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Journal of Economic Behavior & Organization 94 (2013) 183– 189

Contents lists available at ScienceDirect

Journal of Economic Behavior & Organization

j ourna l h om epa ge: w ww.elsev ier .com/ locate / jebo

igh stakes behavior with low payoffs: Inducing preferencesith Holt–Laury gambles

ohn Dickhauta, Daniel Houserb, Jason A. Aimonec,d,∗,orina Tilae, Cathleen Johnsonf

Economics and Accounting, Chapman University, One University Drive, Orange, CA 92866, USAInterdisciplinary Center for Economic Science, George Mason University, 3330 Washington Boulevard, Arlington, VA 22201, USAVirginia Tech Carilion Research Institute, Virginia Polytechnic Institute and State University, 2 Riverside Circle, Roanoke, VA 24016, USADepartment of Economics, Hankamer School of Business, Baylor University, Waco, TX 76798, USAEconomics, University of New York Tirana, Rruga Komuna e Parisit, Tirana, AlbaniaBASIS Independent Schools, Tucson, AZ, USA

a r t i c l e i n f o

rticle history:eceived 3 March 2012eceived in revised form 9 December 2012ccepted 22 March 2013vailable online 3 April 2013

EL classification:909181

eywords:isk

nducing preferencesigh-stakesxperiment

a b s t r a c t

Kahneman and Tversky (1979) argued that risky decisions in high stakes environmentscan be informed using questionnaires with hypothetical choices. Yet results by Holt andLaury (2002) suggest that questionnaire responses and decisions in hypothetical and lowmonetary payoff environments do not well predict decisions in higher monetary payoffenvironments. This raises the question of whether investigating decision making in highstakes environments requires using high stakes. Here we show that one can induce prefer-ences using the binary-lottery reward technique (e.g., Berg et al., 1986) in order to studyhigh-stakes decision making using low-stakes. In particular, we induce preferences suchthat decisions in a low-stakes environment reflect well the choices made in the high stakesenvironment of Holt and Laury (2002). This finding is of interest to anyone interested instudying high-stakes decision behavior without paying high stakes.

© 2013 Elsevier B.V. All rights reserved.

. Introduction

Many pressing economic issues, from financial system bailouts to asset market bubbles to CEO salaries, involve decisionsn high stakes environments. In order to test theories relevant to these environments one might need to wait for monthsor years) for the appropriate data to become available. If the situation is pressing, and advice is needed quickly, laboratoryxperiments are often recommended. Yet laboratory experiments, due to their reliance on typically relatively small pecuniaryewards, may be limited in their ability to study behavior in high stakes environments. Here, we argue that this limitation isot as severe as it might at first seem. Indeed, this paper demonstrates a preference-induction procedure (Berg et al., 1986,

enceforth BDDO) that allows researchers to study high-stakes behavior in a cost-effective low-stakes environment.

The role of stake-size has been long debated. For example, Kahneman and Tversky (1979) defend hypothetical choicesy arguing that subjects have no reason not to tell the truth. Also, Camerer and Hogarth (1999) argue that choices may

nvolve differential productive effort, which can affect what the experimenter observes. Even when choices involve dollars,

∗ Corresponding author. Tel.: +1 678 612 2904.E-mail address: jaimone@vtc.vt.edu (J.A. Aimone).

167-2681/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.jebo.2013.03.036

184 J. Dickhaut et al. / Journal of Economic Behavior & Organization 94 (2013) 183– 189

Table 1A. Holt–Laury paired lottery-choice decisions: low payout treatment.

