政治大. Monte Carlo simulation in our research. Chapter 5 and 6 are the results’ reports in. 立. ultimatum game and Monte Carlo simulation, separately. The final Chapter gives a. ‧ 國. 學. conclusion and directions for further study.. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. 8. i n U. v.

(20) Chapter 2 Related Research 2.1 Ultimatum game The standard ultimatum game was first studied in Güth et al. (1982) in which two players are required to join. One player (the proposer) receives an amount of money provisionally and makes a proposal to the other player (the responder) regarding how to. 政治大 implemented and subjects立 share the money by the proposal; otherwise, both players. divide this money between them. If the responder accepts the proposed offer, the game is. ‧ 國. 學. receive nothing. In investigating subjects’ behavior in ultimatum game, past studies mainly consider two theories: economic rationality which prompts the proposer to exploit. ‧. his strategic advantage (at least to a moderate degree) and tells the responder to accept. sit. y. Nat. low offers; and equity theory which says that the proposer should demand an equitable. n. al. er. io. share (equal to his cost share) and that the responder should reject non-equitable demands (Brandstätter & Königstein, 2001).. Ch. engchi. i n U. v. Remarkable, the modal equal split offer is an extremely robust phenomenon. On average, players in the game tend to offer around 30-50% of the pie in the standard version of the game. Such offers are almost always accepted. Responders’ acceptance rates decrease with smaller offers, and they approach zero quite quickly for offers below 20%. These findings have been replicated across different subject populations, with different monetary stakes and different experimental procedures (Henrich et al., 2007). From an ex post perspective, taking actual rejection rates into account, either the equal. 9.

(21) split or offers around 40% are payoff maximizing for proposers (see Camerer (2003)). Most responders exhibit monotonic rejection strategies, although one consistently observes a small number of rejections of rare “super fair” offers with over 50%(y>(pie/2)) (Güth et al., 2003).. Several alternatives have been studied and developed (Figure 1) aiming at explaining the differences between actual human behavior and the behavioral models of classical game theory. These alternatives include the presence of factors such as altruism, punishment or reciprocity (Fehr & Fischbacher, 2003), learning process (Abbink et al.,. 政治大. 2001; Gale et al., 1995) and strategic evolution (adapting) (Page & Nowak, 2001).. 立. ‧. ‧ 國. 學 UG. sit. y. Nat. n. al. Responder. Trust game Figure 1. Impunity game. Subject number. er. io. Subject type. Ch. engchi. i n U. v. Proposer. 3 people. More people. Dictator game. TUG, TPG, …. Pirate game. The variety of Ultimatum game researches. 10.

(22) Binmore et al. (1985) first attempt to extent the basic one-shot ultimatum game to two-rounds. Their major result inspired the backward induction researches, which based on more or less commonly known material opportunism, is hardly ever in line with the experimentally observed behavior. In other hand, Neelin et al. (1988) comment that learning effect would not lead to behavior consistent with backward induction.. Slonim and Roth (1998) improve their previous research (Roth et al., 1991), and offer a formal treatment of the issue and find no evidence for changes in responders’ behavior. But some recent papers do find evidence of changes in acceptance rates. Duffy. 政治大. and Feltovich (1999) study ultimatum games with and without observation of another. 立. pair’s outcomes. Recently, Cooper and Dutcher (2011) survey seven papers and provide. ‧ 國. 學. evidence in this meta-study that behavior in repeated ultimatum games with stranger interaction seems similar to learning a norm, where offers have to hit some threshold to be. ‧. accepted. sit. y. Nat. n. al. er. io. Additionally, previous research has shown that knowledge of the alternative offers. i n U. v. available to the proposer can alter the decisions of the responder (Falk et al., 2003).. Ch. engchi. Additionally, physical appearance (Solnick & Schweitzer, 1999), intentionality (Blount, 1995; Sanfey et al., 2003; Sutter, 2007); morality (Chapman et al., 2009; Hennig-Schmidt et al., 2008) and social roles (Hoffman et al., 1994) all appear to play a part in decisions. Personal features of proposer and responder participants (such as names or other cues that modify social distance) also influence behavior in the ultimatum game in the predicted direction (Charness & Gneezy, 2008; Marchetti et al., 2011). Zak et al. (2007) administered oxytocin and observed a significantly positive effect on offers. (Andrade & Ariely, 2009) Happy responders were less likely than angry responders to reject unfair 11.

(23) offers in the initial ultimatum game. Surprisingly, proposers who were initially induced to feel happy made more selfish proposals in the second ultimatum game.. 2.2 Emotion Emotions play an essential role in everyday life. Emotions shape how we perceive. 政治大 measure guide how we adapt our behavior to the physical and social environment. Some 立 the world, bias our beliefs, and influence our decisions. And emotions also play in large. people believe that emotions play a functional role in the behavior of humans and animals,. ‧ 國. 學. particularly behavior as part of complex social systems (Toda, 1982).. ‧. Recent trends in cognitive modeling research have emphasized the development. y. Nat. n. al. In contrast with detailed models of specific. er. io. abilities into a single integrated architecture.. sit. of integrated cognitive systems that combine a broad spectrum of human cognitive. i n U. v. phenomena, such systems have potential, not only as a means to formalizing our basic. Ch. engchi. understanding of human cognition, but also as practical proxies for human behavior in a wide range of applications (Gratch & Marsella, 2005).. The acknowledged weakness of such technology, however, is it is particularly ill-suited for capturing the influence that factors such as stress and emotion can have.. Damasio (2008) finds that people with relatively minor emotional impairments have trouble making decisions and, when they do, they often make disastrous ones. A four-fold. 12.

(24) classification of emotions with respect to their functions in decision making is proposed (Pfister & Böhm, 2008). It is argued that emotions are not homogenous concerning their role in decision making, but that four distinct functions can be distinguished concerning emotional phenomena. One function is to provide information about pleasure and pain for preference construction, a second function is to enable rapid choices under time pressure, a third function is to focus attention on relevant aspects of a decision problem, and a fourth function is to generate commitment concerning morally and socially significant decisions.. 學 ‧. ‧ 國. Table 1. 政治大 Four classification of emotions (Pfister & Böhm, 2008) 立. er. io. sit. y. Nat. a. n. 2.2.1. v. i l C in ultimatum game Emotions n U. hengchi. Scientists applied emotion to study ultimatum game very early age. Kirchsteiger (1994) shown that emotion (such as envy) is a potential explanation for the most important experimental ‘anomalies’. Empirical data show that individuals differ largely from the predictions of rational choice theory, often rejecting unfair offers. Such decisions have been interpreted as altruistic punishment (Fehr & Gachter, 2002); that is, proposers making unfair offers are penalized despite the personal costs accompanying this behavior.. 13.

