A Cognitive Foundation for Social Image Concerns

Transcription

1 CIRJE-F-1085 A Cognitive Foundation for Social Image Concerns Yosuke Hashidate CIRJE, Faculty of Economics, The University of Tokyo May 2018 CIRJE Discussion Papers can be downloaded without charge from: Discussion Papers are a series of manuscripts in their draft form. They are not intended for circulation or distribution except as indicated by the author. For that reason Discussion Papers may not be reproduced or distributed without the written consent of the author.

2 A Cognitive Foundation for Social Image Concerns Yosuke Hashidate First Draft: August 8, 2017; This Draft: May 20, 2018 Abstract This paper provides a cognitive foundation for social image concerns by studying preferences over menus; that is, this paper studies the social-image formation in the decision-making process. This framework has a two-stage decision problem. At the first stage, the decision maker chooses a menu; at the second stage, she chooses an option from the chosen menu at the first stage. In social image theory, the decision maker cares about how her choice behaviors are perceived by other agents. We do anticipate such emotions at the second stage and we, therefore, study plausible axioms at the first stage. However, the decision maker may feel the emotions even in the first stage. By capturing such a tradeoff as an endogenous reference-point formation, this paper builds an axiomatic model, in which the trade-offs in the first stage determine social image concerns; that is, the factors behind social image concerns depend on endogenous reference points. This paper explores both the anticipation of image concerns and the formation of image concerns. This paper uniquely identifies the building blocks of the model. Moreover, this paper studies menu effects in terms of pride-seeking preferences, shame-averse preferences, and temptation-driven preferences, which can lead to violations of Weak Axiom of Revealed Preference (WARP). Keywords: Social Image; Social Preferences; Reference-Dependent Preferences; Endogenous Reference Points; Preferences over Menus. JEL Classification Numbers: D01, D63, D64, D81, D91. The earlier version of this paper is presented by Reference-Dependent Fairness Attitudes: An Axiomatic Approach and Reference-Dependent Altruism and Selfishness. I am indebted to my adviser Akihiko Matsui for his unique guidance, constant support, and encouragement. I am very grateful to Youichiro Higashi and Kota Saito for their invaluable suggestions and comments. I also would like to thank Jay Lu and Norio Takeoka for their invaluable discussions, and the participants at UT Summer School in Economics 2017 (University of Tokyo), EEA-ESEM 2017 (ISCTE-IUL Campus, Lisbon) and JEA 2017 Autumn Meeting (Aoyama Gakuin University, Tokyo). Of course, all remaining errors are mine. CIRJE, Faculty of Economics, the University of Tokyo: 7-3-1, Hongo, Bunkyo-ku, Tokyo, ; yosukehashidate@gmail.com

3 1 Introduction The goal of this paper is to provide a cognitive foundation for social image concerns by studying preferences over menus (choice sets); that is, this paper studies the social-image formation in the decision-making processes. We present a unified model of three existing studies: (i) Dillenberger and Sadowski (2012), (ii) Evren and Minardi (2017), and (iii) Saito (2015). In social image concerns, the decision maker cares about how her choice behaviors are perceived by other passive agents. The preferences over menus framework has a two-stage decision problem. At the first stage, the decision maker chooses a menu; at the second stage, she chooses an alternative from the first-stage chosen menu. Due to social pressure, the decision maker may feel shame, when she makes the choices. We do anticipate such an emotion at the second stage in the axiomatic studies of social image and we, therefore, study plausible axioms at the first stage. However, even in the first stage, the decision maker may feel temptation to act selfishly, or exhibit shame-aversion towards their selfish behavior. 1 Such trade-offs between feelings should be considered explicitly. The decision maker may feel temptation, pride-seeking, or shame-aversion even in the first stage. This paper builds on an axiomatic model by capturing such a trade-off as an endogenous reference-point formation at the first stage. In this model, the trade-offs determine the social image concerns, and the factors behind social image concerns depend on endogenous reference points; we explore both the anticipation of image concerns and the formation of image concerns. 1.1 Motivation It is well-known that image concerns motivate prosocial behaviors in behavioral and experimental economics. 2 To explain altruistic behaviors, the prosocial motive for unselfish behaviors has been widely recognized. Of course, this study s direction is related to other motives such as fairness (Fehr and Schmidt (1999)), reciprocity (Rabin (1993), Segal and Sobel (2007)), etc., but there are some evidence (Dana et al. (2006) etc.) that is not consistent with Fehr and Schmidt (1999). Dana et al. (2006) support the prosocial motive for unselfish behaviors. In their innovative experiments, the dictator has the option to exit the dictator game to share $10, but the recipient does not know about it. When the dictator chooses the option of exiting the game, the dictator has $9 for herself, and $0 for the recipient. About one-third of the subjects choose to leave the game. The results in Dana et al. (2006) have challenged the motives 1 See Hiebert (1985). There is a clear distinction between shame and guilt in psychology. A decision maker would suffer from guilt even if no one else knows of her behavior. 2 See Bursztyn and Jensen (2017) for the excellent survey of field experiments in economics. 1