Gamble A Gamble B(Safe) (Risky)

Chance of receiving2 dollars

Chance of receiving1.6 dollars

Chance of receiving3.85 dollars

Chance of receiving0.1 dollars

Decision 1 10% 90% 10% 90%Decision 2 20% 80% 20% 80%Decision 3 30% 70% 30% 70%Decision 4 40% 60% 40% 60%Decision 5 50% 50% 50% 50%Decision 6 60% 40% 60% 40%Decision 7 70% 30% 70% 30%Decision 8 80% 20% 80% 20%Decision 9 90% 10% 90% 10%Decision 10 100% 0% 100% 0%

B. Holt–Laury treatments

Treatment Gamble A Gamble BLow $2.00 $1.60 $3.85 $0.10x20 $40.00 $32.00 $77.00 $2.00x50 $100.00 $80.00 $192.50 $5.00x90 $180.00 $144.00 $346.50 $9.00Hypothetical x20a $40.00 $32.00 $77.00 $2.00

a

Hypothetical x50 $100.00 $80.00 $192.50 $5.00Hypothetical x90a $180.00 $144.00 $346.50 $9.00

a In the hypothetical treatments dollar amounts listed are hypothetical amounts only.

cognitive costs may lead to distortions from a subject’s true preferences. Camerer and Hogarth (1999) assert further thatexperiments using salient rewards do not overturned “anomalies” observed in hypothetical choice environments. Harrison(1994), on the other hand, argues that changing incentives affects choices in the Allais Paradox and also preference reversals.His observations may suggest concerns for experiments using small cash payments.

Responding to such concerns, Holt and Laury (2002) (henceforth, HL) conduct risk-elicitation games using high stakes.Their study focuses on a sequence of paired lottery comparisons under both hypothetical and real-dollar payments. Theyfind that choices under hypothetical payments do not vary with stake-size, while people display increasing risk aversion asreal dollar stakes increase. HL’s finding emphasizes the importance of salient rewards, but also leaves as an open concernwhether one can learn about high-stakes decision making using small-stakes environments. This concern is reinforced byexperiments reported by Fehr-Duda et al. (2010), which point to the importance of emotions in influencing high-stakesdecisions. Even so, if a utility function, such as HL’s power expo utility function, explains stake dependent behavior well, ourinducing procedure should be able to replicate the predictive power of that function, as we show is indeed the case.

Despite these concerns, this paper reports evidence that one can use low stakes experiments to produce choices thatwell-reflect decisions made in that same environment when stakes are much higher. In particular, we show that one caninduce preferences (Roth and Malouf, 1979 and BDDO) in such a way that high-stakes behavior is generated in a low-stakesenvironment.

We incorporate the inducing procedure of BDDO into the HL experimental design, thereby inducing the HL power-expoutility function. We study five treatments. The first four coincide with the four actual stakes treatments in HL: Low payouts,20x payouts, 50x payouts, and 90x payouts. Our replication of the HL subjects’ behavior demonstrates the feasibility ofaccurately inducing high stakes in a low stakes environment. The fifth treatment does not occur in HL, but predicts decisionsthat would occur with 180x the payouts of the HL low payoff treatment. This treatment demonstrates how the high stakesinducing technique can be used to explore behavior in novel environments previously too expensive to feasibly test. Werefer to our treatments as the DHATJ treatments within the tables and figures.1

2. Design

In Holt and Laury (2002), subjects in each treatment made ten decisions between two gambles (illustrated in Table 1a.)One gamble was a “safe” gamble with a small difference between the two possible payouts, while the other was “riskier”with a higher difference between payoffs. As seen in the table, HL’s seven treatments included four levels of increasing

actual stake sizes and three corresponding hypothetical high stakes treatments. In the hypothetical treatments subjects’instructions asked what they would do in the event they faced the decisions in an actual high stakes environment. Subjectsreceived payment based on one randomly selected draw from their ten decisions.

1 The supplemental information contains instructions, and further experimental design details.

J. Dickhaut et al. / Journal of Economic Behavior & Organization 94 (2013) 183– 189 185

Table 2DHATJ paired lottery-choice decisions: low payouts.