(25) Therefore, it has been proposed that a limitation of rational choice theory is that it fails to acknowledge the role in decision making (Harlé & Sanfey, 2007). For example, Hewig et al. (2011) found that unfair offers in the ultimatum and dictator games elicited negative affect, which in turn predicted participants’ decisions to either accept or reject these offers. Pillutla and Murnighan (1996) measured the feelings of responders when confronted with unfair offers and they found that rejection of unfair offers was mediated by feelings of anger, which were particularly pronounced when individuals inferred that proposers intended to cause them harm. Likewise, rejection of unfair offers was also accompanied. 政治大 system(van 't Wout et al., 2006). Furthermore, using a more direct test, emotions induced 立. by higher skin conductance activity, which may reflect involvement of the affect arousal. by video clips were found to bias decision making (Harlé & Sanfey, 2007), with reduced. ‧ 國. 學. acceptance rates after sad clips, compared to clips that were neutral or amusing. Similarly,. ‧. Harle and Sanfey (2010) reported reduced acceptance rates after initial induction of. sit. y. Nat. withdrawal-related affect (disgust, serenity), compared to approach-related affect. io. n. al. er. (amusement, anger).. i n U. v. Recent physiological (van 't Wout et al., 2006) and neuroimaging (Sanfey et al., 2003). Ch. engchi. studies of the ultimatum game have indeed found that responders’ emotion and arousal levels increase when presented with unfair offers and that this increase is reliably associated with the rejection of unfair offers. The responder role in the ultimatum game thus provides an ideal venue to study whether incidental emotions can additionally bias decision making and potentially interact with important task based emotions (e.g., indignation or anger) or whether these emotional states are too subtle to have tangible consequences on economic decisions. 14.

(26) Whereas anger and disgust have respectively been classified in the literature as approach-based and withdrawal-based (because they respectively prompt engagement with, and withdrawal from, an offending stimulus), positive withdrawal-based emotion has been harder to identify (Harle & Sanfey, 2010).. The present findings highlight the potential contribution of studying the influence of specific emotions to reveal the nature of the motives underlying behavior. We are aware of only a single other study that also used affective measures to identify the role of strategic and non-selfish motives in proposers' offers (Haselhuhn & Mellers, 2005). In this study,. 政治大. proposers indicated their anticipated pleasure over a range of possible payoffs (i.e.,. 立. accepted offers) as well as their preference for each of these offers. It was found that some. ‧ 國. 學. proposers derived pleasure from fairness, indicating highest preferences and most pleasure for equal offers whereas their preference and pleasure decreased as offers deviated from the. ‧. 50–50 split. Self-interested proposers showed similar preferences, yet their pleasure. y. Nat. sit. linearly increased with the offer size. This latter discrepancy suggests that preferences are. n. al. er. io. based on strategic considerations (or “strategic pleasure”, cf. Haselhuhn and Mellers (2005)).. Ch. engchi. i n U. v. The main reason for looking into the role of emotions in ultimatum bargaining was our conviction that we cannot exclusively infer motives from ultimatum offers alone, nor from changes in average offers due to various structural manipulations of the ultimatum game. Proposers who make generous ultimatum offers because they fear rejection do recognize that responders may evaluate their offer in terms of fairness criteria. Strategic considerations imply that the proposer is aware of and understands these criteria. Fear and fairness considerations are inextricably linked in that respect(Nelissen et al., 2011). 15.

(27) 2.2.2. Emotion in AI. Since Beaudoin et al. (1996) and Rosalind W Picard (2000; 2003) placed emotion into computational theory, emotions become an important research in. several AI-related. fields (Andrade & Ariely, 2009; Camurri & Coglio, 1998; M. El-Nasr et al., 2000; M. S. El-Nasr & Yen, 1998; Steunebrink et al., 2010), however most prominently in human-robot/computer interaction, which focus on how to express or sense emotions. The influence of emotions on decision-making is largely ignored (Jiang & Vidal, 2006).. 政治大 Philosophers and computer 立 scientists have continued to be interested in integrating. ‧ 國. 學. computing theory with emotions (de Sousa, 2014) in early days. Sloman and Croucher (1981) have elaborated the sort of ideas that were embryonic in Schank et al. (1973) into a. ‧. more sophisticated computational theory of the mind in which emotions are virtual. sit. y. Nat. machines, playing a crucial role in a complex hierarchic architecture in which they control,. n. al. er. io. monitor, schedule and sometimes disrupt other control modules (Beaudoin et al., 1996).. i n U. v. Rosalind W Picard (2000) adverts to the role of emotions in evaluation and the pruning of. Ch. engchi. search spaces. But she is as much or more concerned to provide an emotional theory of computation than to elaborate a computational theory of emotions. Also, a book by Minsky (2007) takes the promising title of “The emotion machine”. Gratch and Marsella (2005) work on “computational models of human emotion”, which typically are studied in simulations in artificial environments.. 16.

(28) Chapter 3 Emotion Index Model In this chapter, we will explain the detail about how to calculate and modify subjects’ emotion into index, and will justify the parameter setting. Basically, the concept of design how to calculate emotion between proposer and responder is quite similar. The basic structure of our model lists below, we would address more details in the first section (proposer section).. . 政治大 nay-based + reference-based (bi-variant model) 立. Proposers .  . nay-based (uni-variant model). . nay-based + reference-based (bi-variant model). Nat. n. al. Ch 3.1 Proposer engchi. er. io. sit. y. ‧. ‧ 國. 學. Responders. i n U. v. As discussed in the introduction section, we consider two kinds of emotions which can be possibly triggered by the interactions between the opponents in the ultimatum game. In our assumption, the possible emotion-behavior models are composed of these two kinds of emotions. For the proposer, the first part of emotions-behavior model is that we consider the direct response, accept or reject, from responder. This nay-based emotion is based on the assumption that the acceptance decision from responder will lead to a. 17.