4 of pure altruism, fairness (Fehr and Schmidt (1999)), and reciprocity (Rabin (1993)). The option ($9, $0) where the dictator has $9, and the recipient has $0 contradicts the motive of pure altruism. If the dictator is purely altruistic, then the option ($9, $1) is strictly preferred, and then the dictator should play the dictator game. Recently, various studies of social image concerns have been explored in decision theory by using the subjective state spaces framework. 3 Dillenberger and Sadowski (2012) are the first to propose a model of shame. 4,5 Second, Evren and Minardi (2017) propose a model of warm-glow which can lead to prosocial behaviors that causes the decision maker to obtain positive feelings, apart from its social implications. 6 Third, Saito (2015) proposes a unified social image model that captures (i) pride in acting altruistically, (ii) shame of acting selfishly, and (iii) temptation to act selfishly. 7 The pride factor is similar to the warm-glow. Existing studies have axiomatically identified the factors behind social image concerns such as pride, shame, and temptation. However, in general, these emotional aspects can depend on situations, such as choice opportunities, the other players personality types, the other players past actions, etc. 8 If the decision maker has a reference-dependent preference, the factors may depend on endogenous reference points. If the decision maker considers the other player s type/personality, the factors will depend on it. For example, suppose that the other player s type is purely altruistic. Then, the decision maker may feel shame if she takes a selfish action. On the other hand, she may exhibit a feeling of temptation to act selfishly in the so-called Prisoners Dilemma-type case. Noor and Ren (2015) propose a model of guilt based on the observation that guiltavoidance itself may cause guilt. 9 Their model generates this concept by treating the guiltavoidance motive as a temptation. 10 The decision maker may experience guilt when a choice behavior deviates from her (subjective) norm. Thus, guilt is interpreted as a private emotion 3 This approach takes preferences over menus as primitives. Kreps (1979) introduces this framework, and Dekel et al. (2001) generalize it. 4 In this paper, decision-making in social contexts means that the decision maker chooses options (allocations) between herself and a passive recipient. The dictator game is a typical example. 5 Dillenberger and Sadowski (2012) identify shame as the moral cost the decision maker experiences if she is observed choosing an allocation that favors her own material payoffs instead of choosing an allocation that she perceives to be in accordance with a social norm (which may include, but is not limited to, considerations of fairness and altruism). 6 Evren and Minardi (2017) study a decision maker who enjoys taking a prosocial decision-making that incurs a private cost because such a behavior improves her social image. Andreoni (1989, 1990) s warmglow theory contains a more generalized notion than that of Evren and Minardi (2017). 7 Gul and Pesendorfer (2001) propose a model of temptation. 8 See Tadelis (2011). 9 According to Noor and Ren (2015), Dillenberger and Sadowski (2012) s main conclusion can be interpreted as guilt causes guilt-avoidance. 10 See the key axiom of this paper, Intrinsic Set-Betweenness in Section 2. This axiom appears to be related to the observation that guilt-avoidance itself may cause guilt. 2

5 in the decision-making process. 11 This idea is similar to this paper s approach in the sense that the decision maker may feel shame-aversion in the ex-ante stage, which leads to a feeling of shame for the resulting behavior. ex-ante choice of menus (private) ex-post choice of allocations (public) 1 2 A 2 A p 2 A time Choosing a menu A is NOT publicly observed. Choosing an allocation p from the menu A is publicly observed. Figure 1: Two-Stage Decision Problem 1.2 Objective We study the framework of preferences over menus based on previous related studies. The framework has a two-stage decision problem structure (see Figure 1). To derive the implications, consider a dictator game. The dictator is the decision maker. At the first stage, the decision maker chooses a menu; at the second stage, she chooses an option based on her first-stage choice. The key procedure is that the choice at the first stage is not observed by the recipient; that is, recipients do not know about the set of menus (denoted by A in Figure 1). The decision maker s ex-ante choices are private. On the other hand, the choice at the second stage is observed publicly. The recipient can observe which option is chosen from the set (menu). In social image theory we do anticipate such an emotion at the second stage; we therefore study plausible axioms at the first stage. However, as mentioned above, even in the first stage, the decision maker may feel temptation to act selfishly, or exhibit shame-aversion towards their selfish behaviors. To capture this, we need to consider new plausible axioms on social image concerns. This paper provides a cognitive foundation for social image concerns. This paper builds a model of image concerns by exploring the endogenous reference point formation. The reference points endogeneity is not new in the present context, but the formation of reference points is interpreted as a cognitive consideration for social image concerns. The reference- 11 Shame is perceived by the decision maker based on observed behaviors. 3

