- Email: [email protected]
A note on coupled lotteries
Economics Letters 124 (2014) 96–99
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
A note on coupled lotteries Marc T.P. Adam a,∗ , Eike B. Kroll b , Timm Teubner a a
Karlsruhe Institute of Technology, Germany
b
buw consulting GmbH, Germany
highlights • • • •
Experimental analysis of individual, symmetric and asymmetric lotteries. When payoffs are symmetrically coupled, subjects make more risky choices. When payoffs are asymmetrically coupled, subjects make less risky choices. Subjects with persistent choices behave more risk averse.
article
info
Article history: Received 2 February 2014 Received in revised form 16 April 2014 Accepted 25 April 2014 Available online 5 May 2014 JEL classification: D8 C9
abstract We study the impact of coupling a decision maker’s lottery payoffs to those of a peer on the preferred level of risk by means of a lab experiment. Compared to the benchmark where the lotteries are paid off individually, symmetrically coupled payoffs increase the willingness to take risks, whereas asymmetrically coupled payoffs have the opposite effect. Moreover, subjects with persistent choices in the different conditions behave more risk averse than subjects with non-persistent behavior. © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
Keywords: Other-regarding preferences Decision under risk Lottery choice
1. Introduction The literature on other-regarding preferences mostly abstracts from uncertainty and focuses on deterministic scenarios; ‘‘few contributions investigate risk taking in a social context’’ (Bolton and Ockenfels, 2010, p. 628). However, recent theoretical and experimental work is increasingly concerned with the interplay of both aspects (see Trautmann, 2009; Trautmann and Vieider, 2011; Gantner and Kerschbamer, 2011). Trautmann and Vieider (2011) found that fairness motives and uncertainty interact if (a) the decision maker observes the payoff of other agents they consider relevant, (b) the outcome of another person serves as a reference point, and (c) people aim for conformity with their peers’ behavior. Therefore, creating a social context in risky choice situations is likely to affect decisions. This holds even when subjects only
∗ Correspondence to: Karlsruhe Institute of Technology, Kaiserstr. 12, Bldg. 01.80, 76131 Karlsruhe, Germany. Tel.: +49 721 6084 8372; fax: +49 721 6084 8399. E-mail address: [email protected] (M.T.P. Adam).
affect their own payoffs or chances without any impact on others’ payoffs. Weigold and Schlenker (1991) found that especially risk averse subjects are affected when their choices are observed by a passive partner and reduce their risk tolerance. In contrast, originally risk seeking subjects showed higher risk tolerance. The question how peer presence affects risk tolerance is important since many decisions take place within a social context (e.g., management decisions, social trading, and gamified applications). Various experiments analyzed choices where risk is introduced to a social context, e.g., probabilistic dictator games where not the payoff is distributed but the probabilistic chance of winning the complete amount (Karni et al., 2008; Krawczyk and Le Lec, 2010; Brock et al., 2013) or where uncertainty about the pie size is introduced (Haisley and Weber, 2010; Ockenfels and Werner, 2012). Brennan et al. (2008) and Güth et al. (2008) analyzed subjects’ willingness to pay and accept for prospects with different combinations of payoffs to oneself and a peer. Other scholars focused on situations with decisions explicitly on behalf of a peer (Chakravarty et al., 2011; Pahlke et al., 2010; Charness and Jackson, 2009), or where a deliberate departure from one’s own
http://dx.doi.org/10.1016/j.econlet.2014.04.024 0165-1765/© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3. 0/).