(29) positive feeling for proposer, whereas the rejection decision will lead to a negative feeling. Thus, according to above description, we can define the reactions to events as a function 𝑋𝑋𝑡𝑡−1 + 𝛼𝛼𝑥𝑥+ , 𝑋𝑋𝑡𝑡 = � 𝑋𝑋𝑡𝑡−1 − 𝛼𝛼𝑥𝑥− ,. 𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎. (1). 𝑖𝑖𝑖𝑖 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟. Notice that, from Equation (1), emotions can accumulate over the courses of the game. 𝑋𝑋𝑡𝑡. is what we call the emotion index value from nay-based emotion at time t, 𝛼𝛼𝑥𝑥+ and 𝛼𝛼𝑥𝑥−. represent the strength of the feeling when the proposal is accepted or rejected at one time,. 政治大 simple, although the time is立 not limit, subjects usually could finish a ten-period ultimatum but this one-time stimulus will be added up over time. Because ultimatum game is so. ‧ 國. 學. game experiment in 10 minutes. We assume the nay-based stimulus would not total decade in such short time. This setting, for example, allows us to anticipate the case where. ‧. the proposer may stay calm when a “fair” offer is rejected for the first time, but may feel. y. sit er. io. third time.. Nat. irritated when it is rejected again, and may respond “angrily” when it is rejected for the. al. n. v i n Ch The second part of our emotions-behavior model is the reference-based emotion. engchi U. This kind of emotions is based on the reference point that the proposer considers fair or reasonable in his mind. Despite so, the responder may actually accept/reject something different from the reference, be it reluctantly or aggressively. For example, the proposer may want to offer a share of 45 as his reference; nonetheless, being facing a “tough” responder (Slembeck, 1999), he actually offered 50 reluctantly. Alternatively, he might actually offer only 35 to take an advantage of a soft responder. We consider two different setting in this reference-emotion index, equation ( 2 ) is a way to quantify the discrete. 18.

(30) type of emotions. A discrete type is that we consider reference as a threshold to determine whether the triggered emotion is positive or negative, similar to equation ( 1 ), 𝑌𝑌𝑡𝑡−1 + 𝛼𝛼𝑦𝑦+ , 𝑌𝑌𝑡𝑡 = �𝑌𝑌𝑡𝑡𝑡𝑡1 , 𝑌𝑌𝑡𝑡−1 − 𝛼𝛼𝑦𝑦− ,. 𝑂𝑂𝑡𝑡 <R 𝑂𝑂𝑡𝑡 =R 𝑂𝑂𝑡𝑡 >R. (2). 𝑌𝑌𝑡𝑡 represents the emotion index value from reference-based emotion at time t, 𝛼𝛼𝑦𝑦+. and 𝛼𝛼𝑦𝑦− are the adjust power when proposer compares his/her offer (𝑂𝑂𝑡𝑡 ) and to his/her. personal reference point (R). From Equation ( 2 ), emotions can also be accumulated over the courses of the game.. 立. 政治大. 學. ‧ 國. On the another hand, if the difference between offer and reference is matter, then one needs to take ( 3 ) into account. ‧ y. (3). io. sit. Nat. 𝐷𝐷𝑡𝑡 = |𝑂𝑂𝑡𝑡 − 𝑅𝑅|. n. al. er. in the emotion calculation. Here, we consider the possible significance of a relative difference (𝑑𝑑𝑡𝑡 ), i.e.,. Ch. engchi. 𝐷𝐷𝑡𝑡 , ⎧𝑑𝑑𝑡𝑡+ = 𝑅𝑅 ⎪ 0, ⎨ ⎪𝑑𝑑− = 𝐷𝐷𝑡𝑡 , ⎩ 𝑡𝑡 𝐹𝐹 − 𝑅𝑅. 𝑂𝑂𝑡𝑡 < R. 𝑂𝑂𝑡𝑡 = R. i n U. v. (4). 𝑂𝑂𝑡𝑡 > R. where F is the full range of offer. In next step, we modify Equation ( 2 ) as follows:. 19.

(31) 𝑌𝑌𝑡𝑡−1 + (𝑑𝑑𝑡𝑡+ )2 𝛼𝛼𝑦𝑦+ , 𝑌𝑌𝑡𝑡 = �𝑌𝑌𝑡𝑡𝑡𝑡1 , 𝑌𝑌𝑡𝑡−1 − (𝑑𝑑𝑡𝑡− )2 𝛼𝛼𝑦𝑦− ,. 𝑂𝑂𝑡𝑡 <R 𝑂𝑂𝑡𝑡 =R 𝑂𝑂𝑡𝑡 >R. (5). In equation ( 5 ), 𝑑𝑑𝑡𝑡 is squared to capture the possibility that the triggered emotion is relatively small when the discrepancy is small, and becomes increasingly larger when the discrepancy gets larger. Like the discrete type emotion, the continuous type emotion is also accumulative. Hence, a responder may be tolerant of an “inferior” offer (𝑂𝑂𝑡𝑡 < R) for one time, for two times, but may suddenly lose the patience and reject the offer when coming to the third time.. 立. 政治大. ‧ 國. 學. Actually, we had test different setting on 𝑑𝑑𝑡𝑡 , not only square it, but proportion, square. root and just random number (Appendix A). After checking the performance under. ‧. different preferences for proposers, we find that we could usually get better results when. sit. y. Nat. using the “square” method. In such case, we decide to use square setting to operate our. n. al. er. io. parameters in the following analysis.. Ch. Since we do not have a theory to tell us. engchi. v i n the U ideal values. of these emotional. parameters and the reference (R), in the following analysis we shall simply assume a possible range for these parameters and then try various random combinations of them to see whether the significance of emotional influence on the offering decision can be found in any of these values. In other words, given a specific range, we are trying to examine whether there is a sub-domain in which the emotional influence can be identified. The range used in this research is given in Table 2.. Hence, in the later Monte Carlo Simulation, in each run, say run j, we shall randomly pick 20.