6 point formation is closely related to emotional aspects such as shame-aversion or temptation in the ex-ante stage. The contributions of this paper are three-fold. First, this paper presents a general model of reference-dependence in other-regarding preferences. The emotional factors of image concerns are reference-dependent. The reference-dependence and social preferences studies have progressed autonomously since they are conceptually independent of each other. Even though the two topics have been traditionally studied in isolation, reference-dependence, in particular, reference-point formations, may be in action in some social contexts. The role of reference points is regarded as an anchor (Kahneman and Frederick (2002)) or a guideline for decision-making such as an emotional heuristic (Slovic et al. (2002)). By applying referencedependence into social preferences, we investigate the decision maker who not only anticipates social image concerns regarding how choice behaviors are perceived by other passive agents, but also cares about its consideration in the decision-making process. Second, this paper studies a formation of reference points as image concerns. In the existing studies, the reference points themselves have already been considered. However, only the existence of reference points is considered. The reference-point formations are not captured. However, the process is closely related to image concerns, and it directly affects the resulting behaviors. The reference points in social contexts can form social image concerns such as pride, shame, and temptation. The menu-preferences capture an anticipation of social image concerns, but this is not enough to study the reference-point formation. To capture it, we induce two menu-preferences that represents feelings at the ex-ante stage. This process captures the observation that shame-aversion causes shame or pride-seeking causes pride. Moreover, we study menu effects due to pride-seeking preferences, shameaverse preferences, and temptation-driven preferences, which can lead to violations of the Weak Axiom of Revealed Preference (WARP) (see subsection 3.5). Third, this paper presents a unified model of social image: (i) Dillenberger and Sadowski (2012), (ii) Evren and Minardi (2017), and (iii) Saito (2015). We consider the case that the existing studies correspond to our model by studying the social-image formation in the decision-making process. Dillenberger and Sadowski (2012) has a single reference point based on personal norm. Evren and Minardi (2017) also has a single reference point based on selfishness. Saito (2015) has a reference point that captures both personal norm and selfishness. Compared with them, our reference point is flexible due to social-image formation process considerations. 1.3 Outline The rest of this paper is organized as follows. In Section 2, we introduce the axioms in this paper. In Section 3, we state the main result. We present the representation theorem and the uniqueness result. Moreover, we study comparative statics and menu effects on social 4

7 image concerns. In Section 4, we provide a literature review. Section 5 concludes. All proofs are in the Appendix. 2 Axioms We introduce notation for social decision-making briefly. Let 1 denote the decision maker, and S be the finite set of other agents. Let I = {1} S be the set of all agents. Let Z be a finite set of outcomes. (Z) is the set of all lotteries with finite support. Let ( (Z)) I be the set of all allocations. The elements of ( (Z)) I are denoted by p = (p 1,, p n ) = (p 1, p S ) where S = {2, n}. The lottery p i is an allocation for an agent i. Let A be the set of all non-empty compact subsets of ( (Z)) I endowed with the Hausdorff metric d h. The Hausdorff metric is defined by { d h (A, B) := max max min p A q B d(p, q), max min p B q A } d(p, q), where d is the Euclidean metric. Menus are denoted by A, B, C A. The primitive of the model is a binary relation over A. The asymmetric and symmetric parts of are denoted by and, respectively. 2.1 Regular Preferences First, we provide a basic requirement in decision theory. Axiom (Standard Preferences): satisfies completeness, transitivity, continuity, and nondegeneracy. (i) (Completeness): For any A, B A, A B or B A. (ii) (Transitivity): For any A, B, C A, if A B and B C, then A C. (iii) (Continuity): The sets {A A A B} and {A A B A} are closed (in the Hausdorff metric d h ). (iv) (Non-Degeneracy): There exists A, B A such that A B. Nest, we induce two binary relations on ( (Z)) j (j {1, S}), individual preference 1 and social preference S. For each j {1, S}, the asymmetric and symmetric parts of j are denoted by j and j respectively. Definition 1. 1 and S are defined as follows. (i) For all p 1, q 1 (Z), p 1 1 q 1 if {(p 1, r S )} {(q 1, r S )} for some r S (Z) S. 5

