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Theory and Decision

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05-03-2019

Individual vs. group decision-making: an experiment on dynamic choice under risk and ambiguity

Authors: Enrica Carbone, Konstantinos Georgalos, Gerardo Infante

Published in: Theory and Decision | Issue 1/2019

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Abstract

This paper focuses on the comparison of individual and group decision-making, in a stochastic inter-temporal problem in two decision environments, namely risk and ambiguity. Using a consumption/saving laboratory experiment, we investigate behaviour in four treatments: (1) individual choice under risk; (2) group choice under risk; (3) individual choice under ambiguity and (4) group choice under ambiguity. Comparing decisions within and between decision environments, we find an anti-symmetric pattern. While individuals are choosing on average closer to the theoretical optimal predictions, compared to groups in the risk treatments, groups tend to deviate less under ambiguity. Within decision environments, individuals deviate more when they choose under ambiguity, while groups are better planners under ambiguity rather than under risk. Our results extend the often observed pattern of individuals (groups) behaving more optimally under risk (ambiguity), to its dynamic dimension.

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See Etner et al. (2012) for a review of the theoretical models and Trautmann and van de Kuilen (2015) for a review of the experimental evidence.

For an extensive review of life-cycle experiments, see Duffy (2014).

The income generation process is described shortly.

Setting the discount rate equal to zero is not expected to have an impact on our results (see Carbone and Hey 2004, footnote 1).

The Ellsberg-type urns have been introduced in the literature by Ellsberg (1961) seminal paper. In this paper, he proposed two thoughts experiment with the scope to challenge the ”sure thing principle” of the Subjective Expected Utility model (Savage 1954) and to introduce non-neutral attitudes towards ambiguity. A significant number of experimental studies are making use of either the two-colour or the three-colour urn to introduce ambiguity in the lab.

This information was only provided during the risk treatments. During the ambiguity treatments, subjects obtained no information regarding the composition of the urn and thus, they were facing ambiguity. During the session they had the chance to observe draws from the urn and obtain information regarding the actual distribution.

Caballero (1990) shows that under the assumption of a CARA utility function, a closed-form solution for the optimal consumption can be derived. Nevertheless, an additional assumption requires that the decision-maker is fully aware of the underlying income stochastic process, condition which is not satisfied in the ambiguity treatments.

We elaborate on this issue later.

We are grateful to a careful referee for drawing our attention to this literature.

The theoretical foundations of the model are presented in Appendix A.

We assume that subjects are risk and ambiguity neutral with regard to monetary payoffs. Controlling for averse or loving attitudes towards risk and ambiguity would add two additional layers of complexity to the function mapping from consumption to monetary payoffs (Carbone and Duffy 2014). If one wants to control for attitudes towards risk and ambiguity, she needs to appropriately extend the experimental design with tasks that will perplex an already complicated decision task (see for example Hey and Dardanoni 1988). As our main objective is to understand the effects of ambiguity to saving decisions, we leave this for future work.

Klibanoff et al. (2005) smooth-ambiguity model provides a flexible specification to capture both FOPs and SOPs and there is also experimental evidence in support of this model (Conte and Hey 2013; Attanasi et al. 2014). Nevertheless, one needs to assume non-neutral ambiguity attitudes and particular belief updating rules.

The optimal solution and the subsequent econometric analysis were conducted using the R programming language (R Core Team 2013). The programs and the data are available upon request.

As Ballinger et al. (2003) and Feltovich and Ejebu (2014) notice, the no-borrowing constraint along with a positive third derivative of the utility function, imply motives for precautionary saving. Both conditions are satisfied in our experimental design.

During the experiment expressions like “income”, “wealth”, “consumption” or “utility” were carefully avoided.

Again, there was no explicit reference to decreasing marginal utility but to “increments at a decreasing rate”.

The software recorded all proposals. When members did not confirm a decision within three minutes, the computer would pick the last proposal of each member and then randomly choose one of those as representative of the group. This did not happen very frequently. We recorded 54 cases of “disagreement” out of 900 decisions (6\(\%\)). Preliminary regressions suggested that disagreement was not a significant regressor.

From the sample we excluded the observations of 1 subject in sequence 1 and 2 subjects in sequence 2 in the I-R treatment, 3 subjects in sequence 1 and 1 subject in both sequences in I-A, 2 subjects in sequence 2 and 1 subject in both sequences in G-R and 1 subject in sequence 1 in G-A. We verified that including in our sample the observations of the participants who although failed the rationality test, they left in their saving accounts less than 9 units, does not change quantitatively the results that we report below.

Individuals (groups) exhibit positive deviation of 4.32 (2.62) consumption units under risk and deviation of 2.56 (3.17) units under ambiguity.

We also conducted the regressions using the mean squared deviation from the conditional optimal as dependent variable. Although the results are magnified compared to those where absolute deviation has been used as the dependent variable, the qualitative results regarding the treatment effects remain the same. We report the results of these regressions in the supplementary material.

In the case, the group consisted of one male and one female member, this dummy variable takes the value 1.

Note that, since during the experiment there were actual draws from the urn, there was no way to implement the same income streams to all treatments.

I-R vs. G-R: \(p=0.780\); I-R vs. I-A: \(p=0.550\); I-A vs. G-A: \(p=0.300\); G-R vs. G-A: \(p=0.900\). All reported p-values were generated using pairwise \(\chi ^2\) tests.

Carbone and Hey (2004).

In our experimental design, this \(\tau \) may range from 1 (extreme myopic behaviour) to 15 (optimal behaviour).

I-R vs. G-R: \(p=0.452\); I-R vs. I-A: \(p=0.269\); I-A vs. G-A: \(p=0.620\); G-R vs. G-A: \(p=0.432\). All p-values reported were generated using rank-sum MWW tests for independent samples.

I-R: \(p=0.008\); G-R: \(p=0.330\); I-A: \(p=0.178\); G-A: \(p=0.743\). All reported p values were generated using rank-sum MWW tests for independent samples for the group treatments and signed-rank MWW tests for the individual ones.

The probability of Low income P(L) is defined as the residual \(P(L)=1-P(H)\).

The material referred to in the “Appendix” is the same for all sets of instructions and can be consulted in subsection 1 (Individual Decision-Making).

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Title: Individual vs. group decision-making: an experiment on dynamic choice under risk and ambiguity
Authors: Enrica Carbone
Konstantinos Georgalos
Gerardo Infante
Publication date: 05-03-2019
Publisher: Springer US
Published in: Theory and Decision / Issue 1/2019
Print ISSN: 0040-5833
Electronic ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-019-09694-8

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