Emotions and decision-making

Emotions are patterned chemical and neural responses to stimuli that elicit physiological and subjective changes to motivate a behavioral responses in order to deal with the relevant event (Frijda Reference Frijda, Ekman and Davidson1994; Damasio Reference Damasio1994). Threatening stimuli often evoke a SAM response. The SAM response is characterized by changes in heart rate, skin conductance, and pupil dilation and can be measured with free salivary α-amylase (Buchanan, Bibas and Adolphs Reference Buchanan, Bibas and Adolphs2010).

The existing literature suggests multiple channels through which fear may impact decisions to participate in risky collective action. Experimental studies in both psychology and economics show that emotions, in particular fear, influence risk perceptions (Johnson and Tversky Reference Johnson and Tversky1983; Lerner and Keltner Reference Lerner and Keltner2000, Reference Lerner and Keltner2001; Lerner et al. Reference Lerner, Gonzalez, Small and Fischhoff2003) and risk aversion (Guiso, Sapienza and Zingales Reference Guiso, Sapienza and Zingales2018; Cohn et al. Reference Cohn, Engelmann, Fehr and Maréchal2015; Young Reference Young2019). First, if fear affects risk perceptions it should influence (a) beliefs about a payoff-relevant state of the world or, in an independent manner, it should affect (b) beliefs about how likely it is that other players will take a risky action (Johnson and Tversky Reference Johnson and Tversky1983; Lerner and Keltner Reference Lerner and Keltner2000, Reference Lerner and Keltner2001; Lerner et al. Reference Lerner, Gonzalez, Small and Fischhoff2003). In the case of (a), an increase in pessimism may make people believe that participating in the risky action is more costly than warranted by the available information. In the case of (b), independently of how costly people believe taking the risky action will be, they might believe that others are less likely to participate. Though related, these are distinct channels. In game theoretic terms, the first channel is through perceptions of fundamental uncertainty, while the latter is through perceptions of strategic uncertainty.

Finally, if fear affects risk aversion, then it changes the concavity of the citizens’ utility functions, making it more likely that players choose the safer choice by lowering the value of their certainty equivalent. Aldama, Vásquez-Cortés and Young (Reference Aldama, Vásquez-Cortés and Young2019) develop a theoretical model of how these effects of fear would influence the decision to join a protest or revolution.

Model

Consider a game in which there are two players deciding whether they want to participate in risky collective action, such as citizens deciding whether to mobilize to bring down an incumbent regime or investors seeking to increase the value of a security. As a running example, we will use the language of mobilization against an incumbent regime. The citizens’ goal, replacing the regime, will only be achieved if both of them participate or mobilize. If the regime remains in place, that is, the status quo remains, the citizens will obtain a payoff of $ - c$ , with $c \in \mathbb{R}$ . This is a measure of how costly it is for the citizens to have the regime in place. The greater c is, the worse it is for them to have the regime prevail. Failure of the regime will result in a positive payoff of R for both citizens. The greater R is, the more citizens would benefit from regime change. Mobilizing has a cost of $\theta $ , which is unknown to both citizens. This captures the idea that even if the regime fails they do not know whether they will suffer physical injury (or worse) if they join the mobilization against the regime. Payoffs are summarized below in Table 1. Although the citizens do not know the true value of $\theta $ , they know that it is drawn from a normal distribution with mean y and variance $1/\alpha $ (precision $\alpha $ ), that is,

$$\theta \sim N(y,1/\alpha ).$$

Table 1

Payoff Summary of the Game

Moreover, note that it is possible that $\theta \lt 0$ , which allows the payment structure to also capture the fact that the regime might co-opt the opposition. This means that there might be cases in which the opposition is better off by mobilizing even if they fail to replace the incumbent regime.