8 (ii) For all p S, q S (Z) S, p S S q S if {(r 1, p S )} {(r 1, q S )} for some r 1 (Z). The first binary relation 1 is an individual preference relation on (Z). Suppose that two allocations are different from an individual allocation, and the allocations for other agents are the same. Then, the decision maker s choice depends on the individual preference. The next binary relation S is a social preference relation on (Z) S. This is the decision maker s preference on other agents allocations. Suppose that two allocations are different from other recipients allocations, and the allocations for her own are the same. Then, the decision maker s choice depends on the social preference. To induce the two binary relations, we focus on singleton menus. We can show that both 1 and S are well-defined (see Appendix A). Hence, 1 and S are separable. We provide a consistency condition between 1 and S. This axiom follows from Saito (2015) (p.344). Axiom (Consistency): For any p S, q S (Z) S, if p i 1 q i for any i S, then p S S q S. This axiom states that if all recipients allocations are desirable in terms of the individual preference, then this ranking holds with the decision maker s social preference. Intuitively speaking, the decision maker 1 may not know about the recipients preference relations directly. The decision maker 1 evaluates other agents allocations by using her own individual preference. We consider the following induced binary relations over menus. 1 and S on A are defined as follows. Definition 2. For each j {1, S}, we say that A j B if for any q B and p A, p j j q j. For each j {1, S}, the asymmetric and symmetric parts of j are denoted by j and j respectively. These definitions ( 1, S ) are suitable extensions of individual preference 1 and social preference S. The next axiom is a standard Pareto condition. Axiom (Pareto): For any p, q ( (Z)) I, if p i 1 q i and p S S q S, then {p} {q}. Moreover, if p i 1 q i and p S S q S, then {p} {q}. 2.2 Menu Preferences: Social Image Concerns and Reference Points We consider the following induced binary relations over menus. 1 and S on A are defined as follows. Definition 3. For each j {1, S}, we say that A j B if for any q B and p A, p j j q j. 6

9 For each j {1, S}, the asymmetric and symmetric parts of j are denoted by j and j respectively. These definitions ( 1, S ) are suitable extensions of individual preference 1 and social preference S. The following axiom is a weaker version of the axiom of Dominance in Saito (2015). This axiom states that, for any singleton menus, the decision maker is indifferent to adding an allocation q that is dominated both in individual menu-preference and in social menupreference. Since we study the reference-point formation, there is a possibility that the axiom of Dominance in Saito (2015) may be violated under arbitrary menus. Axiom (Weak Dominance): For any p, q ( (Z)) I, if {p} 1 {q} and {p} S {q}, then {p} {p, q}. Next, to elicit a reference point endogenously, we introduce a new axiom. The next axiom is a key axiom of this paper. The axiom is an application of the axiom of Disjoint Set-Betweenness in Olszewski (2007). Moreover, the idea is reminiscent of Noor and Ren (2015). Axiom (Intrinsic Set-Betweenness): For each j {1, S}, if A B =, (i) (Temptation-Driven Preference): A 1 B A 1 A B 1 B; (ii) (Shame-Averse Preference): A S B A S A B S B. We explain about the key axiom one-by-one. First, the axiom of Temptation-Driven Preference states that, in terms of individual menu-preference, if a menu A is preferred to another menu B, the decision maker exhibits a preference for commitment; that is, the menu A is preferred to the union of the menus A and B, i.e., A B. This axiom requires that the decision maker has a temptation to act selfishly at the first stage of choosing menus. Second, in the similar say, the axiom of Shame-Averse Preference is introduced. In terms of social menu-preference, if a menu A is preferred to another menu B, then the decision maker exhibits a preference for commitment in the same way. This type of commitment is interpreted as shame-aversion at the first stage. Moreover, we state the axiom of shame, which follows from Saito (2015). This axiom is an anticipation of shame at the ex-post stage. This axiom follows from the observation that shame causes shame-aversion. Axiom (Shame): For any p, q, r ( (Z)) I, if (i) {q} S {p, q}; (ii) {r} 1 {p}; and 7