Option A Option B

Chance of receiving2 points

Chance of receiving1.6 points

Chance of receiving3.85 points

Chance of receiving0.1 points

Decision 1 10% 90% 10% 90%Decision 2 20% 80% 20% 80%Decision 3 30% 70% 30% 70%Decision 4 40% 60% 40% 60%Decision 5 50% 50% 50% 50%Decision 6 60% 40% 60% 40%Decision 7 70% 30% 70% 30%Decision 8 80% 20% 80% 20%

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Decision 9 90% 10% 90% 10%Decision 10 100% 0% 100% 0%

Our goal is to generate high-stakes behavior in a low-stakes environment. To do this, we incorporate the inducing proce-ure of Berg et al. (1986) into the HL experiment design. The inducing procedure requires the utility function to be specified

n advance2. Since we are attempting to replicate HL, and because they estimated a power-expo utility function (see Eq. (1),elow), we attempt to induce behavior consistent with the power-expo utility function under their estimated parameteralues.3

U(X) = 1 − exp(−ax1−r)∝ (1)

.1. Stage 1

In Stage 1, subjects make a decision between two lotteries: A and B. The Stage 1 decision is the subject’s only decisionn the experiment. Subjects receive points from the outcomes of their chosen lotteries instead of cash (as in HL). Table 2escribes each of the ten decisions. As seen in the Table, the first decision includes a 10% (90%) chance of the high (low)umber of points. For each subsequent decision, the chance increases (decreases) by 10 percentage points. After a subjectecides A or B they roll a ten-sided die that determines the number of points they earn. In particular, a roll of 1 in the firstecision means the subject receives the high number of points, a 1 or 2 in the second decision means they receive the highumber of points, a 1, 2, or 3 in the third, and so on.

Table 3 details the number of points associated with the high and low payouts of each A and B lottery in each of the fivereatments. The table indicates that the points earned in each of our treatments coincide precisely with the dollars earnedn the corresponding HL treatment (third and seventh columns.) For example a subject who earned 40 dollars in the HLreatment would earn 40 points in our design.

.2. Stage 2

The conversion of the points earned in Stage 1 into cash earnings occurs in stage 2. The points a subject earned in Stage become Bernoulli probabilities of winning a $2.50 prize (greater points implies greater probability of winning the prize.)able 3 details the probability with which a subject wins the prize for each of the possible number of points earned in eachreatment (fourth and eighth columns.)

The mapping of points into probabilities is where the key to the inducing procedure.4 As seen in Table 3, as stake sizencreases the marginal value of additional points changes, and it is this incentive that can shape behavior in low-stakesnvironments so that it resembles high-stakes decision-making.

Subjects roll a 100-sided die on their desk to determine whether they win the prize. For example, when a subject has a% chance of the prize, if the die lands with sides 1 or 2 facing up they win the prize, otherwise they do not. Likewise, if aubject has a 73% chance of the prize, with any side between (and including) 1 and 73 facing up, they win the prize. After

aving rolled the 100-sided die the subject knows that either they have earned $2.50 or earned nothing at all. Note that theie roll is monitored and cheating is not possible (see, e.g., Houser et al. (2012) for a study of a die roll game where cheatingan occur).

2 A clear limitation to inducing preferences is that, in so doing, one cannot draw inferences about the induced preferences. Instead, one induces preferenceso learn about other parts of the economic environment thought to be affected by such preferences, for example, strategic behavior or the effectiveness ofnstitutional rules governing transactions.

3 HL estimated parameter values are as follows: r=0.269 (0.017), and �=0.029 (0.0025), where standard errors are in parentheses.4 See the appendix for the exact transformations of points to probability for each treatment and details on the BDDO equations.

186 J. Dickhaut et al. / Journal of Economic Behavior & Organization 94 (2013) 183– 189

Table 3Holt-Laury and DHATJ treatment comparison.

Treatment Choice Dollars in HL/points in DHATJ Chance of $2.50 prize in DHATJ

Low

A 2 61%1.6 52%

B 3.85 97%0.1 7%

20

A 40 65%32 56%

B 77 97%2 2%

50

A 100 73%80 64%

B 192.5 99%5 1%

90

A 180 79%144 71%

B 346.5 99%9 1%

180

A 360 89%288 83%

B 693 100%18 1%

Note that in HL (DHATJ) chance of receiving the high number of dollars (points) for choice A or B increases by round starting with 10%, in round 1, andincreasing to 100%, in round 10.