M.T.P. Adam et al. / Economics Letters 124 (2014) 96–99
preferred level of risk benefits another player (e.g., Bradler, 2009). All of these studies analyzed choice situations where at least one of the subjects directly affected the other’s payoff. Other studies, similar to ours, created the social context by the existence of a passive partner. Linde and Sonnemans (2012), found that participants exhibited higher risk aversion when they could earn at most as much as a passive partner (who received a fixed payoff), compared to when they were ensured to earn at least as much. The passive partner seemed to create a social reference point. Prospect Theory, however, does not predict this behavior. Cooper and Rege (2011) considered the impact of peer group choices and concluded that ‘‘social interaction effects driven by social regret can cause peer group effects’’ (p. 109), meaning that an observed choice increases the decision maker’s tendency to choose the observed level of risk as well. Gantner and Kerschbamer (2011) complemented this finding in an experiment in which they explicitly abstracted from material externalities, information on outcomes, and stochastic dependence. They found that being exposed to the decisions of a fictitious peer in risky choices, the decision maker’s level of risk shifts towards that of the peer. Bault et al. (2008) matched participants with fictitious peers and analyzed the impact of lottery outcomes on arousal. They found that contrary outcomes (one loses, the other wins) caused stronger physiological reactions than when participants win or lose concurrently. While most prior studies confronted subjects with risky decisions in light of a peer’s outcome or choice (ex-post), there exist few insights about the impact of how chances and payoffs are coupled from an ex-ante perspective, i.e. before the decision maker knows anything about the other’s actions or results, except that there is another player. In our paper, we address such ex-ante decisions and systematically vary the social context by altering the way in which the participants’ outcomes are coupled. 2. Experimental design Every participant successively faced 3 risk preference elicitation tasks, similar to Holt and Laury (2002), using a within-subject design with varying sequence. The 3 tasks each consisted of 21 choices between 2 alternative lotteries A and B. Every lottery had a high (A: e 20, B: e 15) and a low payoff (A: e 0, B: e 5). The choice set is represented in Table 1. The experiment was conducted using pen and paper at the Institute of Information Systems and Marketing at Karlsruhe Institute of Technology in Karlsruhe, Germany. Altogether, 140 subjects were recruited using ORSEE (Greiner, 2004). Subjects were seated in separated cabins, communication was not allowed. They did not see each other prior or during the experiment. To investigate the influence of the social context, we manipulated the way the subjects’ payoff is linked to that of a partner. The social context was established by the payoff procedure. Depending on the treatment, subjects were called for payoff individually, or in pairs of two. In the latter case, they could observe their (randomly assigned) partner’s decisions and result. At the time of decision making, participants did not know or get to see the partner. First, in the control treatment, lotteries were not coupled but realized for each subject individually (IND). Second, in the symmetric treatment (SYM), lotteries were symmetrically coupled, i.e., either both subjects received the low or the high payoff of their respective lottery choice. Third, in the asymmetric treatment (ASYM), lotteries were asymmetrically coupled, i.e., one subject received the high payoff (e 20 or e 15) while the partner inevitably received the low payoff (e 0 or e 5). Note that the difference between the players’ payoffs in the SYM treatment can at most be e 5 (i.e. e 0 or e 5), whereas it is at least e 10 (i.e. e 10, e 15, or e 20) in the ASYM treatment for any combination of choices. While
97
