\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,english]{babel}



\usepackage{float}








\begin{document}

\title{An experimental approach to examine behavior and brain activity during
decision-making under risk as compared to ambiguity}



\author[1]{Benjamin Albrecht}%
\author[1]{Johannes Hewig}%
\author[2]{Patrick Mussel}%
\author[3]{Isabell Welpe}%
\author[4]{Angela Stanton}%
\author[5]{Wolfgang Miltner}%
\affil[1]{Julius Maximilians University Würzburg}%
\affil[2]{Freie Universität Berlin}%
\affil[3]{Technische Universität München}%
\affil[4]{Affiliation not available}%
\affil[5]{Friedrich Schiller University Jena}%


\vspace{-1em}



  
  \date{June 13, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Neural correlates of decisions under risk and under ambiguity have been
examined for several decades. In the current study, we focus on a
neglected aspect that is a potential confounding of the average risk of
alternatives in a trial, the average magnitude of the outcomes, and the
difference in risk between the two alternatives. We present an
experimental approach to solve this problem here and explicitly separate
risk and ambiguity. In the present fMRI-study with 20 participants, we
created different levels of risk and ambiguity to investigate their
effects on behavior and brain activation. In a first experimental block,
decisions with mixed-risk options (one high-risk option paired with one
low-risk option) were compared to decisions with two high-risk or two
low-risk options in terms of the effects on decision-making and neural
activity. The second block consisted of the same risk levels crossed
with high and low ambiguity by withholding information about the
probabilities of the outcomes. During mixed-risk trials participants
made cautious decision significantly more often. This effect was
strongest during mixed trials with high ambiguity in the second block.
In addition, risk behavior of subjects was correlated with the
subjective importance of the amount of potential monetary losses or wins
and the related probabilities. The fMRI results revealed activation of
the dorsal anterior cingulate cortex (dACC), the insula, and the
orbitofrontal cortex (OFC) during mixed risk trials without ambiguity.
In contrast, activation of the amygdala was specifically present during
mixed-risk trials with high ambiguity.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Decision-making is influenced by the value of outcomes, the probability
of outcomes, and the ambiguity or risk of outcomes (e.g. Kahneman et
al., 1997; Kahneman \& Tversky, 1979). According to a classic
distinction between ambiguity and risk derived from Knight (e.g. Chen \&
Epstein, 2002; Huettel et al., 2006; Knight, 1921; Krain et al., 2006),
a decision situation is defined risky when the actual outcome of the
decision between options is unknown, but the probability distribution
for different outcomes is known. In contrast, a decision is ambiguous
when the actual outcome and the probability distribution of potential
outcomes are both unknown (Ellsberg, 1961; Knight, 1921). In all these
cases, preferences of decision options are defined according to the
chance distributions of options, i.e., according to their expected value
(EV). For risk, these chances are taken to be objective, whereas for
uncertainty, they are subjective. Furthermore, the size of the risk of
options can be described by the spread of outcomes (Rothschild \&
Stiglitz, 1970), and the size of ambiguity by the lack of information
(Ellsberg, 1961; Knight, 1921). The size of risk and ambiguity reduce
the utility of an option. Accordingly, the goal of the present study was
to vary experimentally both risk and ambiguity in order to compare them
on the behavioral and on the neural level. Usually, people are even more
averse to ambiguous options than to risky options supposedly also
indicating a reduction in subjective utility.

During the past decades, many different studies investigated behavior of
people under risk and ambiguity. Many different experimental approaches
were used, which differed in paradigms and parameters, e. g. various
kinds of gambles, known and risky options, or risky options only,
gambles with possible gains and losses or only with gains, and special
tasks like the Iowa Gambling Task (Bechara et al., 1997, 2005; Li et
al., 2010), Blackjack (Hewig et al., 2010; Hewig et al., 2009; Hewig et
al., 2007; Hewig et al., 2008) or the Balloon Analogue Risk Task (Lejuez
et al., 2002; Mussel et al., 2015; Rao et al., 2008). Recent studies
also used functional magnetic resonance imaging (fMRI) to identify blood
oxygen level dependent (BOLD) responses to risky and ambiguous
situations in order to reveal its neural underpinnings (e.g. Bach et
al., 2009; Hsu et al., 2005; Smith et al., 2002; Tobler et al., 2007).
Some of these studies found activations of brain areas associated with
EV, like the ventral striatum (Breiter et al., 2001; Knutson et al.,
2001; Knutson et al., 2005; Tobler et al., 2007; Yacubian et al., 2006)
or the anterior cingulate cortex (Brown \& Braver, 2005, 2007, 2008;
Kuhnen \& Knutson, 2005). Others compared ambiguous and risky
decision-making and showed that ambiguous decision-making is related to
increased neural activity in the dorsolateral prefrontal cortex (DLPFC),
amygdala, posterior inferior frontal cortex, and posterior parietal
cortex (e.g. Bach et al., 2009; Hsu et al., 2005), whereas risky
decision-making is related to activity in OFC, ACC, and parietal cortex
(e.g. Krain et al., 2006; Platt \& Huettel, 2008; Tobler et al., 2007).
These differences may indicate that ambiguity imposes not merely more
intense uncertainty but might even represent a different kind of
uncertainty, which is based on a different neural processing by
different neural sources. To differentiate between risky and ambiguous
decisions, the magnitude, the probability, and the EV of decision
options have to be defined as independent experimental variables and the
functional neural structures have to be described that account for their
differential phenomenological cognitive and behavioral functions.

To master such challenges, Tom, Fox, Trepel, and Poldrack (2007)
investigated risky gambles using a parametric experimental design to
assess BOLD responses related to risk and loss aversion. The network
functional relevant for gains included regions in dorsal and ventral
striatum, ventromedial prefrontal cortex (VMPFC), ventrolateral
prefrontal cortex (VLPFC), ACC, OFC, and other dopaminergic structures
whereas structures relevant for losses included the striatum, the VMPFC,
ventral ACC, and the medial OFC. In relation to loss aversion, they
showed activity in bilateral ventral striatum, bilateral lateral and
superior PFC (pre-supplementary motor area), and right inferior parietal
cortex. The authors termed this pattern a neural system of loss
aversion.

In a subsequent study also using parametric analyses, Canessa et al.
(2013) replicated activations in regions in the left ventral striatum
and in the posterior frontomedial cortex in response to gains and
losses. In addition, they found an interesting differential pattern of
activation between losses and gains of the right posterior insula and
the parietal operculum. These areas showed greater activation to
increasing losses than deactivation to gains. An opposite pattern was
found in the left ventral striatum and the frontomedial cortex, which
showed larger loss-related deactivation than gain-related activation.
Furthermore, they identified a loss-related network involving the right
amygdala, putamen, and portions of the right posterior insula,
indicating that the neural system of loss aversion involves the
amygdala, thalamus, striatum, and posterior insula.

Based on these studies using fMRI we expected risk-related activity in
dorsal and ventral striatum, ventromedial prefrontal cortex (VMPFC),
ventrolateral prefrontal cortex (VLPFC), dACC (mainly BA 32), OFC,
parahippocampus, inferior frontal gyrus IFG (BA 47), SMA (BA 6),
frontomedial cortex, and insular cortex in mixed-risk trials for the
parameter ``wins''. In contrast, for the parameter ''losses'' we
expected activity in insula, parietal operculum, amygdala, thalamus,
striatum (in particular ventral), VMPFC, ventral ACC, the medial OFC,
bilateral lateral and superior PFC (pre-supplementary motor area), and
right inferior parietal cortex. We further expected ambiguity-related
activity in dorsolateral prefrontal cortex (DLPFC), amygdala, posterior
inferior frontal cortex, and posterior parietal cortex. Since our
experimental design eliminated the confounding influence of average risk
levels between our experimental conditions, the remaining regions are
considered to relate specifically to the risk difference in mixed
gambles.