Once $\theta $ is realized, independent signals are privately drawn for each citizen. The signals provide additional information to the citizens. These may come, for instance, from their knowledge of previous mobilizations, public pronouncements by the regime, or whether they observe the regime using intimidation tactics, which might be observed by citizens on the news or social media. The signal each citizen receives is a noisy signal of $\theta $ . In particular, each citizen receives a signal

$${x_i} = \theta + {\varepsilon _i}$$

where ${\varepsilon _i}$ is normally distributed with mean 0 and variance $1/\beta $ (precision $\beta $ ). Citizens’ posterior beliefs about the $\theta $ are derived by Bayes’ rule. In particular, given a signal ${x_i}$ , a citizen’s posterior expectation of θ is normally distributed with mean $\gamma $ and precision $\alpha + \beta ,$ where $\gamma = \displaystyle{{\alpha y + \beta {x_i}} \over {\alpha + \beta }}$ . ^{Footnote 5}

The equilibrium consists of a cutoff signal for citizens ${x_i} = k$ . ^{Footnote 6} Citizens using a cutoff strategy will choose to mobilize if upon receipt of their private signal they believe that $\theta $ is sufficiently low and will abstain from doing so if they believe it is sufficiently high.

Note that if citizen i mobilizes, she will always receive $\theta $ and will receive R if the other citizen also mobilizes. Hence, citizen i will mobilize if she believes that the other citizen will mobilize with high enough probability. In particular, she will mobilize if

(1) $${\mathbb{E}}[Mobilize|{x_i},k] = R\times Pr({x_{ - i}} \lt k|{x_i}) - {\mathbb{E}}[\theta |{x_i}] \gt - c$$

where k is the cutoff of the other citizen (which in equilibrium will be equal to her own cutoff), and $Pr({x_{ - i}} \lt k|{x_i})$ is the probability with which citizen i believes that that citizen $ - i$ will receive a signal smaller than k conditional on the signal she received. We must note that:

$${x_{ - i}}|{x_i}\sim N\left(\gamma ,{1 \over {\alpha + \beta }} + {1 \over \beta }\right).$$

Thus, with some algebra, equation 1 becomes

(2) $$R\Phi \left[{1 \over \displaystyle{{{2\beta + \alpha } \over {\alpha \beta + {\beta ^2}}}}}\left(k - {{\alpha y + \beta {x_i}} \over {\alpha + \beta }}\right)\right] - {{\alpha y + \beta {x_i}} \over {\alpha + \beta }} \gt - c,$$

where $\Phi $ represents the standard normal distribution function. From equation 2, note that since both α and $\beta \gt 0$ , the left-hand side is strictly increasing in k and strictly decreasing in ${x_i}$ . Thus, as noted by Morris and Shin (Reference Morris, Shin, Hansen, Dewatripont and Turnovsky2003) the game has a unique equilibrium in cutoff strategies in which $k = x_i^*$ .

Experimental parameters and predictions

We implement this game in the lab, with participants playing the game under different parametrizations for a number of rounds. In each round of the experiment, the values of the parameters of the model are independently randomly drawn from the five options presented in Table 2.

Table 2

Experimental Parameters

Note that while $y = \alpha = \beta = 1$ for all cases, the pair $\{ R,c\} $ changes from round to round to have different stakes for the game. Given $\alpha = \beta = y = 1$ , we can substitute these values and the equilibrium condition that $k = {x_i}$ into equation 2, which then becomes

(3) $$R\Phi \left[{2 \over 3}\left(k - {{1 + k} \over 2}\right)\right] - {{1 + k} \over 2} \gt - c$$