these ‘‘guaranteed’’ differences were deliberately not highlighted in the instructions, they were implicitly available to subjects by comparing the payoffs on the decision sheet. Neither partner’s identity nor choice was known at the time of decision making. Finally, a dice roll determined the relevant choice set for all participants of a particular session. Then, subjects either individually (IND) or in random groups of two (SYM, ASYM) were called to the experimenter. First, one of the 21 rows was selected with equal probabilities. Then an urn was equipped with 20 balls of 2 colors where the proportions of the colors reflected the probabilities. Then the lottery was played out for one (IND), or for the 2 subjects of the current group with a single draw from the urn (SYM, ASYM). In the SYM treatment, the high payoffs were associated with one, and the low payoffs with the other color. The ASYM treatment realized asymmetrical coupling by one color identifying the high payoff for one subject and the low for the other. 3. Results Expectedly, subjects behave risk averse on average (#sc overall = 14.567 > 11 = #sc risk neutral ). Altogether, 35 subjects (25%) chose the same number of safe choices in all 3 treatments. We refer to this behavior as persistent. In contrast, 105 subjects (75%) deviated at least once (SYM and/or ASYM) from the number of safe choices in the IND condition. We refer to this behavior as non-persistent. The comparison of persistent and non-persistent subjects reveals that persistent subjects (N = 35, M = 15.486, SD = 2.994) made more safe choices than non-persistent subjects (N = 105, M = 14.260, SD = 2.883) (two-tailed independent samples Wilcoxon test: Z = −2.445, p = 0.015). Result 1. Subjects with persistent choices reveal a higher degree of risk aversion than subjects with non-persistent behavior. The majority made varying numbers of safe choices across treatments. A Friedman test reveals that these treatment differences are systematic (χ 2 = 15.961, p < 0.001, average ranks arsym = 1.73, arind = 2.04, arasym = 2.23). We now focus on these non-persistent subjects. The analysis shows that subjects made a lower number of safe choices in the SYM condition than in the IND condition (two-tailed paired samples Wilcoxon test, Z = −2.554, p = 0.011). Result 2a. Subjects make riskier choices when the payoffs are symmetrically coupled, compared to the benchmark treatment with individual payoffs. The number of safe choices in the SYM condition is also smaller than in the ASYM condition (Z = −3.435, p < 0.001). The number of safe choices in the baseline condition IND lies in the middle of SYM and ASYM. It is smaller than in the ASYM condition, this difference, however, is only marginally significant (Z = −1.736, p = 0.083). Result 2b. Subjects make less risky choices when the payoffs are asymmetrically coupled, compared to the benchmark treatment with individual payoffs. We believe that the difference in risk tolerance between persistent and non-persistent subjects (Result 1) substantiates the need for a broken down analysis. Note, however, that Result 2a and Result 2b are robust towards including the persistent subjects (SYM vs. IND: Z = −2.666, p = 0.008 ; SYM vs. ASYM: Z = −3.488, p < 0.001; IND vs. ASYM: Z = −1.757, p = 0.079). Similar to above, the difference between IND and ASYM is only marginally significant. Overall, as can be seen in Fig. 1, the number of safe choices follows the distinct pattern SYM < IND < ASYM (MSYM = 13.762,
98
M.T.P. Adam et al. / Economics Letters 124 (2014) 96–99 Table 1 Lottery probability and payoff structure. Row
P(high payoff)
P(low payoff)
Set of lotteries Option A
1 2
100% 95%
0% 5%
Option B
High payoff
Low payoff
High payoff
Low payoff
20 e 20 e
0e 0e
15 e 15 e
5e 5e
···
···
···
···
···
···
···
i
(21 − i) × 5%
(i − 1) × 5%
20 e
0e
15 e
5e
···
···
···
···
···
···
···
20 21
5% 0%
95% 100%
20 e 20 e
0e 0e
15 e 15 e
5e 5e
17.0
17.0
16.0
16.0
15.0
15.0
14.0
14.0
13.0
13.0
# safe choices
N=105
12.0
N=35
N=105
persistent
non-persistent
12.0 SYM
IND
ASYM
Fig. 1. Average number of safe choices, depending on behavior and treatment. Error bars indicate 95% confidence intervals.