In the gambling paradigm used here, the probability of outcomes was
known to the subjects to elicit decisions under risk in one part of the
experiment, and in the other part of the experiment the probability of
outcomes was unknown in order to induce decisions under ambiguity. We
completely avoided fully known outcomes, because risk and ambiguity may
appear to be more similar in their presence because they both entail
some uncertainty as compared to known outcomes. Instead, we varied both
risk and ambiguity systematically to contrast and compare them to each
other. The degree of risk was varied experimentally by using three
different combinations of high- and low-risk options in each trial of a
two-choice decision-making task. High-risk gambles comprised two
high-risk options, low-risk gambles comprised two low-risk options and
mixed-risk gambles comprised a high- and a low-risk option. EV was
always the same in each gamble. This enabled us to experimentally
separate influences of the difference in risk from the overall level of
risk or EV and from the overall level or magnitude of gains and losses.
Previous studies used known outcomes versus risky gambles, or known
outcomes versus ambiguous gambles. Thus, for each decision between two
gambles the average risk level of both alternatives (high/low) is
confounded with the risk difference between the two alternatives. For
example, many studies use a known outcome option and a risky option. The
risky option can vary in its variance of outcomes. Thus, the average
risk of both alternatives and the average magnitude of the outcomes are
confounded with the difference in risk between the two alternatives. A
trial with a known option and a low-risk option has lower overall risk,
lower difference in risk between the options, and lower outcome
magnitudes. Whereas a trial with a known option and a high-risk option
has higher overall risk, higher difference in risk, and higher outcome
magnitudes. Accordingly, a difference in brain activation in the
comparison of these two kinds of trials may be due to any of these three
differences between trials. For this reason, we combined 2 kinds of
options: high-risk options (larger variance in outcomes) and low-risk
options (smaller variance in outcomes). Thus, we created a high-risk
condition with two high-risk alternatives, a low-risk condition with two
low-risk alternatives and a mixed risk condition with a low and a
high-risk option. If we now compare brain activity between the mixed
condition and the average of the two other conditions, we may
disentangle risk level and risk difference.

We expected that minimizing the risk is primarily triggered by the
difference of outcome variance between the two options, which should
lead to the strongest risk aversive effects in mixed gambles. We further
varied the degree of ambiguity experimentally in another block of trials
by using one condition without any information about the probability
(high ambiguity) as compared to another condition where we provided a
range of probabilities for each outcome (low ambiguity). In a narrow
sense of decision-making under risk, where all information is available,
the latter trials with high ambiguity are not decision-making under
risk. However, according to the definition of the degree of risk with
the spread or variance of outcomes these trials can still be recognized
in terms of higher or lower risk, since the magnitude of the difference
between the potential wins and losses (variance of outcomes) is a
function of risk level even in the absence of probability information.
This allows a systematic comparison of decision-making under risk with
decision-making under ambiguity across experimental blocks keeping all
other aspects of the task comparable.

In the present study, we aimed to clarify and extend previous findings
by using mixed-risk trials with and without ambiguity and compared them
to high- and low-risk trials. Furthermore, we aimed to compare risk and
ambiguity directly with each other. Thus, the target condition is as
similar as possible to the control conditions. We focused on the moment
of decision-making in our analyses. Following previous research (Canessa
et al., 2013; Tom et al., 2007), we also used a parametric fMRI design
to separate effects that are due to potential gains from those of
potential losses. Importantly, previous research focused on the idea of
neural loss aversion, which is related to the different degree of brain
activity in response to gains and losses, and supposedly drives cautious
decision-making under risk. In addition, Vorhold and colleagues (2007)
showed that subjective ratings of risk are moderating decision-making.
We therefore also assessed ratings of riskiness and reports about
reasons of individual decision-making.

\textbf{Methods}

\textbf{Participants}

The study was approved by the local ethics committee. 20 right-handed
volunteers participated in this study (10 females and 10 males; mean
age: 24 years, SD = 3.1 years, range 19 -- 32 years). They were paid 6
Euro per hour for participation and could earn an extra bonus depending
on their success of gambling. Every participant gave written informed
consent for participation after receiving verbal and written information
about the purpose and course of the experiment and after examination by
a physician whether any risk would not allow the MRI application.
Following the MRI recording, participants completed several
questionnaires (see below). For every participant, a log-file recorded
during the time points when a trial started and the latency of choosing
an option. Based on this information, the first-level analyses of
imaging data were conducted, as described below. In addition, log-files
of all three risk levels included information on the decisions of
participants and their choice of riskier or less riskier options.

\textbf{Procedure}

In the MRI scanner, participants performed a two-choice decision-making
task by deciding between two options (see Figure 1). Each option had a
probability \emph{p} (between 5\% and 95\%) for winning and a
corresponding probability 1-\emph{p} for losing. The EV of all options
was kept constant at 0.10 Euro. Each option was either of high or low
risk according to the variance of the monetary outcome per option (as
compared to all options used in the study). A trial was defined as
high-risk trial if both alternatives were high-risk options (both
gambles with large variance in outcome). The range of wins was 15 to 100
Cents and that of losses between -15 to -100 Cents with a difference
between winning and losing outcome of 100 and 200 Cents for high-risk
options. A low-risk trial consisted of two low-risk options, which had a
low variance in outcome. The range of wins here was 11 to 57 Cents and
that for losses between -5 and -60 Cents and the difference between the
winning and losing option ranged between 16 and 75 Cents. Finally, in
mixed-risk trials one option of high risk was paired with one option of
low risk.

The task included three scenario blocks of 99 trials each (see
supplementary Table 4). In the scenario block with pure risk options
every trial had one of the aforementioned risk levels (33 trials each).
A second scenario block consisted of 99 trials with these three
different risk levels transformed into trials with high or low ambiguity
where the probabilities \emph{p} and 1-\emph{p} were either unknown
(high ambiguity, 48 trials, see Figure 1 for an example) or given as a
range of the probabilities (e.g. between 30\% and 50\%; low ambiguity,
51 trials, presented as ``30-50\%'') in half of the trials,
respectively. In the latter case, the range of outcomes was presented
and indicated the level of risk to participants. And finally, in a third
scenario block, risk and ambiguity trials were mixed (results for this
block will be presented elsewhere). The order of the three scenario
blocks was counterbalanced across participants.

Every trial started with an initial fixation cross that was presented on
a monitor screen for 525 ms plus an individual period for each trial
varying between 10 and 25 ms (timeline shown in Figure 1a). After this
initial phase, the trial options to choose were presented on the screen
for up to 3000 ms and participants were requested to decide for one of
the options. If participants did not choose during this time period they
lost the gamble. Then visual feedback with a colored frame around the
chosen option was presented upon button press until 3000 ms elapsed
since presentation of the options screen. Subsequently a screen informed
whether they won or lost the gamble (for additional 1250 ms). Finally, a
last screen showed the total amount of money they won so far (for 1250
ms).

\textbf{fMRI Data Acquisition and Analysis}

Brain activation of participants was measured using a 3 Tesla magnetic
resonance scanner (Magnetom Trio A, Tim System, Siemens Medical Systems;
Erlangen, Germany). For the functional analysis, 110 volumes of
echo-planar-images were acquired using a T2*-weighted sequence (TE = 30
ms, flip angle = 90\selectlanguage{ngerman}°, matrix = 64 x 64, FOV = 192 mm, TR = 2.7 s). Each
volume comprised 40 axial slices with 3 mm thickness and an interslice
space of one millimeter creating a voxel size of 3 x 3 x 3 mm. In
addition, an anatomical scan with high resolution was acquired using a
T1-weighted MPRAGE sequence with a voxel size of 1 x 1 x 1 mm. For data
preprocessing, the first four volumes were discarded to secure
steady-state tissue magnetization. Preprocessing and data analysis was
performed using the software SPM8 (Wellcome Trust Centre for
Neuroimaging, University College London). Data were realigned to
minimize effects of body movement. Realigned data then were normalized
and transposed to the Talairach space (Talairach and Tournoux, 1988)
using the anatomical image that was co-registered with a T1-template and
the mean image of the realigned data. After normalization, the images
were smoothed with a Gaussian kernel of 8 mm full width at half-minimum
(FWHM). Preprocessed data were used for first level analysis where the
onset and duration of the decision-screens were taken to assess the
activation during the three different stimulus conditions (high, low,
and mixed risk). In addition, we added two parameters in the parametric
SPM model for every stimulus condition for the potential gain and the
potential loss. These parameters were calculated as the sum of the
potential wins the sum of potential losses of these two options. For the
first-level analysis, contrasts of predictor estimates (beta-weights)
were defined for each risk level (i.e.: high risk, mixed risk, and low
risk). The expected blood oxygen level-dependent (BOLD) signal changes
were modeled using a canonical hemodynamic response function. The
resulting contrast images of each participant were used for second-level
ANOVA calculations (group level). At the end we got group level
predictor estimates (beta-weights) which we used for calculating
contrasts for comparison between risk and ambiguity, mixed-risk trials
in comparison to high- and low-risk trials with and without ambiguity
and for the parametrical results of potential gains or losses. The
analysis focused on the time of the decision-making. Results of the
analysis within each Region of Interest (ROI) were regarded as
statistically significant when t-values were \textless{} 0.001
uncorrected. ROIs were defined using the Talairach client software
(Talairach Project, International Consortium for Brain Mapping). In
order to prevent false positive activations, results are reported only
for brain areas which showed z-value higher than 3.09 -- i.e., p
\textless{} 0.001, uncorrected -- and a volume greater than 180 mm³ -
i.e., five voxels with a spatial resolution of 3 x 3 x 4 mm (here we
opted for four millimeters, because the thickness of measured slices was
three millimeter plus a distance between slices of one millimeter).