10 (iii) {p, q, r} {q, r}; then {p} {p, q}. This axiom captures an anticipation of the feeling of shame at the second stage. The first condition states that the decision maker exhibits shame-aversion, and q is socially better. The second condition states that an allocation r is individually better than p. In addition, the third condition states that the menu {p, q, r} is strictly preferred to the menu {q, r}; that is, this condition requires that the allocation p that is not more altruistic than q is chosen from the menu {p, q, r}. Under the three conditions, the menu {p} is preferred to {p, q}. This statement captures that the decision maker avoids feeling of shame at the ex-post stage of choosing p from {p, q}. 2.3 Relaxing Independence We relax the axiom of Independence. Independence is stated as follows. For any A, B, C A and λ [0, 1], A B λa + (1 λ)c λb + (1 λ)c. Since we allow for reference-dependent preferences, the resulting behaviors may violate from WARP; that is, irrelevant alternatives may affect decision-making. We weaken the axiom of Independence by using the induced menu preference relations ( 1, S ). Axiom (Singleton Independence): For any A, B A, p (Z) I, and λ [0, 1], A B λa + (1 λ){p} λb + (1 λ){p}. There is no reference effect under any mixtures of singleton menus if the menu A is preferred to the menu B. This axiom states that Independence holds with the mixture of any singleton menus, since the trade-off between altruism and selfishness does not occur. Axiom (Weak Independence): For any A, B, C A and λ [0, 1], if (i) A 1 B, (ii) A S B, and (iii) A B, then λa + (1 λ)c λa + (1 λ)c. This axiom is also a weaker version of the axiom of Independence. The first two conditions are added into the standard axiom, and the condition itself is getting stronger. Then, the axiom itself is getting weaker. The interpretation of this axiom is as follows. First, due the first conditions (i) and (ii), at the ex-ante stage, the decision maker does not feel any trade-offs between selfishness and altruism. Second, in addition to the two conditions, in terms of menu-preferences as primitives, the menu A is preferred to the menu B. Under 8

11 the three conditions, the axiom of Independence holds; that is, the ranking of menus does not change since there is no trade-off between the hidden criteria ( 1, S ) and the primitive menu preference. Consider the dictator game to share $10 between the dictator and the recipient. For simplicity, consider two menus: A = {($10, $0), ($0, $10)} and B = {($5, $5)}. Suppose that the dictator is temptation-driven, and that he is shame-averse; that is, A 1 B and A S B. On the other hand, suppose that the dictator chooses the allocation ($5, $5); that is, B A. In this case, the axiom of Weak Independence does not hold. In this case, there is a conflict between a social image formation at the ex-ante stage and an anticipation of ex-post choices. 3 Result 3.1 Representation Theorem We state the main result. Theorem 1. The following statements are equivalent: (a) satisfies Standard Preferences, Consistency, Pareto, Weak Dominance, Intrinsic Set- Betweenness, Shame, Singleton Independence, and Weak Independence. (b) There exists a four-tuple (u, α, β, γ) where u : (Z) R is a non-constant self-utility function, α is a vector such that α 1 > 0, and α i 0 for each i S with i S α i = 1, β = (β 1, β S ) is a vector such that β 1 : R ( 1, + ) and β S : R R, and γ is the vector such that γ j [0, 1] for each j {1, S} such that is represented by a function V : A R defined by V (A) = max p A [ i I ( ) α i u(p i ) + β 1 (u(a)) α 1 (u(p 1 ) u 1 (A)) β S (u(a)) ( where u(a) = (u 1 (A), u S (A)) is a reference point of the menu A defined by and u 1 (A) = γ 1 max q A u(q 1) + (1 γ 1 ) min r A u(r 1), u S (A) = γ S max q A i S α i u(q i ) + (1 γ S ) min r A i S α i u(q i ). i S )] α i u(p i ) u S (A), We explain about the model in detail. There exists a four-tuple (u, α, β, γ) where (i) u : (Z) R is a non-constant self-utility function; (ii) α is a vector such that α 1 > 0, and α i 0 for each i S with i S α i = 1; (iii) β = (β 1, β S ) is a vector such that β 1 : R 2 ( 1, + ) and β S : R 2 R ; 9

12 (iv) γ is the vector such that γ j [0, 1] for each j {1, S} such that is represented by a function V : A R. We call the value function V, a utility of menus, a reference-dependent utilitarian if satisfies the axioms in Theorem 1. The decision maker chooses the best allocation from a menu by taking into account of the three terms. The first term captures the decision maker s evaluation of allocations without referencedependence. We can re-write the first term by α 1 u(p 1 ) + i S α i u(p i ). Since i S α i S i = 1, α i α 1 = 1 α 1 is the relative weight on the level of pure (referenceindependent) altruism and selfishness. As α 1 is getting smaller, the decision maker is willing to increase the other agents allocation p S (see Proposition 2 in detail). The second and third terms of the reference-dependent utilitarian captures the utility arising from the difference between the utility of an allocation and the endogenous reference point formed by menus (see Figure 2). This part captures reference-dependence. The reference point u(a) = (u 1 (A), u S (A)) where and u 1 (A) = γ 1 max q A u(q 1) + (1 γ 1 ) min r A u(r 1), u S (A) = γ S max q A i S α i u(q i ) + (1 γ S ) min r A α i u(q i ), are formed by menus. u 1 (A) is a reference-dependent criterion of subjective selfishness based on social image concerns. u S (A) is a reference-dependent criterion of subjective altruism based on social image concerns. 12 The ex-post utility U is described by U(p) = (1 + β 1 (u(a)))α 1 u(p 1 ) + (1 β S (u(a))) i S α i u(p i ). i S Comment The key aspect in this paper is that we induce, from the primitive of this paper, two binary relations over menus ( 1, S ). The former is a menu-preference based on one s own allocation, and the latter is a menu-preference based on recipients allocations. The former binary relation 1 is represented by u 1 : A R, and the latter is represented by u S : A R. We introduce the key axiom of Intrinsic Set-Betweenness on the two induced menu preference relations. This axiom is an application introduced in Olszewski (2007), and reminiscent of the Dekel (1986) s Betweenness axiom. This axiom states that, for any disjoint menus, if a 12 Note that even though reference points are changeable in each menu, γ = (γ 1, γ S) is uniquely identified. 10