SDSYM = 3.274, MIND = 14.229, SDIND = 2.923, MASYM = 14.790, SDASYM = 3.591). In 98% of the cases, the choice patterns show only one switching point between lottery A and B. Furthermore, we control for sequence effects. If the IND task is performed before the SYM and ASYM tasks, the number of safe choices in the ASYM task is slightly smaller than when IND is performed after SYM and ASYM (Spearman’s ρ = −0.170, p = 0.044, n = 140). 4. Discussion Our study shows that subjects systematically deviate from their inherent individual risk preference, even when neither knowing the peer’s payoff nor her choice, and the lotteries’ payoffs are coupled. Therefore, we extend the existing literature by a novel aspect. Specifically we show that symmetrically coupled payoffs lead to higher, whereas asymmetrically coupled payoffs lead to lower degrees of risk tolerance, compared to the non-social benchmark. There is reason to believe, however, that the decision maker’s inherent risk preference does not actually change, but that it rather interacts with social motives. We argue that, on the one hand, anticipated social regret, i.e., the fear of ending up in a comparatively disadvantageous situation, can explain the increase in risk aversion. On the other hand, the ‘‘guaranteed’’ difference of at most e 5, i.e. winning or losing together, may reduce these obstructive influences of social comparison. This, in contrast, causes a shift towards risk propensity. Recall that the risk-neutral number of safe choices is 11, which is even lower. Inequality aversion may also (partly) rationalize our findings. While the effect in the SYM treatment remains indefinite, inequality averse subjects may prefer the lowrisk lottery in the ASYM treatment, since it yields strictly lower differences, regardless of the other player’s choice. The differences regarding stated risk attitude across treatments also hold when including participants with identical statements in all 3 treatments. The differentiation seems justified, since this
particular group is associated with a distinctly higher degree of risk aversion, which appears quite intriguing. Stating identical risk preferences across all 3 situations may be regarded a sign of rejection of social motives, deliberately or subconsciously. Such ‘‘persistent’’ behavior (in the sense of social unaffectedness) is then, however, further away from risk-neutrality than the affected participants’ behavior. At the time of decision making, subjects did not know which of the 3 treatment alternatives would actually be realized. They had to anticipate the situation and were not actually facing it when deciding. Therefore, our results may even underestimate the actual impact of the social context. Although, of course, our study must be seen in a wider context of results and the specific characteristics of the experiment, it may be relevant from an ‘‘engineering’’ perspective. The Dutch postcode lottery (e.g., Zeelenberg and Pieters, 2004), for instance, uses the socially reinforced thought of regret in a straightforwardly applied way. The important extension of deciding on how to couple the payoffs among oneself and the peer – we deliberately abstracted from this aspect – is left to future research. We argue that particularly in situations with ex ante considerations regarding the resulting payoff constellations, the role of the peer may be essential for decision making under risk.
Acknowledgments The authors thank Julius Grebbin for his help with conducting the experiment. Financial support by the Young Investigator Group ‘‘Emotions in Markets’’, funded by Karlsruhe Institute of Technology, is gratefully acknowledged. Appendix A. Supplementary data Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.econlet.2014.04.024.
M.T.P. Adam et al. / Economics Letters 124 (2014) 96–99
References Bault, N., Coricelli, G., Rustichini, A., 2008. Interdependent utilities: how social ranking affects choice behavior. PLoS One 3 (10), e3477. Bolton, G.E., Ockenfels, A., 2010. Betrayal aversion: evidence from Brazil, China, Oman, Switzerland, Turkey, and the United States: comment. Amer. Econ. Rev. 100 (1), 628–633. Bradler, C., 2009. Social preferences under risk: an experimental analysis. Working Paper, Zentrum für Europäische Wirtschaftsforschung. Brennan, G., Gonzalez, L., Güth, W., Levati, M., 2008. Attitudes toward private and collective risk in individual and strategic choice situations. J. Econ. Behav. Organ. 67 (1), 253–262. Brock, J.M., Lange, A., Ozbay, E.Y., 2013. Dictating the risk: experimental evidence on giving in risky environments. Amer. Econ. Rev. 103 (1), 415–437. Chakravarty, S., Harrison, G.W., Haruvy, E., Rutström, E., 2011. Are you risk averse over other people’s money? South. Econ. J. 77 (4), 901–913. Charness, G., Jackson, M., 2009. The role of responsibility in strategic risk-taking. J. Econ. Behav. Organ. 69 (3), 241–247. Cooper, D.J., Rege, M., 2011. Misery loves company: social regret and social interaction effects in choices under risk and uncertainty. Games Econom. Behav. 73 (1), 91–110. Gantner, A., Kerschbamer, R., 2011. Distributional preferences, risky choices and social interaction effects: theory and experiment. Working Paper, University of Innsbruck. Greiner, B., 2004. An online recruitment system for economic experiments. In: Forschung und wissenschaftliches Rechnen 2003. In: GWDG Bericht, vol. 63. Gesellschaft für wissenschaftliche Datenverarbeitung mbH, Göttingen, pp. 79–93.