\textbf{Questionnaires}

Questionnaires presented after the fMRI experiment assessed the
perceived risk of options and difficulty of decisions using a rating
scale ranging from 1 (no difficulty) to 9 (very difficult). Participants
were further asked to rate how much they decided between options as a
function of the amount of potential gain or potential loss of the choice
and how much they felt influenced while choosing by the probability of
wins and losses of their decision options. For all of these rating
questions, we presented examples taken from the real experiment, which
represented each of the experimental conditions respectively (one sample
trial for each condition to remind participant of the condition). We
realized all levels of risk and ambiguity; the ratings were made
separately for each experimental trial that represented each condition.

We also included several personality questionnaires (results will be
presented elsewhere) to assess trait-like differences related to
decision-making (Budner, 1962; Carver \& White, 1994; McLain, 2009;
Zuckerman, 1996).

\textbf{Data Analyses}

For the analyses of behavioral decision-making data, we used a general
linear model. Risk (three levels: low, high, mixed risk) served as
within-subject factor and gender as between-subjects factor for
pure-risk trials. For ambiguous trials, the three levels of risk were
fully crossed with either low ambiguity or high ambiguity. Accordingly,
ambiguity served as a second within-subject factor with these two levels
of ambiguity. In addition, an ANOVA comprising both trial types was used
to examine differences between no ambiguity (pure-risk trials) and low
and high ambiguity (ambiguous trials).

We used Huynh-Feldt corrections, when the assumption of sphericity was
violated. Follow-up Helmert-contrasts and t-tests were conducted to
identify the direction of the effects and tested one-tailed for
evaluating directed hypotheses. Significance level was p=.05, and only
significant p-values are reported.

\textbf{Results}

\textbf{Behavioral results}

For the pure-risk trials (low-risk, high-risk, mixed-risk) the ANOVA
revealed a main effect of risk (\emph{F} (2,36) = 5.98, \emph{p} = .007,
eta² = .25, epsilon = .92) on the percentage of choices of the option
with higher variance of the outcomes (higher risk). Follow-up Helmert
contrasts showed the significantly most cautious decisions in the
mixed-risk condition as expected compared to the other two conditions (p
= .016; Mean of mixed (M) = .35, SD = .16 and Mhigh = .44 and Mlow =
.41, see Figure 1b). In addition, the percentage of cautious decisions
was not significantly different between the low-risk and high-risk
condition. There were no further significant effects.

For ambiguous trials, the ANOVA revealed a main effect for risk (F(2,36)
= 12.86, p \textless{} .001, eta² = .42, epsilon = .86). It is important
to note here that the spread or variance of outcomes was the same as in
block 1 and defined the factor risk. As for the pure-risk trials
follow-up Helmert contrasts showed the significantly most cautious
decisions in the mixed-risk condition (\emph{p} = .001, M = .33, SD =
.18). Again, the percentage of cautious decisions was not significantly
different between high and low-risk conditions. All other main effects
and interactions were not significant.

Taken together, for both, the risk and the ambiguity block, mixed-risk
options led to the highest percentage of cautious decisions. A combined
analysis of risk and ambiguity blocks revealed a significant main effect
of risk (F(2,36) = 15.7, p \textless{} .001, eta² = .47, epsilon = .84)
and an interaction of risk with ambiguity (F(2,36) = 3.03, p = .023,
eta² = .14, epsilon = .99). Post-hoc Helmert-contrasts showed that the
interaction was due to more cautious decisions under high ambiguity for
the mixed-risk condition compared to high-risk and low-risk trials in
the conditions of pure risk and low ambiguity (p=.008). The condition
with mixed-risk and high ambiguity led to the most cautious decisions (M
= .30, SD = .18). Accordingly, high ambiguity further increased the
risk-minimizing behavior in the context of mixed risk. Further,
participants were relatively less cautious in the high-risk condition as
compared to the low-risk condition under low ambiguity as compared to
pure risk (p=.036). No other effects were significant.

\textbf{Correlations with ratings}

Participants' ratings about how much the potential amount of loss or
gain or the respective probabilities influenced their decisions were
correlated with behavioral decision-making (i.e., the relative choice of
high-risk alternative). Results showed that subjects decided riskier if
their choice depended more on the amount (\emph{r} = .55, \emph{p} =
.012) and on the probability of the gain (\emph{r} = .47, \emph{p} =
.042) for pure risk decisions. In addition, participants acted more
cautious if they their decision was more based on the variance of
potential losses in an ambiguous situation (\emph{r} = -.46, \emph{p} =
.040, all other tests not significant).

\textbf{Imaging data results}

\emph{Condition-based non-parametric analysis.}

For the neuronal analyses we focused on mixed-risk trials with and
without ambiguity in comparison to high- and low-risk trials. During
mixed-risk trials as compared to high- and low-risk trials in the
pure-risk block significant activation was observed in the left
parahippocampal gyrus (Table 1, Figure 2). In the ambiguity block
activations were present in the right inferior frontal gyrus IFG (BA 47)
for mixed-risk trials with high ambiguity compared to high- and low-risk
trials with high ambiguity (Table 2, Figure 3). For the same contrast
with low ambiguity, activity in the left supplementary motor area (BA 6)
and in the left posterior insula was significant (Table 2, Figure 4).

The contrast high versus low ambiguity showed a significant BOLD effect
in the mixed-risk condition. High compared to low ambiguity was
correlated with activations in the right inferior parietal cortex and
the left DLPFC in BA 9 (Table 2, Figure 5). As noted above, mixed-risk
trials under high ambiguity showed the highest amount of low-risk
decisions on the behavioral level.

\emph{Parametric analysis.}

The parametric design analysis, with all the magnitudes of possible
gains and losses included as parameters for each trial, revealed three
main results: First, when examining the influence of wins, the dorsal
ACC was significantly more activated during mixed-risk trials than in
high- or low-risk trials (Table 3, Figure 6). Second, losses
significantly activated the insular cortex (BA 13) and parts of the
lateral OFC only during mixed-risk trials but not during high- or
low-risk trials (Table 3, Figure 7). Third, for ambiguous trials,
significant activation was found in the amygdala during mixed-risk
trials with high ambiguity but not in response to mixed-risk trials with
low ambiguity for the parameter magnitude of gains (Table 3, Figure 8).
For ambiguous trials we found no significant activation with respect to
the loss parameter.

\textbf{Discussion}

The present study on decision-making under risk and ambiguity
investigated the decisions of participants under different levels of
uncertainty. We aimed to contrast risk and ambiguity on the behavioral
and the neural level by experimentally varying these two types of
uncertainty. Subjects were exposed to three different levels of risk:
i.e., low, high, and mixed-risk and two levels of ambiguity: i.e. high
and low ambiguity. Probabilities and outcomes were composed such that
the expected value for all decisions was the same. Further, we defined
the different levels of risk based on a suggestions of Rothschild \&
Stiglitz (1970) as the spread of potential outcomes. On the behavioral
level, data confirmed classical effects of risk and ambiguity (see
Ellsberg, 1961; Kahneman et al., 1997; Kahneman \& Tversky, 1979;
Knight, 1921). Subjects behaved significantly more cautiously when they
had to decide between one high-risk option and one low-risk option. In
addition, we found an effect of ambiguity on decision-making. High
ambiguity -- i.e., during a condition where any probability information
was absent -- led to the highest percentage of cautious decisions.

On the neuronal level, we found increased activity in the
parahippocampal region during mixed-risk trials compared to high- and
low-risk trials in the risk block indicating an effect specific for the
risk difference between options. This region is closely linked to the
amygdala (e.g. Roy et al., 2009; Stein et al., 2007) and part of the
network that became activated during loss aversion in previous research
(e.g. Canessa et al., 2013) and we are thus able to replicate earlier
findings.