(32) + + − − a quadruple 𝛼𝛼𝑗𝑗 ≡ �𝛼𝛼𝑥𝑥,𝑗𝑗 , 𝛼𝛼𝑥𝑥,𝑗𝑗 , 𝛼𝛼𝑦𝑦,𝑗𝑗 , 𝛼𝛼𝑦𝑦,𝑗𝑗 � from their given range (Table 2), place them into. Equations ( 1 ) and ( 2 ), or ( 1 ) and ( 5 ), and use these two equations to trace the. dynamics of emotions during the game. To demonstrate how the emotion index looks like, Figure 2 gives an illustration of the reference-based emotion index (Equation 2 ) of five subjects in their money experiments (the left panel), and that of another five subjects in their chocolate experiments (the right panel), with only subject 005 been chosen in both demonstrations. What shown in Figure 2 is based on one randomly generated parameters 𝛼𝛼𝑗𝑗 under R = 45 (for the money experiment) and R = 4 (for the chocolate experiment).. 政治大 developing during the game; some were up and down alternately, and some were 立. From these small samples, we can see that quite different patterns of emotions were. persistently getting higher or lower.. ‧ 國. Range for Emotional Parameters and the Reference Range. 𝑹𝑹𝑴𝑴 𝑹𝑹𝑪𝑪. [0,5]. y. sit. al. er. [0,5]. 𝜶𝜶− 𝒚𝒚. n. 𝜶𝜶+ 𝒚𝒚. [0,5]. io. [0,5]. Nat. 𝜶𝜶+ 𝒙𝒙 𝜶𝜶− 𝒙𝒙. ‧. Parameter. 學. Table 2. [0,10,15,20,25,30, … ,50,55,60,70, … ,100] [0,1,2,3, … ,10]. Ch. engchi. i n U. v. Given that the applied numeracies differ in the money experiment and the chocolate experiment, the possible numbers used for reference differ accordingly. Hence, the notations R 𝑀𝑀 and R 𝐶𝐶 are used to differentiate the references under the money experiments and the references under the chocolate experiment.. 21.

(33) Chocolate-D2. 35. 30. 25. 20 accumulated emotion index. accumulated emotion index. Money-D2. 15 5 -5 -15 -25. 10 0 -10 -20. -35. -30. -45. -40. Subject 005. Subject 006. Subject 007. Subject 008. 立. 政治大. subject 003. subject 004. subject 005. ‧ 國. Figure 2. subject 002. 學. Subject 009. subject 001. Reference-Based Emotion Index, Equation ( 2 ). ‧. sit. y. Nat. If emotion has an effect on decision of the proposer, we shall expect that influence. io. er. can be observed through the change of the offer. Hence, we consider the following three possibilities: the offer is increased, decreased or remained the same. Equation ( 6 ) shows. n. al. the three decision values.. Ch. 1, 𝑍𝑍𝑡𝑡 = � 0, −1,. engchi. i n U. v. 𝑂𝑂𝑡𝑡 > 𝑂𝑂𝑡𝑡−1 𝑂𝑂𝑡𝑡 = 𝑂𝑂𝑡𝑡−1 𝑂𝑂𝑡𝑡 < 𝑂𝑂𝑡𝑡−1. (6). To model the influence of emotions on the decision of the proposer, we first combine the two factors into one using a linear sum, as shown in Equation ( 7 ).. 22.

(34) 𝑍𝑍𝑡𝑡∗ = 𝛽𝛽0 + 𝛽𝛽1 𝑋𝑋𝑡𝑡 + 𝛽𝛽2 𝑌𝑌𝑡𝑡 + 𝜖𝜖𝑡𝑡. (7). 𝑍𝑍𝑡𝑡∗ can be broadly interpreted as the state of the mood. Notice that we also add a standard. error term 𝜖𝜖𝑡𝑡 as an aggregation of other less systematic influences. We then use the threshold based decision rule ( 8 ) as the emotional model of decision making. 1, 𝑍𝑍𝑡𝑡 = � 0, −1, Where θ1 and θ2. 𝑍𝑍𝑡𝑡∗ ≥ 𝜃𝜃1 𝜃𝜃1 > 𝑍𝑍𝑡𝑡∗ > 𝜃𝜃2 𝜃𝜃2 ≥ 𝑍𝑍𝑡𝑡∗. (8). 政治大 are the two thresholds on which the decisions are based and 立. ‧ 國. 學. these two parameters are endogenous given. Equations ( 6 ) to ( 8 ) lead to the familiar. io. al. 1 1 + 𝑒𝑒 −𝑥𝑥. sit. Nat. 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃(𝜖𝜖𝑡𝑡 ≤ 𝑥𝑥) = 𝐹𝐹(𝑥𝑥) =. (9). er. distribution, i.e.,. y. ‧. ordered logit model if we assume the cumulative function of 𝜖𝜖𝑡𝑡 is the logistic. n. v i n By rearranging Equation (C 8 )husing Equation(i 7 U e n g c h ) , we can derive the probability of each decision conditional on the given emotion indexes X t and Yt , as shown in Equation ( 10 ) and from there we can further derive the odds ratios, as shown in Equation ( 11 ).. 23.

(35)  prob ( Z t = F (θ 2 − b 0 − b1 X t − b 2Yt ) −1) =   prob ( Z t = 0 ) = F (θ1 − b 0 − b1 X t − b 2Yt )  − F (θ 2 − b 0 − b1 X t − b 2Yt )   prob ( Z = 1) =− 1 F (θ1 − b 0 − b1 X t − b 2Yt ) t . ( 10 ).  prob ( Z t > 0 ) −θ + b + b X + b Y = e( 1 0 1 t 2 t )  0 prob Z ≤ ( t )    prob ( Z t > −1) = e( −θ2 + b0 + b1 X t + b2Yt )  prob ( Z ≤ −1) t . ( 11 ). 政治大. Taking the logarithm of the odds ratio ( 11 ), one can have the following linear. 立. version of the threshold-based decision model, also known as logit ( 12 ).. ‧ 國. 學 ‧.   p1   ln   = −θ1 + βββ 0 + 1 X t + 2Yt   1 − p1   ln  1 − p−1  = −θ + βββ 2 0 + 1 X t + 2Yt   p    −1 . er. io. sit. y. Nat. al. ( 12 ). v. n. Where p1 and Prob ( Z t = −1) are the abbreviations for Prob ( Z t = 1) and. Prob ( Z t = −1) , respectively.. Ch. engchi. 24. i n U.