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Güth, W., Levati, M., Ploner, M., 2008. On the social dimension of time and risk preferences: an experimental study. Econ. Inquiry 46 (2), 261–272. Haisley, E., Weber, R., 2010. Self-serving interpretations of ambiguity in otherregarding behavior. Games Econom. Behav. 68 (2), 614–625. Holt, C.A., Laury, S.K., 2002. Risk aversion and incentive effects. Amer. Econ. Rev. 92 (5), 1644–1655. Karni, E., Salmon, T., Sopher, B., 2008. Individual sense of fairness: an experimental study. Exp. Econ. 11 (2), 174–189. Krawczyk, M., Le Lec, F., 2010. ‘Give me a chance!’ an experiment in social decision under risk. Exp. Econ. 13 (4), 500–511. Linde, J., Sonnemans, J., 2012. Social comparison and risky choices. J. Risk Uncertain. 44 (1), 45–72. Ockenfels, A., Werner, P., 2012. ‘Hiding behind a small cake’ in a newspaper dictator game. J. Econ. Behav. Organ. 82 (1), 82–85. Pahlke, J., Strasser, S., Vieider, F., 2010. Responsibility effects in decision making under risk. Working Paper, Münchener Wirtschaftswissenschaftliche Beiträge. Trautmann, S., 2009. A tractable model of process fairness under risk. J. Econ. Psychol. 30 (5), 803–813. Trautmann, S., Vieider, F.M., 2011. Social influences on risk attitudes: applications in economics. In: Roeser, S. (Ed.), Handbook of Risk Theory. Springer, pp. 1–28. (Chapter 29). Weigold, M.F., Schlenker, B.R., 1991. Accountability and risk taking. Pers. Soc. Psychol. Bull. 17 (1), 25–29. Zeelenberg, M., Pieters, R., 2004. Consequences of regret aversion in real life: the case of the Dutch postcode lottery. Organ. Behav. Hum. Decis. Process. 93 (2), 155–168.
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
A note on coupled lotteries Marc T.P. Adam a,∗ , Eike B. Kroll b , Timm Teubner a a
Karlsruhe Institute of Technology, Germany
b
buw consulting GmbH, Germany
highlights • • • •
Experimental analysis of individual, symmetric and asymmetric lotteries. When payoffs are symmetrically coupled, subjects make more risky choices. When payoffs are asymmetrically coupled, subjects make less risky choices. Subjects with persistent choices behave more risk averse.
article
info
Article history: Received 2 February 2014 Received in revised form 16 April 2014 Accepted 25 April 2014 Available online 5 May 2014 JEL classification: D8 C9
abstract We study the impact of coupling a decision maker’s lottery payoffs to those of a peer on the preferred level of risk by means of a lab experiment. Compared to the benchmark where the lotteries are paid off individually, symmetrically coupled payoffs increase the willingness to take risks, whereas asymmetrically coupled payoffs have the opposite effect. Moreover, subjects with persistent choices in the different conditions behave more risk averse than subjects with non-persistent behavior. © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
Keywords: Other-regarding preferences Decision under risk Lottery choice
1. Introduction The literature on other-regarding preferences mostly abstracts from uncertainty and focuses on deterministic scenarios; ‘‘few contributions investigate risk taking in a social context’’ (Bolton and Ockenfels, 2010, p. 628). However, recent theoretical and experimental work is increasingly concerned with the interplay of both aspects (see Trautmann, 2009; Trautmann and Vieider, 2011; Gantner and Kerschbamer, 2011). Trautmann and Vieider (2011) found that fairness motives and uncertainty interact if (a) the decision maker observes the payoff of other agents they consider relevant, (b) the outcome of another person serves as a reference point, and (c) people aim for conformity with their peers’ behavior. Therefore, creating a social context in risky choice situations is likely to affect decisions. This holds even when subjects only
∗ Correspondence to: Karlsruhe Institute of Technology, Kaiserstr. 12, Bldg. 01.80, 76131 Karlsruhe, Germany. Tel.: +49 721 6084 8372; fax: +49 721 6084 8399. E-mail address: [email protected] (M.T.P. Adam).