Which upon further analysis becomes

$$R\Phi \left[{{k - 1} \over 3}\right] - {{1 + k} \over 2} \gt - c$$

Figure 1 graphs the left-hand side, the expected benefit of mobilizing, and the right-hand side of this equation, the expected benefit of not mobilizing, for various values of k for $R = 1$ and $c = 0.5$ . It shows that for these values, the unique cutoff is ${x_i} = k = 1$ . The results remain unchanged for the rest of the set of parameters. Hence, a citizen that is fully rational (and has common knowledge of rationality) should choose to mobilize if she receives a signal smaller than 1 and should abstain if it is larger than 1. However, given our theoretical discussion, we expect that subjects that are in a state of fear would abstain at lower values of the signal. Moreover, given fear’s tendency to make people amplify risks, we expect that this effect would be amplified if they believe that other players will also abstain at lower values of the signal, whether this is caused by an increase in fundamental or strategic uncertainty. Aldama, Vásquez-Cortés and Young (Reference Aldama, Vásquez-Cortés and Young2019) model these effects as people believing the signal is higher than it actually is (an increase in fundamental uncertainty) and as people believing that other players are more likely to make mistakes when deciding to mobilize (an increase in strategic uncertainty). Clearly, both effects would demobilize people.

Figure 1

Equilibrium Cutoff.

Finally, to the extent that fear increases risk aversion, we would expect that at higher stakes the effects of fear would be stronger. To see why this is the case, consider the following simple example. Let the utility over the material payoffs be $u(\pi ) = 3 + \pi $ , where $\pi $ represents the corresponding material payoffs depicted in Table 1 when people are not afraid. Suppose that as a result of an increase in risk aversion when people are afraid, their utility is given by $u(\pi ) = (3 + \pi {)^{0.6}}$ . A generalized form of equation (1) reveals that in both option 1 and option 5 in Table 2, without fear the cutoff would be given by $k = 1$ . However, in the case with fear, the cutoff in option 1 is $k = .98$ and $k = .72$ for option 5, revealing that is more likely for subjects in the fear condition not to mobilize in option 5 than in option 1. Though generally increases in risk aversion also lead to less mobilization, particularly under higher stakes, Aldama, Vásquez-Cortés and Young (Reference Aldama, Vásquez-Cortés and Young2019) also note that increases in risk aversion can lead to greater mobilization if they lead to a “nothing-to-lose” effect. This effect prevails if a player’s utility is so affected by fear that the expected payoffs for the status quo become very similar to those of mobilizing and failing to replace the regime.

Although we describe this model in terms of citizens mobilizing against an authoritarian regime, it can be generalized to a wide range of situations in which more than one decision-maker is considering engaging in potentially action against a singular opponent who can selectively punish. This also describes situations in which civilians consider taking collective action against criminal organizations or workers considering reporting an abusive employer. One key assumption is that the actions of players are at least partially visible to the regime, which enables it to impose costs conditional on individual mobilization decisions.

Experimental design

To test the predictions of this model, we use an experimental design that allows us to compare the decisions of participants who are experiencing the emotion of fear to those of otherwise similar participants in a neutral emotional state. We carried out the experiment in the labs of a large private university in the northeast and a large public university on the west coast. We recruited participants from their preexisting pools, primarily composed of undergraduate students. The experiment was implemented using z-Tree (Fischbacher Reference Fischbacher2007). Sessions lasted about 60 min, and participants were paid on average 16 dollars. After providing consent, participants first watched a relaxing seven-minute video clip, after which we took a saliva sample in order to measure their levels of α-amylase, a salivary enzyme that serves as an index of noradrenergic activity (Nater and Rohleder Reference Nater and Rohleder2009; Raio et al. Reference Raio, Orederu, Palazzolo, Shurick and Phelps2013; van Stegeren et al. Reference van Stegeren, Rohleder, Everaerd and Wolf2006). Second, to build familiarity with the game, a member of the research team read the instructions out loud, and participants played five practice rounds. ^{Footnote 7} Third, participants were randomly assigned at the session level to watch a video intended to either induce a state of fear or keep them in a neutral emotional state. Finally, participants played 15 rounds of the game in which we vary key parameters in order to shut down some of the channels by which fear might influence behavior. In random order, participants played three sets of 5 rounds of the game: a standard global game with a human, a standard global game with a computer, and a full information game with a human. Finally, participants answered a few questions about their current emotional state and how they played the game. After all measurement, the sum of three randomly selected rounds (one from each condition) is paid out, and the participants’ payouts revealed. ^{Footnote 8} Figure 2 shows the timing of the game for participants.