2.3. Procedures

Upon arriving to the laboratory, the experimenter directs subjects to the appropriate room where they read the instruc-tions in private and listen to the instructions read aloud by the experimenter. The instructions include paid practice toensure subjects understand the procedures. Following the instructions, subjects make their first decision between lotteriesA and B. Subjects then roll a ten-sided die at their desk (with the monitor watching) to determine the number of points theyreceive, which is recorded. The subject follows that roll, immediately, with the roll of a 100-sided die to determine if theywin a $2.50 prize. This procedure repeats for each of the ten HL decisions, meaning a subject can earn a maximum of $25regardless of treatment.) Subjects receive an additional seven dollars for arriving to the laboratory on time, and receive theircash payments immediately prior to leaving the laboratory.

3. Results

We report data from 98 subjects in five treatments: 19 in the Low treatment, 20 in the x20 treatment, 17 in the x50, 21in the x90, and 21 in the x180. Similar numbers to the sample sizes used by HL (19 and 18 in their x50 and x90 treatmentsrespectively.)

Result 1. The distribution of safe choices (choice A) from our choice data based on induced preferences is statisticallyindistinguishable from the HL distribution of safe choices for each of the four HL real stakes treatments.

As the four graphs in Fig. 1 show, the distribution of safe choices in each of our induced preference treatments followsthat of the distribution of safe choices in HL. We find no significant difference between these two distributions in any of thefour treatments with either Kolmogorov–Smirnov two-tailed tests or Kruskal–Wallis two-tailed tests (p > .10 in all cases.)

Failure to reject the null hypothesis when comparing behavior between our induced high stakes and real high stakes isinitial evidence that the inducing procedure succeeded. However, it is important to show that differences if present couldin principle be discovered with our sample size and that the inability to reject the null hypothesis is not due to insufficientstatistical power. In order to demonstrate this, we next compare our data to the HL hypothetical high stakes treatments,where we expect to find both economically as well as statistically significant differences in behavior.

Result 2. The distribution of safe choices from our choice data based on induced preferences is statistically different fromthe HL distribution of safe choices for each of the three HL hypothetical high stakes treatments.

Kolmogorov–Smirnov and Kruskal–Wallis tests show significant differences at standard levels for all three treatments.For the Kolmogorov–Smirnov tests: p = 0.046, p = 0.087, and p = 0.016 for the x20, x50, and x90 treatments respectively. Forthe Kruskal–Wallis: p = 0.032, p = 0.006, p = 0.006 for these same conditions, respectively.

J. Dickhaut et al. / Journal of Economic Behavior & Organization 94 (2013) 183– 189 187

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Fig. 1. HL vs. DHATJ Comparison.

esult 3. The actual distribution of safe choices (choice A) with induced preferences, under simulated high stakes that are80 times that of HL’s low stakes, follows the distribution of safe choices predicted by the HL power-expo utility function.

Fig. 2 shows what the predicted noisy distribution of decisions would be (using HL’s power-expo function) under anctual 180x stakes environment compared to the actual decisions of subjects in our experiment under an induced 180xtakes environment. A chi-squared goodness-of-fit test shows no significant difference between these two distributionsp > 0.25).

Overall, we see an increasing trend in risk aversion as stake sizes increase in our induced environment, number of safehoices (Cuzick two-tailed trend test, p = 0.000), just as HL saw an increase in risk aversion as stake sizes rise in their realtakes (p = 0.000) but not as their hypothetical stakes rise (p = 0.461).

The non-parametric tests used in the results above provide support for our hypotheses. Parametric analysis, throughse of maximum likelihood estimation, can provide further evidence that we are inducing high stakes behavior. The moreowerful nature of the parametric analysis not only makes it easier to find a difference between our data and the HL data ifne exists, but also uses the information that each of the ten decisions a subject makes are correlated. The non-parametric

ests do not incorporate the correlation between the decisions of each subject.

We reach result 4, below, by calculating the maximum likelihood estimates (using the methods of Harrison, 2008) of HL’sower-expo utility parameters. We slightly modify HL’s original equations by including parameters �2, r2, and ˛2, which

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Fig. 2. DHATJ induced high stakes 180x HL.

188 J. Dickhaut et al. / Journal of Economic Behavior & Organization 94 (2013) 183– 189

Table 4Cost comparison.