affect their own payoffs or chances without any impact on others’ payoffs. Weigold and Schlenker (1991) found that especially risk averse subjects are affected when their choices are observed by a passive partner and reduce their risk tolerance. In contrast, originally risk seeking subjects showed higher risk tolerance. The question how peer presence affects risk tolerance is important since many decisions take place within a social context (e.g., management decisions, social trading, and gamified applications). Various experiments analyzed choices where risk is introduced to a social context, e.g., probabilistic dictator games where not the payoff is distributed but the probabilistic chance of winning the complete amount (Karni et al., 2008; Krawczyk and Le Lec, 2010; Brock et al., 2013) or where uncertainty about the pie size is introduced (Haisley and Weber, 2010; Ockenfels and Werner, 2012). Brennan et al. (2008) and Güth et al. (2008) analyzed subjects’ willingness to pay and accept for prospects with different combinations of payoffs to oneself and a peer. Other scholars focused on situations with decisions explicitly on behalf of a peer (Chakravarty et al., 2011; Pahlke et al., 2010; Charness and Jackson, 2009), or where a deliberate departure from one’s own
http://dx.doi.org/10.1016/j.econlet.2014.04.024 0165-1765/© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3. 0/).
M.T.P. Adam et al. / Economics Letters 124 (2014) 96–99
preferred level of risk benefits another player (e.g., Bradler, 2009). All of these studies analyzed choice situations where at least one of the subjects directly affected the other’s payoff. Other studies, similar to ours, created the social context by the existence of a passive partner. Linde and Sonnemans (2012), found that participants exhibited higher risk aversion when they could earn at most as much as a passive partner (who received a fixed payoff), compared to when they were ensured to earn at least as much. The passive partner seemed to create a social reference point. Prospect Theory, however, does not predict this behavior. Cooper and Rege (2011) considered the impact of peer group choices and concluded that ‘‘social interaction effects driven by social regret can cause peer group effects’’ (p. 109), meaning that an observed choice increases the decision maker’s tendency to choose the observed level of risk as well. Gantner and Kerschbamer (2011) complemented this finding in an experiment in which they explicitly abstracted from material externalities, information on outcomes, and stochastic dependence. They found that being exposed to the decisions of a fictitious peer in risky choices, the decision maker’s level of risk shifts towards that of the peer. Bault et al. (2008) matched participants with fictitious peers and analyzed the impact of lottery outcomes on arousal. They found that contrary outcomes (one loses, the other wins) caused stronger physiological reactions than when participants win or lose concurrently. While most prior studies confronted subjects with risky decisions in light of a peer’s outcome or choice (ex-post), there exist few insights about the impact of how chances and payoffs are coupled from an ex-ante perspective, i.e. before the decision maker knows anything about the other’s actions or results, except that there is another player. In our paper, we address such ex-ante decisions and systematically vary the social context by altering the way in which the participants’ outcomes are coupled. 2. Experimental design Every participant successively faced 3 risk preference elicitation tasks, similar to Holt and Laury (2002), using a within-subject design with varying sequence. The 3 tasks each consisted of 21 choices between 2 alternative lotteries A and B. Every lottery had a high (A: e 20, B: e 15) and a low payoff (A: e 0, B: e 5). The choice set is represented in Table 1. The experiment was conducted using pen and paper at the Institute of Information Systems and Marketing at Karlsruhe Institute of Technology in Karlsruhe, Germany. Altogether, 140 subjects were recruited using ORSEE (Greiner, 2004). Subjects were seated in separated cabins, communication was not allowed. They did not see each other prior or during the experiment. To investigate the influence of the social context, we manipulated the way the subjects’ payoff is linked to that of a partner. The social context was established by the payoff procedure. Depending on the treatment, subjects were called for payoff individually, or in pairs of two. In the latter case, they could observe their (randomly assigned) partner’s decisions and result. At the time of decision making, participants did not know or get to see the partner. First, in the control treatment, lotteries were not coupled but realized for each subject individually (IND). Second, in the symmetric treatment (SYM), lotteries were symmetrically coupled, i.e., either both subjects received the low or the high payoff of their respective lottery choice. Third, in the asymmetric treatment (ASYM), lotteries were asymmetrically coupled, i.e., one subject received the high payoff (e 20 or e 15) while the partner inevitably received the low payoff (e 0 or e 5). Note that the difference between the players’ payoffs in the SYM treatment can at most be e 5 (i.e. e 0 or e 5), whereas it is at least e 10 (i.e. e 10, e 15, or e 20) in the ASYM treatment for any combination of choices. While