Figure 2

Timing of Play During the Experiment.

To induce a mild state of fear in a random sample of our sessions, we used a video clip from a horror film. We pre-tested the video on both Amazon Mechanical Turk and with a sample of subjects from one of the experimental pools and found in both pilots that the video significantly increased self-reported levels of fear. Participants in the treatment condition also heard loud unexpected noises during three randomly selected rounds. In the control treatment, subjects watched a typical placebo video about the solar system. Both videos were of the same length, about seven minutes. The fear treatment is similar to those used in previous studies to create specific emotions (Westermann et al. Reference Westermann, Spies, Stahl and Hesse1996; Lench, Flores and Bench Reference Lench, Flores and Bench2011). After receiving the corresponding treatment, participants were paired with another player and, based on the given parameters, the participants received a signal of the strength of the regime x _i and were then asked whether they wished to mobilize or abstain. ^{Footnote 9} After each round, participants were randomly rematched. Participants do not receive feedback until the end of the game to eliminate the possibility that learning the outcomes of each round would affect participants’ moods in subsequent rounds.

Randomization occurs at the session level, and participants know that they are all watching the same video. This implies that participants have common knowledge that others are also experiencing the same treatment that they receive.

We use three different versions of the game to disentangle the possible mechanisms by which fear could affect mobilization: standard, computer, and full information. In each session, participants play a set of five rounds of each version of the game, the order of which is randomly assigned. In standard rounds, participants know that they are playing with another human who has viewed the same treatment video. Thus, their behavior could be affected by pessimism about the signal, pessimism about others’ behavior, or risk aversion. However, in the computer rounds, participants play against a computer that always plays optimal strategies, that is, it will play mobilize for sufficiently low signals. This eliminates the possibility that the effect of fear might work through pessimism about other players’ actions. In the third type of round, full information participants receive the true value for θ, which eliminates the potential mechanism of pessimism about its true value. ^{Footnote 10} Finally, in order to analyze whether fear reduces mobilization by increasing risk aversion, the values of R and c are varied together to vary the stakes of the game while maintaining the same equilibrium prediction. If fear increases risk aversion, we should see that people are less likely to mobilize when the stakes of the game are higher.

Analysis

This experimental design enables us to estimate several parameters of interest. Specifically, we test first for the overall effect of fear on mobilization decisions and then use the variations in the game to test for the relative importance of several potential mechanisms by which fear could reduce cooperation. For each quantity of interest, we estimate the average treatment effect (ATE) with and without demographic and round controls.

The main outcome of interest is whether the participant chooses to mobilize. We hypothesized that participants assigned to the fear treatment should be less likely to mobilize than those in the control group. For each participant, we observe 15 different mobilization decisions in 15 slightly different scenarios. To test for the main effect of fear, we use the results of the rounds in which we do not shut down any of the potential channels (i.e., the five rounds in which players are paired with a human and there is noise on the signal). ${Y_{i,t,standard}}(T)$ therefore represents the decision of individual i in round t of the five standard rounds in condition $T \in \{ 0,1\} $ , where 1 is the fear treatment and 0 the control. It takes a value of 1 if i plays $Mobilize$ and 0 is she does not. $AT{E_T}$ represents the ATE of fear across individuals and rounds.

(4) $$AT{E_T} = E[{Y_{standard}}(1) ]- E[{Y_{standard}}(0)]$$

We estimate the ATE using a linear probability model in which the individual decision to mobilize is the dependent variable and includes round fixed effects. We carry out analysis at the level of the participant-round. Because randomization occurs at the session level, we cluster standard errors by session.