(36) 3.2 Responder To illustrate the behavior of responder, same as proposer, we propose two measures for this reference-based emotion. One is discrete (dichotomous) which only cares about the direction (sign) of the discrepancy, and the other is continuous, which goes further to differentiate the size of the difference.. 3.2.1. Uni-variant model. 立. 政治大. Furthermore, there are two possible emotion-behavior models are composed of. ‧ 國. 學. two kinds of emotions (nay-based & reference-based). For the responder, the first kind. ‧. of emotions-behavior model, the uni-variant model, is that we only consider reference. sit. y. Nat. as a threshold to determine whether the triggered emotion is positive or negative.. io. er. Namely, there is no nay-based motion in this mode. Equation ( 13 ) is a way to quantify the discrete type of emotions.. n. al. Ch. i e n g c𝑂𝑂h𝑡𝑡 >R. 𝑌𝑌𝑡𝑡−1 + 𝛼𝛼𝑦𝑦+ , 𝑌𝑌𝑡𝑡 = �𝑌𝑌𝑡𝑡𝑡𝑡1 , 𝑌𝑌𝑡𝑡−1 − 𝛼𝛼𝑦𝑦− ,. i n U. 𝑂𝑂𝑡𝑡 =R 𝑂𝑂𝑡𝑡 <R. v. ( 13 ). From Equation ( 13 ), emotions can accumulate over the courses of the game. 𝛼𝛼𝑦𝑦+. and 𝛼𝛼𝑦𝑦− represent the strength of the feeling when the responder receives the offer (𝑂𝑂𝑡𝑡 ) and compares to his/her personal reference point (R). The reference point for. responder means the floor offer which would be accepted.. 25.

(37) Here, we modify the possible significance of a relative difference (𝑑𝑑𝑡𝑡 ) from( 4 ), i.e., 𝐷𝐷𝑡𝑡 , ⎧𝑑𝑑𝑡𝑡+ = 𝐹𝐹 − 𝑅𝑅 ⎪ 0, ⎨ ⎪𝑑𝑑− = 𝐷𝐷𝑡𝑡 , ⎩ 𝑡𝑡 𝑅𝑅. 𝑂𝑂𝑡𝑡 > R. 𝑂𝑂𝑡𝑡 = R. ( 14 ). 𝑂𝑂𝑡𝑡 < R. In next step, we modify Equation ( 5 )as follows: 𝑌𝑌𝑡𝑡−1 + (𝑑𝑑𝑡𝑡+ )2 𝛼𝛼𝑦𝑦+ , 𝑌𝑌𝑡𝑡 = �𝑌𝑌𝑡𝑡𝑡𝑡1 , 𝑌𝑌𝑡𝑡−1 − (𝑑𝑑𝑡𝑡− )2 𝛼𝛼𝑦𝑦− ,. 𝑂𝑂𝑡𝑡 >R 𝑂𝑂𝑡𝑡 =R 𝑂𝑂𝑡𝑡 <R. ( 15 ). 政治大 for one time, for two times, 立but may suddenly lose the patience and reject the offer Although R is the reference, a responder may be tolerant of an “inferior” offer (𝑂𝑂𝑡𝑡 < R). ‧ 國. ‧. 3.2.2. 學. when coming to the third time.. Bi-variant model. sit. y. Nat. n. al. er. io. The second emotion-behavior model for responder is Bi-variant model that we. i n U. v. consider the synergy of both nay-based and reference-based emotions. The style of. Ch. engchi. Bi-variant model is the same as what we mention in proposer, and the big difference is the definition of nay-based emotion. The nay-based emotion here is triggered by the acceptance or rejection decision made by the responder him-/herself in previous round. This nay-based emotion is based on the assumption that the acceptance decision leads to a positive feeling and the feeling will influence responder’s next decision, whereas the rejection decision leads to a negative feeling. We adopt the bi-variant model to compare the emotion between proposer ad responder. Following the design of proposer, the nay-based for responder is 26.

(38) 𝑋𝑋𝑡𝑡−1 + 𝛼𝛼𝑥𝑥+ , 𝑋𝑋𝑡𝑡 = � 𝑋𝑋𝑡𝑡−1 − 𝛼𝛼𝑥𝑥− ,. 𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎. ( 16 ). 𝑖𝑖𝑖𝑖 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟. and the reference-based emotions are coherent as the settings in uni-variant model, equation( 13 ) and ( 15 ).. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 27. i n U. v.

(39) Chapter 4 Experiment design and procedures 4.1 Ultimatum game The ultimatum game experiments were run in the NCCU EEL (National. 政治大. Cheng-Chi University, Experimental Economics Lab). There are three sequential. 立. stages different on the medium of bid administered in this study, which were based on. ‧ 國. 學. repeated ultimatum game. In stage 1 (S1), the money treatment, a normal ultimatum game is played in this stage, the proposer was asked to allocate NT$100 to the. ‧. responder. If the responder states acceptance for the offer, they share the money;. y. Nat. sit. otherwise, both receive nothing. In stage 2 (S2), the chocolate treatment, the proposer. n. al. er. io. was allowed to make allocate 10 chocolates to the responder. Every piece of chocolate. i n U. v. is worth NT$10 which was also informed to the players ahead of the game and the. Ch. engchi. total value of all chocolate are NT$100, the same as the amount of cash in stage 1. To reduce further uncertainty which may come with the use of chocolates as the medium, we use a well-branded chocolate in Taiwan, i.e., Ferrero Rocher. In the final stage (S3), the medium in stage l and 2 are combined in use. The proposer has NT$100 and 10 chocolates in hand and is asked to propose one offer including both money and chocolate. We repeatedly play ultimatum game ten times in each stage. Given the complexity of how to analysis and model the final combinatorial game, our analysis in this research is only based on the first two stages. 28.