97
these ‘‘guaranteed’’ differences were deliberately not highlighted in the instructions, they were implicitly available to subjects by comparing the payoffs on the decision sheet. Neither partner’s identity nor choice was known at the time of decision making. Finally, a dice roll determined the relevant choice set for all participants of a particular session. Then, subjects either individually (IND) or in random groups of two (SYM, ASYM) were called to the experimenter. First, one of the 21 rows was selected with equal probabilities. Then an urn was equipped with 20 balls of 2 colors where the proportions of the colors reflected the probabilities. Then the lottery was played out for one (IND), or for the 2 subjects of the current group with a single draw from the urn (SYM, ASYM). In the SYM treatment, the high payoffs were associated with one, and the low payoffs with the other color. The ASYM treatment realized asymmetrical coupling by one color identifying the high payoff for one subject and the low for the other. 3. Results Expectedly, subjects behave risk averse on average (#sc overall = 14.567 > 11 = #sc risk neutral ). Altogether, 35 subjects (25%) chose the same number of safe choices in all 3 treatments. We refer to this behavior as persistent. In contrast, 105 subjects (75%) deviated at least once (SYM and/or ASYM) from the number of safe choices in the IND condition. We refer to this behavior as non-persistent. The comparison of persistent and non-persistent subjects reveals that persistent subjects (N = 35, M = 15.486, SD = 2.994) made more safe choices than non-persistent subjects (N = 105, M = 14.260, SD = 2.883) (two-tailed independent samples Wilcoxon test: Z = −2.445, p = 0.015). Result 1. Subjects with persistent choices reveal a higher degree of risk aversion than subjects with non-persistent behavior. The majority made varying numbers of safe choices across treatments. A Friedman test reveals that these treatment differences are systematic (χ 2 = 15.961, p < 0.001, average ranks arsym = 1.73, arind = 2.04, arasym = 2.23). We now focus on these non-persistent subjects. The analysis shows that subjects made a lower number of safe choices in the SYM condition than in the IND condition (two-tailed paired samples Wilcoxon test, Z = −2.554, p = 0.011). Result 2a. Subjects make riskier choices when the payoffs are symmetrically coupled, compared to the benchmark treatment with individual payoffs. The number of safe choices in the SYM condition is also smaller than in the ASYM condition (Z = −3.435, p < 0.001). The number of safe choices in the baseline condition IND lies in the middle of SYM and ASYM. It is smaller than in the ASYM condition, this difference, however, is only marginally significant (Z = −1.736, p = 0.083). Result 2b. Subjects make less risky choices when the payoffs are asymmetrically coupled, compared to the benchmark treatment with individual payoffs. We believe that the difference in risk tolerance between persistent and non-persistent subjects (Result 1) substantiates the need for a broken down analysis. Note, however, that Result 2a and Result 2b are robust towards including the persistent subjects (SYM vs. IND: Z = −2.666, p = 0.008 ; SYM vs. ASYM: Z = −3.488, p < 0.001; IND vs. ASYM: Z = −1.757, p = 0.079). Similar to above, the difference between IND and ASYM is only marginally significant. Overall, as can be seen in Fig. 1, the number of safe choices follows the distinct pattern SYM < IND < ASYM (MSYM = 13.762,
98
M.T.P. Adam et al. / Economics Letters 124 (2014) 96–99 Table 1 Lottery probability and payoff structure. Row
P(high payoff)
P(low payoff)
Set of lotteries Option A
1 2
100% 95%
0% 5%
Option B
High payoff
Low payoff
High payoff
Low payoff
20 e 20 e
0e 0e
15 e 15 e
5e 5e
···
···
···
···
···
···
···
i
(21 − i) × 5%
(i − 1) × 5%
20 e
0e
15 e
5e
···
···
···
···
···
···
···
20 21
5% 0%
95% 100%
20 e 20 e
0e 0e
15 e 15 e
5e 5e
17.0
17.0
16.0
16.0
15.0
15.0
14.0
14.0
13.0
13.0
# safe choices
N=105
12.0
N=35
N=105
persistent
non-persistent
12.0 SYM
IND
ASYM
Fig. 1. Average number of safe choices, depending on behavior and treatment. Error bars indicate 95% confidence intervals.