In the ambiguity block we found activation of the supplementary motor
area (SMA), which we showed for mixed-risk trials with low ambiguity in
comparison to high- and low-risk trials with low ambiguity. SMA
activation has been repeatedly related to reinforcement signals that may
be used to guide decision-making and action planning under risk and
uncertainty. Recently, Canessa and colleagues (2013) found greater
activation in SMA for individuals with greater loss aversion. Our data
also corroborated earlier findings that activity of the insular plays an
important role in the emotional evaluation of ambiguous decision in
conditions for which information about probabilities of options are
missing.

Higher ambiguity activated the dorsolateral prefrontal cortex (DLPFC).
Activation of this region was previously found to be related to
ambiguity (Krain et al., 2006). This activation is likely related to
rule-based action selection and likely indicates the conscious or
cognitive evaluation and manipulation of the relevant information in
working memory and the integration of negative evaluative emotional
information from the amygdala under ambiguous choice conditions. In
addition, the inferior parietal cortex (IPC) was during mixed trials
with high ambiguity in comparison to mixed trials with low ambiguity as
well. Accordingly, DLPFC and IPC accordingly seem to respond
specifically to higher ambiguity independent of risk. This region may be
directly linked to the DLPFC activity and was described as neural index
of working memory functions (e.g. Friedman \& Goldman Rakic, 1994) and
mathematical operations (e.g. Arsalidou \& Taylor, 2011). Further, we
found significant inferior frontal gyrus activation under high ambiguity
when participants where exposed to mixed risk blocks as compared to low-
and high-risk blocks, which indicates a role in the interaction of risk
and ambiguity. This also replicates previous research (e.g. Bach et al.,
2009; Hsu et al., 2005).

We could also identify greater activity in the dACC for gain and in the
insula and lateral OFC for loss in the mixed-risk condition as compared
to the average activation during low- and high-risk levels. This ensured
that our activations were independent from the overall level of risk and
the overall level of outcomes or from EV. Activation of dACC was also
observed during action selection under uncertain reward (Hampton \&
O'Doherty,(2007) and by Christopoulos et al. (2009) who characterized
dACC activity as an objective metric of risk. Furthermore, Canessa et
al. (2013) showed increased activation in clusters of the dACC for the
parameter representing the magnitude of gains and deactivation for the
magnitude of losses. Our results replicate these findings and are
particularly well in line with those of Christopoulos et al. (2009) who
observed stronger activity in dACC and more cautious decisions during
conditions of pure risk. It has further been suggested that dACC
activity reflects conflict (Botvinick et al., 2001) or a decrease in
reward expectation (Holroyd \& Coles, 2002) when the choice condition is
risky.

Further, activation of the OFC was found during decisions under risk
(Bach et al., 2009; Bhatt \& Camerer, 2005; Krain et al., 2006). Bhatt
et al. (2005) associated the OFC activity to the probability of gains,
which was positively correlated with the level of ambiguity, whereas
Krain et al. (2006) described a bilateral OFC activation for decisions
under risk. We found activations in the OFC in mixed-risk trials when
the possible loss was integrated into the analysis. Our results are in
compliance to Kringelbach \& Rolls (2004) suggesting that activity in
the lateral OFC ``is related to the evaluation of punishers which may
lead to a change in ongoing behavior''. Therefore, we suggest that the
present orbitofrontal activation relates to the coding of punishment
contingencies and may be related to the emotional evaluation of losses
in the decision alternatives. This is underlined by additional
activation of the insular cortex, which is an important structure for
the integration of emotions, subjective awareness, and experience, and
the representation of internal states of affect and arousal (e.g. Craig,
2011; Duerden et al., 2013). In summary, the effects of losses seem to
be primarily of emotional nature reflecting the representation of the
value of losses and at the same time the effect of losses on subjective
emotional awareness in conditions of mixed risk.

The fMRI analysis of integrated gain and loss parameters that compared
the two ambiguous situations, identified significant activations for
gains. Here, the amygdala was activated. This is in compliance with
studies both on risk and ambiguity (Breiter et al., 2001 ; Hsu et al.,
2005; Krain et al., 2006; Kuhnen \& Knutson, 2005; Platt \& Huettel,
2008). Since our experimental design controls for the overall level of
risk, outcomes and EV, our result may suggest that increasingly high
wins under ambiguity may act as a conditioned cue for excessive risk.
This may bias subsequent processing towards a more negative evaluation
of the risky gamble in total. This seems to be in line with the
amygdala's prominent role in affective conditioning (e.g. LeDoux, 2003).

Further, we asked the participants why they chose an option.
Correlational analyses indicated that focusing on the amount and the
probability of the gain in pure-risk situations led to incautious
decisions. This provides further evidence that risk-taking becomes
modulated by the expected value of options. Thus, we observed higher
risk-taking under decision-conditions where a gain is more likely (for
related evidence see Fochmann et al., 2017; Vorhold et al., 2007). In
contrast, when participants realize a greater likelihood of loss in
ambiguous situations, the behavior is more cautious. One limitation of
the present study is certainly sample size in particular, in relation to
the correlational findings. Future research should aim to corroborate
these findings in larger samples.

In summary, for a risky context dorsal anterior cingulate cortex (dACC),
insula, and OFC were activated in mixed trials that led to the highest
percentage of cautious decisions in risk trials. Accordingly, these
regions might reflect risk aversion in decision-making under risk and
support previous research (e.g. Krain et al., 2006; Platt \& Huettel,
2008; Tobler et al., 2007). Because we integrated potential losses, our
findings do not provide evidence for a clear differentiation of risk
aversion and loss aversion. Recent evidence suggests that these two
kinds of effects have the same neural basis. For example, Canessa et al.
(2013) found a significant correlation of loss aversion with risk
aversion and Rabin (2000) postulated that loss aversion explains risk
aversion in gambles with wins and losses. In particular, our
experimental design focuses on the evaluation of humans in decision
situations with different amounts of uncertainty that may all drive
cautious decisions The behavioral phenomenon of risk aversion may be
motivationally driven by loss aversion. In line with this argument, we
found activation in regions that were demonstrated being relevant for
loss aversion by Canessa et al. (2013) and/or linked to these areas,
i.e., activation of the amygdala and the posterior insula; the SMA, the
parahippocampal region. In summary, our results corroborate and extend
the findings of Canessa et al. (2013) and supports a link between loss
aversion and risk aversion and highlights a neural network for it. For a
more extensive analysis and interpretation of individual differences in
our data, our sample was too small.

Concerning ambiguity, we found that activity of the amygdala and
activation of the IFG was present in mixed trials with high ambiguity
when participants made the most cautious decisions. Further, an increase
in ambiguity from low to high was indicated by increased activity in
DLPFC and parietal cortex. Again our findings corroborate previous
results showing activity for dorsolateral prefrontal cortex (DLPFC),
amygdala, inferior frontal cortex, and parietal cortex (e.g. Bach et
al., 2009; Hsu et al., 2005; Krain et al., 2006) in the ambiguous
context and not in the risky context for trials inducing cautious
decisions.

Taken together, we replicated that both kinds of uncertainty -- risk and
ambiguity -- induce more cautious decision-making. As argued by
Rothschild \& Stiglitz (1970), the risk of options can be described by
the spread of outcomes and risk avoidance behavior is primarily driven
by the difference of risk between options. Ambiguity amplifies
behavioral risk avoidance in such situations entailing risk differences
between options in a non-additive, interactive way. Although some of our
evidence suggests that risk avoidance under both ambiguity and risk may
be driven by neural systems related to loss aversion, the systematic
differences in patterns of neural responses between conditions of risk
and ambiguity suggest basic differences between risk and ambiguity
(Ellsberg, 1961; Knight, 1921) and their underlying neural sources (e.g.
Bach et al., 2009; Hsu et al., 2005; Krain et al., 2006). Our own
findings particularly support a special role of working memory related
structures in DLPFC and parietal cortex that showed significantly
different activity between high and low ambiguity conditions. The latter
structures might be involved in integrating information from affective
structures like posterior insula and amygdala in order to compensate for
the missing cognitive numerical information to assess uncertainty and
potential losses.

Acknowledgements: This study was supported by a grant from
VolkswagenStiftung to JH.