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sha1_base64="zjgvjnaqfwfvm4briv6niwne0aw=">aaacexichvhlssnafd2nr1pfvreen8wivbflvsxxqulgzx1ubsslidmatjoqpiua+gp+gatxfutuz3djd7joj4hlbtcuvekdoqlekjkz595z58ymyuma4xk1iljhz1d3t7q31tc/mdguhx7zdcyqryq8auqmva/ijta1q+rdzdxfvmulualoyk85wffzezvho5pp7lh1sxxw5lkhltrvdpkqxsckjqd9tecvlfki2mik1mak8sslf8mpbkxpg8ieiikwcmb8ggucwyskkioqmoay1ihd4e8agras5g7hmwcz0ok8qamx1la5sncfzowjj2vehysswwu/pxoovd5f599mzqjt9eg39eipdedp9p5rly/o4xup86y0tciqdp2nb7/9q6rw7ol4u/wnzxclladenfzubyx/crwtr52ev2yvbk1503rjz+y/ss265xmytvf1alnsxsdgd5d5ft0/qx4uvzlobc4ks8vhs0qxgumk+lqxkmugcsjzth6aumvd5f2alflsbltuiosauxwjaf4dopssra==</latexit> u(p 1 ) u 1 (A) temptation / pride Figure 2: Reference-Dependent Utilitarian menu A is preferred to another B, then a preferred menu A is preferred to the union of the two menus, i.e., A B. And, the union of the two menus A B is preferred to the inferior menu B. Note that this axiom is also reminiscent of the Gul and Pesendorfer (2001) s Set- Betweenness axiom. In Noor and Ren (2015), the concept that guilt-aversion causes guilt is justified by treating the guilt-avoidance motive as a temptation. In the similar way, the cognitive process in this paper is captured by temptation-driven preferences. The endogenous formation of reference points is represented by both the maximum and minimum values of the variable. This is the main difference between this paper and the related studies. For example, in Dillenberger and Sadowski (2012), the decision maker has in mind a single reference point, which is determined by maximization of a subjective norm function on each menu (see Section 4). The difference between the maximum social utilities and the actual social utilities represents the disutility due to shame. On the other hand, in this paper, the reference point sits between the maximum and minimum values. If the actual utility beats the reference point, the associated effect to the overall utility is positive. This is the effect of shame-aversion in the ex-ante stage, which may cause the altruistic behaviors. The opposite holds otherwise. This way of formulations of reference points can make it possible for us to shed light on that image concerns depend on choice situations, since even in the ex-ante stage, some emotional aspects such as shame-aversion affects the decision maker s reasoning. 3.2 Uniqueness Result We state the uniqueness result. 11

14 Proposition 1. Suppose that the two representations (u, α, β, γ) and (u, α, β, γ ) represent the same binary relation. Then, the following statements hold: (i) u = au + b for some a > 0 and b R; (ii) α = α ; (iii) β = β ; (iv) γ = γ. The uniqueness result follows from the axiom of Consistency. Because of this axiom, the decision maker evaluates allocations by using one self-utility function u. u is an expected utility. α is uniquely identified. By applying the result in Olszewski (2007), γ is uniquely identified. Notice that the parameter for social image β depends on menus. Given menus, β is uniquely identified. 3.3 Comparative Statics on Pure Altruism We provide comparative statics on α = (α 1, α S ). α 1 is the level of pure selfishness for the decision maker 1. In the same way in Saito (2015), we study a comparative attitude toward pure altruism. The attitude toward pure altruism is captured by singleton menus. Consider two decision makers X and Y. In this paper, both Mr.X and Mr.Y are denoted by a decision maker 1. Assume that the set of other agents S is fixed. Definition 4. For any X and Y on A such that X j = Y j for each j {1, S}, X is more purely altruistic than Y if, for any p, q (Z) I with p S h S q S for each h {X, Y }, {p} Y {q} {p} X {q}. We consider the case that an allocation p is superior to q in the social preference: p S h S q S for each h {X, Y }. Under the assumption that X j = Y j for each j {1, S}, if a decision maker Y prefers p to q with p S Y S q S, then another decision maker X also prefers p to q with p S X S q S. Proposition 2. Suppose that for each h {X, Y }, h is represented by a four-tuple (u, α h, β h, γ). Then, X is more altruistic than Y if and only if α1 X αy 1. For any A A, let u(a) := { (u 1 (p 1 ), u S (p S )) R 2 p = (p 1, p S ) A } where u 1 (p 1 ) = α 1 u(p 1 ) and u S (p S ) = i S α iu(p i ). Let A be denoted by {u(a) A A }. Then, let A = u(a), and suppose that A is depicted on the two-dimensional utility space (see Figure 3). As α 1 is getting smaller, the resulting behaviors are more purely altruistic. 12