Second, we test for potential channels by which fear could reduce mobilization by examining variations of the game. The first potential mechanism, M1, is pessimism about how partners will behave. To test whether fear makes people pessimistic about what their human partner will do, we test (1) the effect of fear in the rounds in which someone is paired with a computers, and (2) whether the effect of fear is larger in the standard rounds in which the participant is paired with a human than in those in which she is paired with a computer. The first effect is obtained analogously to that in equation (4), estimated using the rounds in which players are paired with a computer. The second, $AT{E_{M1}}$ , represents the portion of the ATE attributable to M1, expectations about others’ actions.

$$AT{E_{M1}} = (E[{Y_{standard}}(1)] - E[{Y_{standard}}(0)] )- (E[{Y_{computer}}(1)] - E[{Y_{computer}}(0)])$$

The portion of the total effect that we will attribute to expectations about how other humans will behave is captured in the difference in mobilization between the 5 standard rounds and the 5 rounds in which the participant plays against a computer. This effect is recovered by ${\beta _2}$ in the following linear probability model:

$${Y_{i,t}} = \alpha + {\beta _0}Compute{r_t} + {\beta _1}Fea{r_i} + {\beta _2}Fea{r_i} \times Compute{r_t} + {\varepsilon _{i,t}}$$

where $Compute{r_t}$ is an indicator of whether someone was facing a computer in that round and Fear_i and indicator that the subject was in the treatment condition, ${\varepsilon _{i,t}}$ is the error term. The second potential channel is pessimism about the signal that participants receive. Similar to the above case, we estimate both whether this channel is at play and the effect that fear has when we shut down the channel. The first is done by comparing participants’ decisions in the treatment condition to those in the control condition when there is no noise in the signal. For the latter, we compare the effect in the standard rounds in which the participant receives a noisy signal (a signal drawn from a normal distribution around the true strength of the regime) to those in which they receive a true signal.

$$AT{E_{M2}} = (E[{Y_{standard}}(1)] - E[{Y_{standard}}(0)]) - (E[{Y_{fullinfo}}(1)] - E[{Y_{fullinfo}}(0)])$$

This quantity of interest is obtained by estimating ${\beta _2}$ in the following regression:

$${Y_{i,t}} = \alpha + {\beta _0}FullInfot + + {\beta _1}Fea{r_i} + {\beta _2}Fea{r_i} \times FullInf{o_t} + {\epsilon _{i,t}}$$

Third, fear could reduce mobilization by increasing risk aversion. We test for changes in risk aversion by testing whether fear has a larger effect on rounds with higher spreads between the payoffs for winning and losing. We randomize the payoffs such that each participant gets a randomly selected payoff scheme in each round. ATE _spread=1.5 ATE _spread=5.5 Because we predict that the ATE will reduce linearly with the increase in the spread if fear increases risk aversion, our main test of whether the effect of fear is larger for higher payoff spreads will be based on regression analysis that allows us to use the full variation in the payoffs across rounds:

$${Y_{i,t}} = \alpha + {\beta _0}Sprea{d_{i,t}} + {\beta _1}Fea{r_i} + {\beta _2}Fea{r_i} \times Sprea{d_t} + {\epsilon _{i,t}}$$

where Fear _i is a dummy variable that takes a value of 1 if the subject is assigned to the fear emotion induction and Spread _i is a measure of the spread of the payoffs for the round that vary from 1.5 to 3.5 experimental currency units. The coefficient β ₂ estimates the extent to which the effect of the fear treatment varies based on the spread of the payoffs.

In addition to these substantive analyses, we carry out several manipulation checks. Our main manipulation check tests whether the treatment successfully induced fear without inducing substantively large levels of other emotions using self-reported levels of six emotions after all rounds were played. In addition to these self-reports, we also analyze salivary α-amylase as an indicator of the SAM response (Buchanan, Bibas and Adolphs Reference Buchanan, Bibas and Adolphs2010).