\textbf{Table 1. Activations for mixed-risk trials compared to high and
low risk in the risk block}\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Region & & Talairach coordinates & Talairach coordinates & Talairach
coordinates & Max. & N\tabularnewline
& & X & Y & Z & T-value & Voxel\tabularnewline
Risk\_mixed \textgreater{} Risk\_high/low & & & & & &\tabularnewline
Parahippocampus & L & -36 & -18 & -18 & 4.24 & 14\tabularnewline
\bottomrule
\end{longtable}

R = right; L = left; TAL = Talairach coordinates (x, y, z) of activated
clusters; Max T = T level at this cluster; N = number of activated
voxels. Activation threshold: p \textless{} 0.001 for ROI, uncorrected,
explorative clusters \textgreater{} 5 Voxels

\textbf{Table 2. Activations for mixed risk level with high or low
ambiguity}\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Region & & Talairach coordinates & Talairach coordinates & Talairach
coordinates & Max. & N\tabularnewline
& & X & Y & Z & T-value & Voxel\tabularnewline
Risk\_mixed\_amb\_high\textgreater{} Risk\_high/low\_amb\_high & & & & &
&\tabularnewline
IFG (BA 47) & R & 34 & 18 & -6 & 4.89 & 49\tabularnewline
Risk\_mixed\_amb\_low\textgreater{} Risk\_high/low\_amb\_low & & & & &
&\tabularnewline
Supplementary motor area (SMA, BA6) & L & -16 & -4 & 58 & 4.11 &
36\tabularnewline
Posterior Insula (BA 13) & L & -42 & 8 & -8 & 3.45 & 16\tabularnewline
Risk\_mixed\_amb\_high \textgreater{} Risk\_mixed\_amb\_low & & & & &
&\tabularnewline
Inferior parietal cortex & R & 36 & -20 & 30 & 4.06 & 18\tabularnewline
DLPFC (BA 9) & L & -24 & 44 & 10 & 3.59 & 9\tabularnewline
\bottomrule
\end{longtable}

R = right; L = left; TAL = Talairach coordinates (x, y, z) of activated
clusters; Max T = T level at this cluster; N = number of activated
voxels; DLPFC = dorsolateral prefrontal cortex (BA 9, 46); IFG =
inferior frontal gyrus (BA 47). Activation threshold: p \textless{}
0.001 for ROI, uncorrected, explorative clusters \textgreater{} 5 Voxels

\textbf{Table 3. Activations for mixed-risk trials with potential win
and loss regressors}\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Region & & Talairach coordinates & Talairach coordinates & Talairach
coordinates & Max. & N\tabularnewline
& & X & Y & Z & T-value & Voxel\tabularnewline
Risk\_mixed\_win \textgreater{} Risk\_high/low\_win & & & & &
&\tabularnewline
dACC (BA 32) & L & -12 & 24 & 22 & 4.65 & 24\tabularnewline
Risk\_high/low\_loss\textgreater{}Risk\_mixed\_loss & & & & &
&\tabularnewline
Posterior Insula (BA 13) & R & 26 & 20 & -10 & 4.28 & 27\tabularnewline
OFC (BA 11) & R & 26 & 38 & -14 & 3.55 & 6\tabularnewline
Risk\_mixed\_amb\_high\_win \textgreater{} Risk\_mixed\_amb\_low\_win &
& & & & &\tabularnewline
Amygdala & R & 32 & 0 & -20 & 4.12 & 21\tabularnewline
\bottomrule
\end{longtable}

R = right; L = left; Tailarach coordinates = coordinates (x, y, z) of
activated clusters; Max T = T level at this cluster; N = number of
activated voxels; dACC = dorsal anterior cingulate cortex (BA 32); OFC =
orbitofrontal cortex. Activation threshold: p \textless{} 0.001 for ROI,
uncorrected, explorative clusters \textgreater{} 5 voxels