15 us us A* α1 X u1(p1) + us(ps) A* α1 Y u1(p1) + us(ps) u1 u1 Figure 3: Comparative Statics on Pure Altruism 3.4 Comparative Statics on Endogenous Reference Points We study comparative statics on γ. Consider two decision makers X and Y. In this paper, both Mr.X and Mr.Y are denoted by a decision maker 1. Assume that the set of other passive agents S is fixed. Let h j (h {X, Y }) be the decision maker h s induced menu preferences conditional on j {1, S}. Definition 5. Suppose that X and Y satisfies the axioms in Theorem 1. We say that X 1 is more temptation-driven than Y 1 if for any A, B A with B A, A Y 1 B A X 1 B. In terms of individual menu preferences ( 1 ), if the decision maker Y prefers larger menus, then the decision maker X also does. Since 1 reflects 1, preferring larger menus is not worse off in terms of individual preferences (at the first stage of choosing menus). Definition 6. Suppose that X and Y satisfies the axioms in Theorem 1. We say that X S is more shame-averse Y S if for any A, B A with B A, A Y S B A X S B. In terms of social menu preferences ( S ), if the decision maker Y prefers larger menus, then the decision maker X also does. Since S reflects S, preferring larger menus is not worse off in terms of social preferences (at the first stage of choosing menus). Proposition 3. Suppose that for each h {X, Y }, h is represented by a four-tuple (u, α, β, γ h ). Then, the following statements hold: (i) X 1 is more temptation-driven than Y 1 if and only if γx 1 γy 1. (ii) X S is more shame-averse than Y S if and only if γx S γy S. 13

16 us : Mr. X s reference point : Mr. Y s reference point γs A* shame-aversion temptation-driven γ1 u1 γ1 pride-seeking temptation-driven γs Figure 4: Comparative Statics on Reference Points In the same way, both the more pride-seeking case and the less shame-averse (temptationdriven) case are studied. If the decision maker X has both more temptation-driven and more shame-averse preference than the decision maker Y does, the decision maker X s reference point is getting higher than that of the decision maker Y. Moreover, if the decision maker has both more pride-seeking and more shame-averse preference than the decision maker Y does, then the resulting behaviors can be more pro-social than the decision maker Y s behaviors. Conversely, if the decision maker has both more temptation-driven and less shame-averse preference than the decision maker Y does, then the resulting behaviors can be in a more selfish manner than the decision maker Y s behaviors. This result is summarized in Figure 4. Intuitively, the position of reference points captures reference-dependent criterion of selfimage concerns. One remark is that Noor and Ren (2015) observe that guilt aversion cause guilt. In this paper, as γ S is larger, i.e., γ S is close to one, the decision maker is more and more shame-averse. Even though we need to consider menu effects (see Subsection 3.5), the factor of shame β S can be getting larger as γ S is larger. This aspect corresponds to the observation that shame-aversion causes shame in Noor and Ren (2015), unlike the previous studies ( shame causes shame-aversion ). 3.5 Menu Effects: Social Image Concerns We study the menu effects for social image concerns. Consider a menu {p, q}. We consider the two cases. The first one is the case that a selfish option r is added. The second one is the case that an altruistic option r is added. First, we study the case that a selfish option r is added. Fix the menu {p, q}, and suppose 14