SDSYM = 3.274, MIND = 14.229, SDIND = 2.923, MASYM = 14.790, SDASYM = 3.591). In 98% of the cases, the choice patterns show only one switching point between lottery A and B. Furthermore, we control for sequence effects. If the IND task is performed before the SYM and ASYM tasks, the number of safe choices in the ASYM task is slightly smaller than when IND is performed after SYM and ASYM (Spearman’s ρ = −0.170, p = 0.044, n = 140). 4. Discussion Our study shows that subjects systematically deviate from their inherent individual risk preference, even when neither knowing the peer’s payoff nor her choice, and the lotteries’ payoffs are coupled. Therefore, we extend the existing literature by a novel aspect. Specifically we show that symmetrically coupled payoffs lead to higher, whereas asymmetrically coupled payoffs lead to lower degrees of risk tolerance, compared to the non-social benchmark. There is reason to believe, however, that the decision maker’s inherent risk preference does not actually change, but that it rather interacts with social motives. We argue that, on the one hand, anticipated social regret, i.e., the fear of ending up in a comparatively disadvantageous situation, can explain the increase in risk aversion. On the other hand, the ‘‘guaranteed’’ difference of at most e 5, i.e. winning or losing together, may reduce these obstructive influences of social comparison. This, in contrast, causes a shift towards risk propensity. Recall that the risk-neutral number of safe choices is 11, which is even lower. Inequality aversion may also (partly) rationalize our findings. While the effect in the SYM treatment remains indefinite, inequality averse subjects may prefer the lowrisk lottery in the ASYM treatment, since it yields strictly lower differences, regardless of the other player’s choice. The differences regarding stated risk attitude across treatments also hold when including participants with identical statements in all 3 treatments. The differentiation seems justified, since this
particular group is associated with a distinctly higher degree of risk aversion, which appears quite intriguing. Stating identical risk preferences across all 3 situations may be regarded a sign of rejection of social motives, deliberately or subconsciously. Such ‘‘persistent’’ behavior (in the sense of social unaffectedness) is then, however, further away from risk-neutrality than the affected participants’ behavior. At the time of decision making, subjects did not know which of the 3 treatment alternatives would actually be realized. They had to anticipate the situation and were not actually facing it when deciding. Therefore, our results may even underestimate the actual impact of the social context. Although, of course, our study must be seen in a wider context of results and the specific characteristics of the experiment, it may be relevant from an ‘‘engineering’’ perspective. The Dutch postcode lottery (e.g., Zeelenberg and Pieters, 2004), for instance, uses the socially reinforced thought of regret in a straightforwardly applied way. The important extension of deciding on how to couple the payoffs among oneself and the peer – we deliberately abstracted from this aspect – is left to future research. We argue that particularly in situations with ex ante considerations regarding the resulting payoff constellations, the role of the peer may be essential for decision making under risk.
Acknowledgments The authors thank Julius Grebbin for his help with conducting the experiment. Financial support by the Young Investigator Group ‘‘Emotions in Markets’’, funded by Karlsruhe Institute of Technology, is gratefully acknowledged. Appendix A. Supplementary data Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.econlet.2014.04.024.
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