(40) All experimental stages began with an introductory talk. Subjects then were encouraged to ask questions. All participants were fully informed on all features of the experimental design and the procedures. The subjects were randomly assigned to be as the proposers and responders at beginning and the pair relationship will be maintained in all three stages. Table 3. Subjects: Gender and the Role-to-Play Proposer. Responder. Male. 40. 39. Female. 43. 44. 政治大. 立. Total 166 individuals were recruited to join our experiments, 79 male and 87. ‧ 國. 學. female (see Table 3). These subjects all enrolled from the NCCU EEL Recruiting. ‧. System and mostly are students coming from different schools. Their ages were ranged from 18 to 30. Subjects received a show-up fee of NT$150 1 that was. y. Nat. io. sit. independent of their earnings in the experiment. Participants could receive a bonus. n. al. er. calculated as the average amount of the money or chocolate they actually acquired. Ch. i n U. v. during the ten rounds ultimatum game of each stage. Hence, if there is a half-half deal. engchi. accepted by both side through the whole 30 periods of the game, the bonus will be a total pay of NT$ 100 and 10 10-dollar chocolates. Considering that the total duration of our experiment was 90 minutes (including pre-experiment information session, 3-stage game, post-experiment questionnaire and payment), this structure of pay should be reasonably attractive.. 1. The normal on-campus work-study hourly rate, NT$95 29.

(41) All test procedures were conducted and controlled by the z-Tree 3.2.12 (Fischbacher, 2007). It means that the subjects interaction through the monitor and they don’t know the gender of his/her partner.. 4.2. Monte Carlo simulation. 政治大 our results will be presented. To show how the Monte Carol simulation is implemented, we use Table 4 as an illustration. In this research,. 立. by the following. categorizations: money experiment and chocolate experiment, each then subgrouped. ‧ 國. 學. by gender. Therefore, there are six categories as structured in Table 4. The simulation. ‧. is repeated 10 times, but the first time is reserved for the initialization for the emotion. sit. y. Nat. dynamics (1) and (2) or (3). We, therefore, have nine observations for each subject.. io. er. There are a total of 83 subjects, 40 male subjects and 43 female subjects. The number of observations for each category is, accordingly, shown in the last row of the table.. al. n. v i n C hwith all subjects, the Let us take the money experiment first category, as an example. engchi U As shown in the second column of the last row, there are a total of 747 observations.. For each single run of the Monte Carlo simulation, the emotion index X and Y are developed based on these 747 observations. For each single run the four parameters,. α x+ , α x− , α y+ , α y− are randomly sampled from the given range (Table 2). An example is given in Table 4: ( α x+ , α y+ ) = (1.1608, 1.3908), and ( α x− , α y− ) = (2.2355, 4.7792). By the homogeneity assumption applied in this research, in this specific run, we assume that these parameter values are applied to all subjects when estimating their emotions. 30.

(42) We shall repeat this process for 2,000 times 2 for each of the assumed reference R. In this specific example, R is assumed to be 40. When all this is done, we move to the next category, for example, the money experiment with male proposers only, then with female proposers only, then moving to the chocolate experiments in the order as demonstrated in Table 4.. Table 4. Monte Carlo Simulation: One Specific Runs Money. Proposer. all subjects. R. male. αy. αx. αx. Chocolate female. αy. αx. 40. 40. 立. 1.3908. 1.7854. 1.8815. −(α ,α ). 2.2355. 4.7792. 3.65. ˆ, ˆ ββ 1 2. -0.0718. -0.041. p-value. 0***. ,. female. αy. αx. 4. 4. 4. 1.6239. 2.0517 3.7082 3.0011 4.2143 0.5895. 4.624. 3.2511. 4.4678. 0.0185. 0.0513. -0.0664. 0.3231. -0.0197 0.0824 -0.0109 0.0971 -0.0811. 360(9x40). 387(9x43). 3.071. αy. αx. 0.1219. 0.3141 0.0019*** 0.5902 0.0009*** 0.0182**. 747(9x83). αy. 3.6841 2.079 0.8908. 2.8294 2.67 0.0351. 0.1571 0.0215** 0.3119 0.1172 0.0388** 0.5373 747(9x83). 360(9x40). ‧. * **. 0.0747. αx. 政治大. male. 學. observation. ‧ 國. 1.1608. − y. αy. αx. 40. + (α x+ ,α y+ ) − x. all subjects. 387(9x43). and *** denote the significance of estimates at the 10 percent, 5 percent and 1 percent levels, respectively.. sit. y. Nat. n. al. er. io. At the end of each run, what we have is the derived ( X i ,t , Yi ,t ) for each. i n U. v. individual i and the observed Z i ,t (i =1, ..., 83, t = 2, ..., 9). We then pool these. Ch. engchi. variables together and apply the maximum likelihood estimator to estimate the coefficients of the ordered logit model (8). The statistical software applied to this estimation is Matlab 2008b. The estimates of these specific runs are given in the first row of the fourth block of Table 4. Immediately below it is the p-value of the. 2. We had test to repeat the simulation for 2000, 10000, and 20000 times and the outcomes were quite similar. Therefore, we believe that repeating the Monte Carlo simulation for 2000 times is enough for our model to get convergence results. 31.

(43) estimated coefficients. Again, taking the all-subject case as an example, βˆ1 and βˆ2 are -0.0718 and 0.0747, with only βˆ1 being statistically significant. Therefore, we have this run for the significance of X as well as one for the insignificance of Y. In the end of the 2,000 trials, we shall count how many runs having significant X and how many runs having significant Y. These will be main results to be reported in the next section. Also, to make sure that both X and Y are measuring different parts of emotions, we calculate the correlation coefficient between X and Y, as shown in the last row of the fourth block, to confirm that they are not highly correlated. As shown. 政治大. in these specific runs, X and Y in general are not highly correlated, which indicates. 立. that they are not measuring the same kind of emotions.. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 32. i n U. v.

(44) Chapter 5 Ultimatum game experiment results In this chapter, we show the fundament results in our ultimatum game experiments. Table 5 represents regarding proposers and Table 6regards responders. There are a few points deserving to be highlighted. First, our mean offer rate for the money experiment is. 政治大 Japan, where the mean offer 立rate is 44.73% (a survey from Oosterbeek et al., 2004). 43.52%. In an international context, this number is very close to our neighboring country,. ‧ 國. 學. Second, the mean offer rate of chocolates, 45.6%, is slightly, but statistically significantly, higher than that of money (Table 7). This may concur positively with the observation. ‧. made by Bowles et al. (1997). Third, if we separate the group by gender, an issue which. sit. y. Nat. have received tremendous attention in experimental economics (Croson & Gneezy, 2009;. n. al. er. io. García-Gallego et al., 2012; McGee & Constantinides, 2013), we find that the mean offer. v. rates between men (43.43%) and women (43.60%) are very close and the difference is not. Ch. engchi. i n U. significant (Table 7), while the rate offered by women is significantly higher. However, in the chocolate experiment, the result is opposite; now men become more generous (47.1%) than women (44.1%), and the difference is also statistically significant (Table 7). At the same time, both in money and chocolate treatments, the male responders ask for higher offer (Table 8). Hence, as already noticed in the literature, the gender effect can be context sensitive (Croson & Gneezy, 2009), and, in this case, the medium can play a role.. 33.