\textbf{Supplementary Table 4. All trials of an experimental block.}\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
condition of risk & pwin1 & win1 & ploss1 & loss1 & pwin2 & win2 &
ploss2 & loss2\tabularnewline
\midrule
\endhead
L & 0,9 & 17 & 0,1 & -50 & 0,65 & 23 & 0,35 & -15\tabularnewline
L & 0,7 & 31 & 0,3 & -40 & 0,45 & 41 & 0,55 & -15\tabularnewline
L & 0,35 & 47 & 0,65 & -10 & 0,95 & 12 & 0,05 & -30\tabularnewline
L & 0,85 & 14 & 0,15 & -15 & 0,9 & 13 & 0,1 & -20\tabularnewline
L & 0,6 & 30 & 0,4 & -20 & 0,95 & 12 & 0,05 & -20\tabularnewline
L & 0,6 & 27 & 0,4 & -15 & 0,75 & 25 & 0,25 & -35\tabularnewline
L & 0,5 & 25 & 0,5 & -5 & 0,55 & 30 & 0,45 & -15\tabularnewline
L & 0,85 & 21 & 0,15 & -50 & 0,3 & 45 & 0,7 & -5\tabularnewline
L & 0,6 & 40 & 0,4 & -35 & 0,7 & 19 & 0,3 & -10\tabularnewline
L & 0,9 & 15 & 0,1 & -35 & 0,55 & 26 & 0,45 & -10\tabularnewline
L & 0,75 & 27 & 0,25 & -40 & 0,65 & 34 & 0,35 & -35\tabularnewline
L & 0,6 & 23 & 0,4 & -10 & 0,95 & 13 & 0,05 & -40\tabularnewline
L & 0,9 & 13 & 0,1 & -15 & 0,85 & 13 & 0,15 & -5\tabularnewline
L & 0,5 & 30 & 0,5 & -10 & 0,6 & 20 & 0,4 & -5\tabularnewline
L & 0,6 & 33 & 0,4 & -25 & 0,8 & 18 & 0,2 & -20\tabularnewline
L & 0,95 & 12 & 0,05 & -25 & 0,95 & 11 & 0,05 & -10\tabularnewline
L & 0,65 & 32 & 0,35 & -30 & 0,8 & 25 & 0,2 & -50\tabularnewline
L & 0,7 & 23 & 0,3 & -20 & 0,3 & 57 & 0,7 & -10\tabularnewline
L & 0,9 & 14 & 0,1 & -25 & 0,85 & 16 & 0,15 & -25\tabularnewline
L & 0,75 & 22 & 0,25 & -25 & 0,75 & 18 & 0,25 & -15\tabularnewline
L & 0,55 & 43 & 0,45 & -30 & 0,8 & 15 & 0,2 & -10\tabularnewline
L & 0,7 & 25 & 0,3 & -25 & 0,55 & 39 & 0,45 & -25\tabularnewline
L & 0,9 & 17 & 0,1 & -55 & 0,75 & 15 & 0,25 & -5\tabularnewline
L & 0,85 & 14 & 0,15 & -10 & 0,95 & 12 & 0,05 & -35\tabularnewline
L & 0,95 & 13 & 0,05 & -55 & 0,95 & 11 & 0,05 & -5\tabularnewline
L & 0,5 & 45 & 0,5 & -25 & 0,65 & 26 & 0,35 & -20\tabularnewline
L & 0,65 & 18 & 0,35 & -5 & 0,8 & 14 & 0,2 & -5\tabularnewline
L & 0,8 & 16 & 0,2 & -15 & 0,4 & 55 & 0,6 & -20\tabularnewline
L & 0,4 & 48 & 0,6 & -15 & 0,95 & 11 & 0,05 & -15\tabularnewline
L & 0,45 & 34 & 0,55 & -10 & 0,75 & 17 & 0,25 & -10\tabularnewline
L & 0,5 & 40 & 0,5 & -20 & 0,8 & 19 & 0,2 & -25\tabularnewline
L & 0,85 & 17 & 0,15 & -30 & 0,55 & 22 & 0,45 & -5\tabularnewline
L & 0,7 & 16 & 0,3 & -5 & 0,35 & 38 & 0,65 & -5\tabularnewline
M & 0,9 & 12 & 0,1 & -10 & 0,55 & 71 & 0,45 & -65\tabularnewline
M & 0,8 & 20 & 0,2 & -30 & 0,6 & 53 & 0,4 & -55\tabularnewline
M & 0,75 & 23 & 0,25 & -30 & 0,75 & 38 & 0,25 & -75\tabularnewline
M & 0,8 & 21 & 0,2 & -35 & 0,15 & 95 & 0,85 & -5\tabularnewline
M & 0,95 & 13 & 0,05 & -45 & 0,6 & 83 & 0,4 & -100\tabularnewline
M & 0,85 & 20 & 0,15 & -45 & 0,85 & 29 & 0,15 & -95\tabularnewline
M & 0,9 & 16 & 0,1 & -45 & 0,65 & 53 & 0,35 & -70\tabularnewline
M & 0,9 & 12 & 0,1 & -5 & 0,95 & 16 & 0,05 & -100\tabularnewline
M & 0,35 & 56 & 0,65 & -15 & 0,8 & 35 & 0,2 & -90\tabularnewline
M & 0,75 & 28 & 0,25 & -45 & 0,65 & 67 & 0,35 & -95\tabularnewline
M & 0,65 & 29 & 0,35 & -25 & 0,65 & 69 & 0,35 & -100\tabularnewline
M & 0,55 & 35 & 0,45 & -20 & 0,85 & 25 & 0,15 & -75\tabularnewline
M & 0,25 & 55 & 0,75 & -5 & 0,2 & 90 & 0,8 & -10\tabularnewline
M & 0,7 & 21 & 0,3 & -15 & 0,45 & 77 & 0,55 & -45\tabularnewline
M & 0,65 & 21 & 0,35 & -10 & 0,7 & 40 & 0,3 & -60\tabularnewline
M & 0,4 & 33 & 0,6 & -5 & 0,5 & 95 & 0,5 & -75\tabularnewline
M & 0,7 & 29 & 0,3 & -35 & 0,8 & 30 & 0,2 & -70\tabularnewline
M & 0,55 & 88 & 0,45 & -85 & 0,85 & 19 & 0,15 & -40\tabularnewline
M & 0,8 & 34 & 0,2 & -85 & 0,7 & 27 & 0,3 & -30\tabularnewline
M & 0,55 & 59 & 0,45 & -50 & 0,9 & 16 & 0,1 & -40\tabularnewline
M & 0,25 & 100 & 0,75 & -20 & 0,95 & 13 & 0,05 & -50\tabularnewline
M & 0,8 & 33 & 0,2 & -80 & 0,95 & 14 & 0,05 & -60\tabularnewline
M & 0,55 & 92 & 0,45 & -90 & 0,45 & 47 & 0,55 & -20\tabularnewline
M & 0,7 & 51 & 0,3 & -85 & 0,8 & 24 & 0,2 & -45\tabularnewline
M & 0,7 & 46 & 0,3 & -75 & 0,6 & 37 & 0,4 & -30\tabularnewline
M & 0,75 & 37 & 0,25 & -70 & 0,75 & 20 & 0,25 & -20\tabularnewline
M & 0,7 & 49 & 0,3 & -80 & 0,4 & 40 & 0,6 & -10\tabularnewline
M & 0,8 & 31 & 0,2 & -75 & 0,5 & 35 & 0,5 & -15\tabularnewline
M & 0,6 & 73 & 0,4 & -85 & 0,45 & 28 & 0,55 & -5\tabularnewline
M & 0,55 & 55 & 0,45 & -45 & 0,9 & 14 & 0,1 & -30\tabularnewline
M & 0,65 & 45 & 0,35 & -55 & 0,85 & 15 & 0,15 & -20\tabularnewline
M & 0,45 & 89 & 0,55 & -55 & 0,85 & 18 & 0,15 & -35\tabularnewline
M & 0,5 & 65 & 0,5 & -45 & 0,8 & 23 & 0,2 & -40\tabularnewline
H & 0,85 & 26 & 0,15 & -80 & 0,4 & 85 & 0,6 & -40\tabularnewline
H & 0,55 & 96 & 0,45 & -95 & 0,5 & 90 & 0,5 & -70\tabularnewline
H & 0,65 & 58 & 0,35 & -80 & 0,55 & 63 & 0,45 & -55\tabularnewline
H & 0,75 & 35 & 0,25 & -65 & 0,6 & 57 & 0,4 & -60\tabularnewline
H & 0,5 & 100 & 0,5 & -80 & 0,25 & 85 & 0,75 & -15\tabularnewline
H & 0,6 & 77 & 0,4 & -90 & 0,65 & 50 & 0,35 & -65\tabularnewline
H & 0,75 & 40 & 0,25 & -80 & 0,65 & 56 & 0,35 & -75\tabularnewline
H & 0,7 & 44 & 0,3 & -70 & 0,9 & 21 & 0,1 & -85\tabularnewline
H & 0,7 & 42 & 0,3 & -65 & 0,6 & 63 & 0,4 & -70\tabularnewline
H & 0,45 & 71 & 0,55 & -40 & 0,75 & 47 & 0,25 & -100\tabularnewline
H & 0,95 & 16 & 0,05 & -95 & 0,75 & 45 & 0,25 & -95\tabularnewline
H & 0,35 & 75 & 0,65 & -25 & 0,55 & 100 & 0,45 & -100\tabularnewline
H & 0,75 & 42 & 0,25 & -85 & 0,45 & 96 & 0,55 & -60\tabularnewline
H & 0,85 & 28 & 0,15 & -90 & 0,65 & 48 & 0,35 & -60\tabularnewline
H & 0,65 & 64 & 0,35 & -90 & 0,65 & 61 & 0,35 & -85\tabularnewline
H & 0,5 & 75 & 0,5 & -55 & 0,7 & 57 & 0,3 & -100\tabularnewline
H & 0,4 & 70 & 0,6 & -30 & 0,55 & 75 & 0,45 & -70\tabularnewline
H & 0,35 & 94 & 0,65 & -35 & 0,7 & 53 & 0,3 & -90\tabularnewline
H & 0,6 & 70 & 0,4 & -80 & 0,75 & 43 & 0,25 & -90\tabularnewline
H & 0,9 & 22 & 0,1 & -95 & 0,6 & 60 & 0,4 & -65\tabularnewline
H & 0,8 & 36 & 0,2 & -95 & 0,55 & 67 & 0,45 & -60\tabularnewline
H & 0,8 & 38 & 0,2 & -100 & 0,4 & 100 & 0,6 & -50\tabularnewline
H & 0,95 & 15 & 0,05 & -90 & 0,9 & 22 & 0,1 & -100\tabularnewline
H & 0,85 & 29 & 0,15 & -100 & 0,7 & 55 & 0,3 & -95\tabularnewline
H & 0,6 & 80 & 0,4 & -95 & 0,5 & 85 & 0,5 & -65\tabularnewline
H & 0,35 & 84 & 0,65 & -30 & 0,55 & 84 & 0,45 & -80\tabularnewline
H & 0,9 & 21 & 0,1 & -90 & 0,85 & 27 & 0,15 & -85\tabularnewline
H & 0,45 & 83 & 0,55 & -50 & 0,5 & 60 & 0,5 & -40\tabularnewline
H & 0,45 & 65 & 0,55 & -35 & 0,5 & 80 & 0,5 & -60\tabularnewline
H & 0,6 & 50 & 0,4 & -50 & 0,4 & 78 & 0,6 & -35\tabularnewline
H & 0,5 & 70 & 0,5 & -50 & 0,4 & 93 & 0,6 & -45\tabularnewline
H & 0,3 & 92 & 0,7 & -25 & 0,6 & 67 & 0,4 & -75\tabularnewline
H & 0,55 & 80 & 0,45 & -75 & 0,3 & 80 & 0,7 & -20\tabularnewline
\bottomrule
\end{longtable}

Conditions of risk: L = low, M = mixed, H = high; probabilities of the 2
alternative wins and losses in gamble options 1 and 2 of each trial:
pwin1, ploss1, pwin2, ploss2; monetary outcome for wins and losses in
the gambles 1 and 2: win1, loss1, win2, loss2.

FIGURE CAPTIONS (for files attached)

Figure 1a: Example trial with high ambiguity showing all events and
their timing. The fixation cross (1\textsuperscript{st} frame) was
followed by the option screen (2\textsuperscript{nd} frame). Upon button
press green colour indicated the choice (3\textsuperscript{rd} frame)
and subsequently feedback of the current trial was presented
(4\textsuperscript{th} screen) followed by the sum of all trials
(5\textsuperscript{th} screen) and the fixation cross of the next trial.

Figure 1b: Probability of choosing the higher risk option during the
risk block (upper panel) and the ambiguity block (lower panel) for the
three levels of risk.