17 the following: (i) {q} 1 {p}, (ii) {p} S {q}, and (iii) {p, q} {q}. The first condition states that q is individually superior to p. On the contrary, the second condition states that p is socially superior to q. The third condition states that p is chosen from {p, q}; that is, p is better than q at the ex-post stage. We say that an allocation r is selfish for a menu A if for all p A, r 1 1 p 1. We study the menu effects that stems from a pride-seeking preference or temptation-driven preference. Definition 7. Consider the menu {p, q} such that (i) {q} 1 {p}, (ii) {p} S {q}, and (iii) {p, q} {q}. (i) exhibits a temptation-driven preference if {p} {p, q}. (ii) exhibits a pride-seeking preference if {p, q} {p}. Moreover, we define the following: Definition 8. Consider the menu {p, q} such that (i) {q} 1 {p}, (ii) {p} S {q}, and (iii) {p, q} {q}. And, suppose that an allocation r is more selfish than p, q. (i) exhibits more temptation-driven preferences if {p} {p, q} {p} {p, r}. (ii) exhibits more pride-seeking preferences if {p, q} {p} {p, r} {p}. Proposition 4. Consider the menu {p, q} such that (i) {q} 1 {p}, (ii) {p} S {q}, and (iii) {p, q} {q}. Suppose that a selfish allocation r is added into {p, q}. Then, the following statements hold: (i) exhibits more temptation-driven preferences if and only if β 1 (u({p, q})) β 1 (u({p, q, r})). (ii) exhibits more pride-seeking preferences if and only if β 1 (u({p, q})) β 1 (u({p, q, r})). Consider the case of temptation-driven preferences. As a selfish option r for the menu {p, q} is added into the menu {p, q}, the reference level of u 1 increases. Notice that p is chosen from the menu {p, q}. Due to temptation-driven preferences, q can be chosen from the menu {p, q, r}, since β 1 (u({p, q})) β 1 (u({p, q, r})). A violation of WARP can occur due to temptation-driven preferences. In the same way, pride-seeking preferences may lead to violations of WARP. Second, we study the case that an altruistic option r is added. Fix a menu {p, q}, and suppose the following. Take an arbitrary option r (Z) I. Suppose (i) {r} 1 {p}, (ii) {q} S {p}, and (iii) {p, q, r} {q, r}. The first condition states that r is individually optimal, and p is not individually optimal. The second condition states that q is socially superior to p. The third condition states that p is chosen from {p, q, r}; that is, p is better than q at the ex-post stage. This conditions follow from the axiom of Shame. By the axiom, the decision maker prefers {p} to {p, q}. 15

18 We say that an allocation r is altruistic if for all p A, r S S p S. We define the following: Definition 9. Consider the menu {p, q} and an arbitrary option r (Z) I such that (i) {r} 1 {p}, (ii) {q} S {p}, and (iii) {p, q, r} {q, r}. And, suppose that an allocation r is more altruistic than p, q. exhibits more shame-averse preferences if {p} {p, q} {p} {p, r }. Proposition 5. Consider the menu {p, q} and an arbitrary option r (Z) I such that (i) {r} 1 {p}, (ii) {q} S {p}, and (iii) {p, q, r} {q, r}. Suppose that an altruistic allocation r is added into {p, q}. Then, the following statements hold: exhibits more shame-averse preferences if and only if β S (u({p, q})) β S (u({p, q, r})). As an altruistic option r for the menu {p, q} is added into the menu {p, q}, the reference level of u S increases. Notice that p is chosen from the menu {p, q}. Due to shame-averse preferences, q can be chosen from the menu {p, q, r }, since β S (u({p, q})) β S (u({p, q, r })). Thus, a violation of WARP can occur due to shame-averse preferences. 4 Literature Review In this section, we provide the literature review. We mainly discuss the three related studies: (i) Dillenberger and Sadowski (2012), (ii) Evren and Minardi (2017), and (iii) Saito (2015). These studies take preferences over menus as primitives. The studies axiomatically identify the factors behind social image concerns. Compared with these studies, this paper focuses on a cognitive foundation for social image concerns. In particular, this paper studies how such image concerns are formed by applying reference-dependent preferences into social preferences. Dillenberger and Sadowski (2012) develop the theory of shame of acting selfishly. 13 Shame, one of the factors behind social image concerns is only considered. In Dillenberger and Sadowski (2012), shame is captured by a personal norm function φ and a function g. Because of shame, the decision maker may deviate from WARP. On the other hand, in this paper, shame is captured by β S, which depends on the decision maker s reference point. The factor of shame is determined by reference-dependence. Evren and Minardi (2017) develop a theory of warm glow, which refers to other-serving behavior that is valuable for the decision maker, apart from its social implications. 14 They 13 Neilson (2009) also presents a (non-axiomatic) model to study the effect of shame. As an experimental evidence for social image concerns, see Dana et al. (2006). 14 See also Andreoni (1989, 1990), which are seminal studies on warm glow. Specifically, the Evren and Minardi (2017) s model is based on the notion of warm glow to the freedom to be selfish. 16