(45) Table 5. Descriptive Statistics of the Ultimatum Game: Proposers Money-. Money-. Chocolate-. Chocolate-. male. female. chocolate. money male. female. 830. 400. 430. 830. 400. 430. 43.52. 43.44. 43.60. 4.56. 4.71. 4.42. Median. 45. 45. 45. 5. 5. 4. Max offer. 100. 100. 80. 10. 10. 10. Min offer. 0. 0. 10. 0. 0. 0. Std. Dev.. 9.53. 10.38. 8.68. 1.34. 1.35. 1.33. Observations Mean. Descriptive Statistics of the Ultimatum Game: Responders. 政治大. Moneymoney 592. 281. 311. 641. 305. 336. 45.5524. 46.9466. 44.2926. 4.7956. 4.8918. 4.7083. 47. 50. 45. 5. 5. 5. 100. 80. 100. 10. 10. 10. 10. 20. 10. 1. 8.6832. 8.3905. 8.7636. 1.2724. 71.33%. 72.05%. 70.68%. 77.23%. 238. 109. 129. 189. 38.47. 38.91. 38.1. 3.76. Mean. io. Observations (accepted). Max offer. 65. Min offer. 0. Std. Dev. Rejected rate. n. Median. a 40l. 40 C h 4060 e n g c65h i. 1. 1.2662. 1.2736. y. Nat. Acceptance rate. 1. 78.21%. 76.36%. 85. 104. 4.02. 3.88. 4. 4. 7. 6. 6. sit. Std. Dev.. female. ‧. Min offer. male. female. 立. ‧ 國. Max offer. Chocolate-. 學. Median. Chocolate-. chocolate. male. Observations (rejected) Mean. Money-. er. Table 6. 4i v n U. 5. 0. 0. 0. 0. 9.69. 8.63. 10.52. 1.28. 1.17. 1.14. 28.67%. 27.95%. 29.32%. 22.77%. 21.79%. 23.64%. 34.

(46) Table 7. Stastics test in defferent Medium and gender : proposer Mean offer (offer rate). t-test (two tailed) p-value. Mann-Whitney test p-value. ***. 0.000004***. money chocolate. 43.52 (43.52%) 4.56 (45.6%). 0.000013. m_male m_female. 43.43 (43.43%) 43.6 (43.6%). 0.801924. 0.655700. c_male c_female. 4.71 (47.1%) 4.41 (44.1%). 0.001330***. 0.000011***. * **. , and *** denote the significance of estimates at the 10 percent, 5 percent and 1 percent levels, respectively.. 政治大 t-test (two tailed). Stastics test in defferent Medium and gender : responder. 立. m_male m_female. 46.95 (46.95%) 44.29 (44.29%). 0.000191***. c_male c_female. 4.89 (48.9%) 4.71 (47.1%). Nat. 0.068248*. 0.000026*** 0.000048*** 0.004977***. io. sit. 0.000102***. ‧. 45.55 (45.55%) 4.80 (48.00%). p-value. 學. money chocolate. , and *** denote the significance of estimates at the 10 percent, 5 percent and 1 percent levels, respectively.. n. al. er. * **. Mann-Whitney test. p-value. ‧ 國. Mean offer (offer rate). y. Table 8. Ch. engchi. i n U. v. Table 9. Average Offer Rates in Money and Chocolate Experiments. Money. round 1 round 2 round 3 round 4 round 5 round 6 round 7 round 8 round 9 round 10. All. 41.39% 43.59% 43.52% 42.72% 43.75% 43.59% 44.90% 43.18% 44.23% 44.35%. Men. 42.28% 43.84% 43.40% 42.00% 43.02% 42.53% 44.12% 42.14% 43.19% 43.63%. Women. 40.43% 43.33% 43.65% 43.50% 44.53% 44.73% 45.75% 44.30% 45.35% 45.13%. Chocolate round 1 round 2 round 3 round 4 round 5 round 6 round 7 round 8 round 9 round 10 All. 44.70% 45.06% 43.49% 46.99% 43.86% 45.06% 48.43% 44.22% 46.27% 47.95%. Men. 46.51% 46.51% 43.26% 47.44% 44.42% 46.28% 49.30% 44.88% 47.21% 48.37%. Women. 42.75% 43.50% 43.75% 46.50% 43.25% 43.75% 47.50% 43.50% 45.25% 47.50%. 35.

(47) Table 9 shows the basic statistics of the responders’ behavior under the condition when the offers were accepted (the upper panel) and when the offers were rejected (the lower panel). In the upper panel, we show the statistics of the offers accepted by the respective responders. For the money experiment, we see that men are more demanding by requesting a statistically significant higher offer rate (46.95%) than women (44.29%); nonetheless, the acceptance rates between men and women (72.05% vs. 70.68%) are not significantly different. When coming to the chocolate experiment, unlike their corresponding proposers, men were not getting generous here. Instead, they were still. 政治大 rates (78.21% vs. 76.36%) are not 立. statistically significantly more demanding (48.9%) than women (47.0%), while the resultant acceptance. 學. ‧ 國. different.. statistically significantly. Comparing the proposers’ offer behavior in our experiments (Figure 4) to an. ‧. international meta-survey (Figure 3)(Cooper & Dutcher, 2011), our data show some. y. Nat. sit. difference. In Cooper’s survey, for the two leftmost categories of offers, acceptance. n. al. er. io. rates are lower for Rounds 6–10 than in Rounds 1–5, but we have reverse results. The. i n U. v. magnitude of the increase for small offers is larger, but given the infrequency of low. Ch. engchi. offers we would once again struggle to identify the effect without a sizable dataset.. The lower panel of Table 6 gives the result conditional on the rejection. Basically, the result can be read similarly to those conditional on the acceptance. The mean offer rate under rejection is higher for men than women in both the money and chocolate experiments. The rejection rate of the money experiment is high, up to 28.67%, and the rejection rate of the chocolate experiment is 22.77%. An international comparison of the rejection rate in repeated ultimatum game is not known to us. 36.