Figure 2: Activation in parahippocampus during mixed-risk trials in
comparison to high- and low-risk trials.

Figure 3: Activation of inferior frontal gyrus IFG (BA 47) during
mixed-risk trials with high ambiguity versus averaged high- and low-risk
trials with high ambiguity

Figure 4: Activation of SMA (BA 6) during mixed-risk trials with low
ambiguity versus averaged high- and low-risk trials with low ambiguity

Figure 5: Activation of DLPFC (BA 9) during mixed-risk trials with high
ambiguity versus mixed-risk trials with low ambiguity

Figure 6: Activation of dACC (BA 32) during mixed-risk trials for
parameteric analysis of potential wins in comparison to high- and
low-risk trials

Figure 7: Activation of the insular cortex and the OFC during mixed-risk
trials for the parameteric analysis of potential losses in comparison to
high- and low- risk trials

Figure 8: Activation of the amygdala during mixed-risk trials for trials
with high ambiguity in the parameteric analysis of potential wins versus
mixed-risk trials with low ambiguity.

References

Arsalidou, M., \& Taylor, M. J. (2011, Feb 1). Is 2+2=4? Meta-analyses
of brain areas needed for numbers and calculations. \emph{Neuroimage,
54} (3), 2382-2393. https://doi.org/10.1016/j.neuroimage.2010.10.009

Bach, D. R., Seymour, B., \& Dolan, R. J. (2009, Feb 11). Neural
activity associated with the passive prediction of ambiguity and risk
for aversive events. \emph{Journal of Neuroscience, 29} (6), 1648-1656.
https://doi.org/10.1523/JNEUROSCI.4578-08.2009

Bechara, A., Damasio, H., Tranel, D., \& Damasio, A. R. (1997). Deciding
advantageously before knowing the advantageous strategy. \emph{Science,
275} (5304), 1293-1295.

Bechara, A., Damasio, H., Tranel, D., \& Damasio, A. R. (2005). The Iowa
Gambling Task and the somatic marker hypothesis: some questions and
answers. \emph{Trends in Cognitive Sciences, 9} (4), 159-162; discussion
162-154.

Bhatt, M., \& Camerer, C. F. (2005, Aug). Self-referential thinking and
equilibrium as states of mind in games: FMRI evidence {[}Print
Electronic; Print{]}. \emph{Games and Economic Behavior, 52} (2),
424-459.

Botvinick, M. M., Braver, T. S., Barch, D. M., Carter, C. S., \& Cohen,
J. D. (2001, Jul). Conflict monitoring and cognitive control.
\emph{Psychological Review, 108} (3), 624-652. \textless{}Go to
ISI\textgreater{}://000170892100006

Breiter, H. C., Aharon, I., Kahneman, D., Dale, A., \& Shizgal, P.
(2001, May). Functional imaging of neural responses to expectancy and
experience of monetary gains and losses.\emph{Neuron, 30} (2), 619-639.
https://doi.org/Doi 10.1016/S0896-6273(01)00303-8

Brown, J. W., \& Braver, T. S. (2005, Feb 18). Learned predictions of
error likelihood in the anterior cingulate cortex. \emph{Science, 307}
(5712), 1118-1121. https://doi.org/10.1126/science.1105783

Brown, J. W., \& Braver, T. S. (2007, Dec). Risk prediction and aversion
by anterior cingulate cortex.\emph{Cognitive Affective \& Behavioral
Neuroscience, 7} (4), 266-277. https://doi.org/Doi 10.3758/Cabn.7.4.266

Brown, J. W., \& Braver, T. S. (2008, Apr 2). A computational model of
risk, conflict, and individual difference effects in the anterior
cingulate cortex. \emph{Brain Research, 1202} , 99-108.
https://doi.org/10.1016/j.brainres.2007.06.080

Budner, N. Y. S. (1962). Intolerance of Ambiguity as a Personality
Variable. \emph{Journal of Personality, 30} (1), 29--50

Canessa, N., Crespi, C., Motterlini, M., Baud-Bovy, G., Chierchia, G.,
Pantaleo, G., Tettamanti, M., \& Cappa, S. F. (2013, Sep 4). The
functional and structural neural basis of individual differences in loss
aversion {[}Research Support, Non-U.S. Gov't{]}. \emph{The Journal of
neuroscience : the official journal of the Society for Neuroscience, 33}
(36), 14307-14317. https://doi.org/10.1523/JNEUROSCI.0497-13.2013

Carver, C. S., \& White, T. L. (1994). Behavioral inhibition, behavioral
activation, and affective responses to impending reward and punishment:
The BIS/BAS scales.\emph{Journal of Personality and Social Psychology,
67} , 319-333.

Chen, Z., \& Epstein, L. (2002). Ambiguity, risk, and asset returns in
continuous time.\emph{Econometrica, 70} (4), 1403-1443.

Christopoulos, G. I., Tobler, P. N., Bossaerts, P., Dolan, R. J., \&
Schultz, W. (2009, Oct 7). Neural Correlates of Value, Risk, and Risk
Aversion Contributing to Decision Making under Risk. \emph{Journal of
Neuroscience, 29} (40), 12574-12583.
https://doi.org/10.1523/Jneurosci.2614-09.2009

Craig, A. D. (2011, Apr). Significance of the insula for the evolution
of human awareness of feelings from the body {[}Review{]}. \emph{Annals
of the New York Academy of Sciences, 1225} , 72-82.
https://doi.org/10.1111/j.1749-6632.2011.05990.x

Duerden, E. G., Arsalidou, M., Lee, M., \& Taylor, M. J. (2013, Sep).
Lateralization of affective processing in the insula {[}Research
Support, Non-U.S. Gov't{]}. \emph{Neuroimage, 78} , 159-175.
https://doi.org/10.1016/j.neuroimage.2013.04.014

Ellsberg, D. (1961, November). Risk, ambiguity, and the Savage axioms.
\emph{Quarterly Journal of Economics, 75} , 643-669.

Fochmann, M., Hewig, J., Kiesewetter, D., \& Sch\selectlanguage{ngerman}üßler, K. (2017).
Affective reactions influence investment decisions: evidence from a
laboratory experiment with taxation.\emph{Journal of Business Economics,
87} (6), 779-808.

Friedman, H. R., \& Goldman Rakic, P. S. (1994). Coactivation of
prefrontal cortex and inferior parietal cortex in working memory tasks
revealed by 2DG functional mapping in the rhesus monkey.
\emph{J-Neurosci, 14} (5 Pt 1), 2775-2788.

Hampton, A. N., \& O'Doherty, J. P. (2007, Jan 23). Decoding the neural
substrates of reward-related decision making with functional MRI.
\emph{Proceedings of the National Academy of Sciences of the United
States of America, 104} (4), 1377-1382.
https://doi.org/10.1073/pnas.0606297104

Hewig, J., Kretschmer, N., Trippe, R. H., Hecht, H., Coles, M. G.,
Holroyd, C. B., \& Miltner, W. H. (2010, Apr 15). Hypersensitivity to
reward in problem gamblers. \emph{Biol Psychiatry, 67} (8), 781-783.
https://doi.org/10.1016/j.biopsych.2009.11.009

Hewig, J., Straube, T., Trippe, R. H., Kretschmer, N., Hecht, H., Coles,
M. G., \& Miltner, W. H. (2009, Aug). Decision-making under risk: an
fMRI study. \emph{J Cogn Neurosci, 21} (8), 1642-1652.
https://doi.org/10.1162/jocn.2009.21112

Hewig, J., Trippe, R., Hecht, H., Coles, M. G., Holroyd, C. B., \&
Miltner, W. H. (2007, Apr). Decision-making in Blackjack: an
electrophysiological analysis.\emph{Cereb Cortex, 17} (4), 865-877.
https://doi.org/10.1093/cercor/bhk040

Hewig, J., Trippe, R. H., Hecht, H., Coles, M. G., Holroyd, C. B., \&
Miltner, W. H. (2008, Oct). An electrophysiological analysis of coaching
in Blackjack. \emph{Cortex, 44} (9), 1197-1205.
https://doi.org/10.1016/j.cortex.2007.07.006

Holroyd, C. B., \& Coles, M. G. (2002). The neural basis of human error
processing: reinforcement learning, dopamine, and the error-related
negativity.\emph{Psychological Review, 109} (4), 679-709.