Expected cost per observationif paying for 1 of 10 choices

Expected cost per observationif paying for all 10 choices

HL DHATJ HL DHATJ

Low $2.41 $1.67 $24.87 $17.06x20 $47.18 $1.71 $486.18 $17.44x50 $113.73 $1.85 $1168.98 $18.75x90 $204.71 $1.97 $2104.16 $19.85

x180 $388.17 $2.19 $3974.67 $21.99

Expected costs calculated by power-expo utility maximizing behavior by all agents.

act to capture any differences between our data and HL’s (ı is a dummy variable equal to one for our data and zero for HL’sdata.) If induction is successful, �2, r2, and ˛2 should be zero.

Pr(choose option A) = U1/(�1+�2ı)A

U1/(�1+�2ı)A + U1/(�1+�2ı)

B

(2)

U(x) = 1 − exp(−(˛1 + ˛2ı)x1−(r1+r2ı))˛1 + ˛2ı

(3)

Result 4. The noise, �, relative risk aversion, r, and absolute risk aversion, ˛, parameters calculated from the induced highstakes sessions’ decisions do not differ significantly from the parameters calculated from the HL actual high stakes session’sdecisions.

As summarized in Result 4, maximum likelihood estimations of �2, r2, and ˛2 each are not significantly different fromzero (p = .267, p = .111, and p = .472 respectively). Thus, our estimates (�1 = 0.134 (.009), r1 = 0.267 (.0255), and ˛1 = 0.029(0.004); log-pseudolikelihood −1651.7) do not differ significantly from what HL originally reported (�1 = 0.134 (0.0046),r1 = 0.269 (0.017), and ˛1 = 0.029 (0.0025); S.E. in parentheses).

Result 5. The use of induced high stakes environments in experiments is less costly than the use of actual high stakesenvironments.

Table 4 displays Result 5 in greater detail. As seen, the expected cost differences are substantial. In the induced stakesenvironment, experimenters can pay subjects for all ten-lottery decisions, without wealth effects concerns, due to expectedutility maximization (see BDDO). This increases the saliency of subject decisions. As a comparison, our induced stakesenvironment has an expected cost per observation of about 22 dollars in the 180x stakes treatment when paying for all tendecisions, while paying for one decision in an actual 180x stakes environment has an expected cost of over 388 dollars perobservation.

4. Conclusions

The importance of salient rewards, long emphasized by Vernon Smith and formalized with his seminal “Induced ValueTheory” (Smith, 1976), is a defining feature of experimental economics. It separates experimental economics research frommuch related work on decision making occurring in other social science and business school environments. Unfortunately,some may misconstrue this emphasis to entail an inability to use laboratory investigations to study behavior and decisionsin very high stakes environments, unless a large amount of money is available to spend. Here we have argued that thislimitation is not as severe as it might at first seem. In particular, we have demonstrated that using the “induced preference”procedure (e.g., BDDO) one is able to generate high-stakes behavior using a low-stakes environment.

We focused on the behavior reported by HL. They found that risk attitudes varied systematically with the magnitude ofpayoffs. Moreover, they estimated a utility function that captured the relation between choice and size of payoff. This paperspecifically showed that, in a low-stakes environment, the BDDO procedure can be used to generate choices in this risk taskthat follow the same patterns HL found in their high-stakes conditions.

Economically important decisions under risk often occur in high-stakes environments, lending special importance toour study. In future research we intend to induce preferences within game and market environments. Experimenterscan implement a preference induction procedure in any environment where the appropriate data exist to inform par-ticipant preferences (e.g., research inference of trader risk-aversion from financial market data). Further development ofpreference inducement would be valuable; it holds the promise of becoming a key tool for the empirical study of newmechanisms.

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J. Dickhaut et al. / Journal of Economic Behavior & Organization 94 (2013) 183– 189 189

ppendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jebo.013.03.036.

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ehr-Duda, H., Bruhin, A., Epper, T., Schubert, R., 2010. Rationality on the rise: why relative risk aversion increases with stake size. Journal of Risk andUncertainty 40, 147–180.

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