(48) 政治大 Figure 3 Acceptance rate as a function of experience. Note: The numbers above the 立 bars give the number of observations for that bar (Cooper & Dutcher, 2011). 0.6. y. sit er. al. n. 0.7. io. 0.8. ‧. ‧ 國. 學. 0.9. Nat. Acceptance rate 1. 0.5 0.4. Ch. engchi. i n U. v. 0.3 0.2 0.1 0. 0≦offer<10% 10%≦offer<20% 20%≦offer<30% 30%≦offer<40% 40%≦offer<50%. 50%≦offer. Offer rate (M) 1-5 rounds. (M) 6-10 rounds. (C) 1-5 rounds. (C) 6-10 rounds. Figure 4 Acceptance rate as a function of experience in our experiments. (M) means the money treatment and (C) means the chocolate treatment.. 37.

(49) Since we don’t get data about rejection rate in repeated ultimatum games across countries, and we could not test if there are any difference between our subjects and literatures. We enrolled subjects to play one-shot ultimatum game, not reported the details here, our rejection rate is 13.24% for the money experiment and 5.88% for the chocolate experiment. Therefore, our result of having a higher rejection rate in the repeated game than in the one-shot game is consistent with the findings in other studies, e.g., Slembeck (1999).. 政治大. 立. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. Figure 5 Offer Rates through Time 38. i n U. v.

(50) Since what we run is a multiple-round ultimatum game, we, therefore, also briefly summarize the key statistics over time. Figure 5 gives the time series of the average offer rates made by proposers (the upper panel) and the average acceptance rate accepted by responders (the lower panel). The average offer rate started low around 40 to 45, then gradually moved up to the level of the average and fluctuated around there. Except in the third and the fifth period, the average offer rate in the chocolate experiment is always higher than that in the money experiment.. Also, in Figure 5 (the lower panel), we can see that the accepted offer rate, from. 政治大. the beginning to the end, is very much fluctuating around their mean level, with no. 立. noticeable tendency to increase or decrease. Except in round 5, the accepted offer rate in. ‧ 國. 學. the chocolate experiment is either equal to or larger than that in the money experiment.. ‧. Table 9 shows the gender difference over time in both money and chocolate. sit. y. Nat. experiments. In the money experiment, except in the first two periods, women’s. n. al. er. io. generosities compared to men were consistently shown in the rest of the remaining. v. periods. On the other hand, men’s generosities in the chocolate experiment were also. Ch. engchi. i n U. consistently shown in all periods except round 3. In sum, the inequality properties shown in Table 4 and 5 are consistent in each individual round over time to a substantial extent. In sum, even though the difference between men and women observed through these two tables is limited, the evidence is slightly in line with our understanding of gender differences in fairness preference or social preference. There are more basic statistics tables and figures on Appendix B for reference.. 39.

(51) Chapter 6 Simulation results Our simulation results will be presented using the significance curve in the following. Let us first provide a description of the curve. The significance curve reports, out of 2,000 trials, the number of the trials which the setting of emotion index X (or Y) is significant under different references (Rs); hence, the x axis of the curve is the reference level (R), and the y axis shows the number of significant trials.. 立. C-2. sit. 100 90 80 70 60 55 50 45 40 35 30 25 20 15 10 0 reference. io. al. n. Figure 6. C-1. y. Nat. 0. D-2. ‧. 500. D-1. er. 1000. ‧ 國. 1500. 學. significance. 2000. 治政 Money 大. i n U. Money Experiments: All subiects (proposers). Ch. engchi. v. Figure 6 shows some examples of the significance curves. The four curves represent the number of significant X and Y under different settings of R. However, since we have two versions of Y, one dichotomous (Equation ( 2 )) and one continuous (Equation ( 5 )), we shall abbreviate the former with D (dichotomous) and the latter with C (continuous). Then D−1 and D−2 refer to the number of significant X and Y, respectively, under Y using D; likewise, C−1 and C−2 refer to the number of significant X and Y, respectively, under Y using C.. 40.

(52) 6.1 Proposer 6.1.1. Money and Chocolate: General. From Figure 6, the money experiment, we see that the nay-based emotion X (D-1 or C-1) is always significant. As to the reference-based emotion, the discrete version of Y (D-2) does not indicate strong evidence, in all references the significance ratio is. 政治大 inverted V shape and tops at立 an assumed reference of 45 with a number of significant Y always below 50%. Nevertheless, the continuous Y (C-2), the significance curve has an. ‧ 國. y. sit er. al. n. significance. ‧. io. 1500. Chocolate. Nat. 2000. 學. up to 1,400 (70% of the total).. 1000 500. Ch. engchi U. v ni. D-2 C-1 C-2. 0 10. Figure 7. 9. 8. 7. 6. 5. 4. 3. 2. D-1. 1. 0. reference. Chocolate Experiments: All subjects (proposers). Using the result of the money experiments as the contrast, we can see immediately that the influence of emotions has demonstrated a very different pattern in the chocolate experiment (Figure 7). First of all, the significant ratio of the nay-based emotion X now depends on the accompanying Y (D−1 vs C−1) and the assumed reference, while it is 41.

(53) still uniformly above 50%. For both versions of Y, we do not see much difference in the significance ratio except in the chocolate experiment their peaks come to a higher level of the assumed preference. For an easier comparison, a direct contrast between the money experiment and the chocolate experiment on Y (C−2) is shown in Figure 8.. 立. ‧ 國. 學. Figure 8. 政治大. Reference-Based Emotion: Money and Chocolate Experiments (proposer). ‧. In sum, if both of our artificial emotions can be viewed as a realistic approximation. sit. y. Nat. of emotions, then its influence on decision making is stronger in the money game, but. io. er. weaker in the chocolate game. Furthermore, if the model does work, then the reference suggested by the chocolate game is slightly higher than the money game. This is. al. n. v i n Crate evidenced by a higher mean offer in the chocolate experiment than in the h eobserved ngchi U. money experiment (Table 5, Table 9 and Figure 5). The significance ratio is uniformly below 70% for both versions of the reference-based emotion.. 42.