Hsu, M., Bhatt, M., Adolphs, R., Tranel, D., \& Camerer, C. F. (2005,
Dec). Neural Systems Responding to Degrees of Uncertainty in Human
Decision-Making {[}Empirical Study

Quantitative Study{]}. \emph{Science, 310} (5754), 1680-1683.
https://doi.org/10.1126/science.1115327

Huettel, S. A., Stowe, C. J., Gordon, E. M., Warner, B. T., \& Platt, M.
L. (2006). Neural signatures of economic preferences for risk and
ambiguity. \emph{Neuron, 49} (5), 765-775.

Kahneman, D., Schwartz, A., Thaler, R. H., \& Tversky, A. (1997, Jul).
The Effect of Myopia and Loss Aversion on Risk Taking: An Experimental
Test. \emph{Journal of Finance, 52} (3), 1237-1237. \textless{}Go to
ISI\textgreater{}://000209883900062

Kahneman, D., \& Tversky, A. (1979). Prospect Theory - Analysis of
Decision under Risk. \emph{Econometrica, 47} (2), 263-291.
https://doi.org/Doi 10.2307/1914185

Knight, F. H. (1921). \emph{Risk, Uncertainty, and Profit} . Hart,
Schaffner \& Marx; Houghton Mifflin. Library of Economics and Liberty.

Knutson, B., Adams, C. M., Fong, G. W., \& Hommer, D. (2001).
Anticipation of increasing monetary reward selectively recruits nucleus
accumbens. \emph{Journal of Neuroscience, 21} (16), NIL\_1-NIL\_5.

Knutson, B., Taylor, J., Kaufman, M., Peterson, R., \& Glover, G. (2005,
May 11). Distributed neural representation of expected value.
\emph{Journal of Neuroscience, 25} (19), 4806-4812.
https://doi.org/10.1523/Jneurosci.0642-05.2005

Krain, A. L., Wilson, A. M., Arbuckle, R., Castellanos, F. X., \&
Milham, M. P. (2006, Aug 1). Distinct neural mechanisms of risk and
ambiguity: a meta-analysis of decision-making. \emph{Neuroimage, 32}
(1), 477-484. https://doi.org/10.1016/j.neuroimage.2006.02.047

Kringelbach, M. L., \& Rolls, E. T. (2004, Apr). The functional
neuroanatomy of the human orbitofrontal cortex: evidence from
neuroimaging and neuropsychology. \emph{Progress in Neurobiology, 72}
(5), 341-372. https://doi.org/10.1016/j.pneurobio.2004.03.006

Kuhnen, C. M., \& Knutson, B. (2005). The neural basis of financial risk
taking. \emph{Neuron, 47} (5), 763-770.

LeDoux, J. (2003, Oct). The emotional brain, fear, and the amygdala
{[}Review{]}. \emph{Cellular and molecular neurobiology, 23} (4-5),
727-738. http://www.ncbi.nlm.nih.gov/pubmed/14514027

Lejuez, C. W., Read, J. P., Kahler, C. W., Richards, J. B., Ramsey, S.
E., Stuart, G. L., Strong, D. R., \& Brown, R. A. (2002, Jun).
Evaluation of a behavioral measure of risk taking: The Balloon Analogue
Risk Task (BART). \emph{Journal of Experimental Psychology-Applied, 8}
(2), 75-84. https://doi.org/10.1037//1076-898X.8.2.75

Li, X. R., Lu, Z. L., D'Argembeau, A., Ng, M., \& Bechara, A. (2010,
Mar). The Iowa Gambling Task in fMRI Images. \emph{Human Brain Mapping,
31} (3), 410-423. https://doi.org/10.1002/hbm.20875

McLain, D. L. (2009, Dec). Evidence of the Properties of an Ambiguity
Tolerance Measure: The Multiple Stimulus Types Ambiguity Tolerance
Scale-Ii (Mstat-Ii).\emph{Psychological Reports, 105} (3), 975-988.
https://doi.org/10.2466/Pr0.105.3.975-988

Mussel, P., Reiter, A. M., Osinsky, R., \& Hewig, J. (2015, Apr). State-
and trait-greed, its impact on risky decision-making and underlying
neural mechanisms. \emph{Soc Neurosci, 10} (2), 126-134.
https://doi.org/10.1080/17470919.2014.965340

Platt, M. L., \& Huettel, S. A. (2008, Apr). Risky business: the
neuroeconomics of decision making under uncertainty. \emph{Nature
Neuroscience, 11} (4), 398-403. https://doi.org/10.1038/nn2062

Rabin, M. (2000, September). Risk Aversion and Expected-Utility Theory:
A Calibration Theorem.\emph{Econometrica, 68 5} , 1281-1292.
http://www.econometricsociety.org/tocs.asp

Rao, H., Korczykowski, M., Pluta, J., Hoang, A., \& Detre, J. A. (2008,
Aug 15). Neural correlates of voluntary and involuntary risk taking in
the human brain: an fMRI Study of the Balloon Analog Risk Task (BART).
\emph{Neuroimage, 42} (2), 902-910.
https://doi.org/10.1016/j.neuroimage.2008.05.046

Rothschild, M., \& Stiglitz, J. E. (1970). Increasing Risk: I. A
definition \emph{Journal of Economic Theory, 2} ( 3), 225-243.

Roy, A. K., Shehzad, Z., Margulies, D. S., Kelly, A. M. C., Uddin, L.
Q., Gotimer, K., Biswal, B. B., Castellanos, F. X., \& Milham, M. P.
(2009, Apr 1). Functional connectivity of the human amygdala using
resting state fMRI.\emph{Neuroimage, 45} (2), 614-626.
https://doi.org/10.1016/j.neuroimage.2008.11.030

Smith, K., Dickhaut, J., McCabe, K., \& Pardo, J. V. (2002, Jun).
Neuronal substrates for choice under ambiguity, risk, gains, and losses
{[}Empirical Study{]}.\emph{Management Science, 48} (6), 711-718.
https://doi.org/10.1287/mnsc.48.6.711.194

Stein, J. L., Wiedholz, L. M., Bassett, D. S., Weinberger, D. R., Zink,
C. F., Mattay, V. S., \& Meyer-Lindenberg, A. (2007, Jul 1). A validated
network of effective amygdalla connectivity. \emph{Neuroimage, 36} (3),
736-745. https://doi.org/10.1016/j.neuroimage.2007.03.022

Tobler, P. N., O'Doherty, J. P., Dolan, R. J., \& Schultz, W. (2007,
Feb). Reward value coding distinct from risk attitude-related
uncertainty coding in human reward systems.\emph{Journal of
Neurophysiology, 97} (2), 1621-1632.
https://doi.org/10.1152/jn.00745.2006

Tom, S. M., Fox, C. R., Trepel, C., \& Poldrack, R. A. (2007, Jan 26).
The neural basis of loss aversion in decision-making under risk.
\emph{Science, 315} (5811), 515-518.
https://doi.org/10.1126/science.1134239

Vorhold, V., Giessing, C., Wiedemann, P. M., Schutz, H., Gauggel, S., \&
Fink, G. R. (2007, Nov 5). The neural basis of risk ratings: evidence
from a functional magnetic resonance imaging (fMRI) study.
\emph{Neuropsychologia, 45} (14), 3242-3250.
https://doi.org/10.1016/j.neuropsychologia.2007.06.023

Yacubian, J., Glascher, J., Schroeder, K., Sommer, T., Braus, D. F., \&
Buchel, C. (2006, Sep 27). Dissociable systems for gain- and
loss-related value predictions and errors of prediction in the human
brain (vol 26, pg 9530, 2006).\emph{Journal of Neuroscience, 26} (39).
\textless{}Go to ISI\textgreater{}://000240825700027

Zuckerman, M. (1996, Apr). Item revisions in the sensation seeking scale
form V (SSS-V).\emph{Personality and Individual Differences, 20} (4),
515-515. https://doi.org/Doi 10.1016/0191-8869(95)00195-6\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure1a-qula/Figure1a-qula}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-1b/Figure-1b}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure2-qula/Figure2-qula}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure3-qula/Figure3-qula}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure4-qula/Figure4-qula}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure5-qula/Figure5-qula}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure6-qula/Figure6-qula}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure7-qula/Figure7-qula}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure8-qula/Figure8-qula}

\end{center}
\end{figure}

\selectlanguage{english}
\FloatBarrier
\end{document}

