Download Impact of Game Conditions on Cooperative Behavior: Benign vs. Malign Games and more Study notes Psychology in PDF only on Docsity!
Correspondence Bias
Yi Han, Yiming Liu, and George Loewenstein∗
June 4, 2020
Abstract When drawing inferences about a person’s enduring characteristics from her actions, corre- spondence bias is the tendency to overestimate the influence of the person’s enduring character- istics and underestimate the influence of transient situational factors. Focusing on incentives as one important situational factor, we build a simple model to formalize correspondence bias, and test predictions of the model in an online experiment. All players first play the dictator game, as the dictator, with an unknown receiver. Next, depending on their experimental condition, players are assigned to play a ‘benign’ game that encourages cooperation with another player, a ‘ma- lign’ game that encourages selfish behavior, or both games with different players. Everyone then chooses to receive the dictator givings from one of two players who they may have played the be- nign or malign game with. Consistent with correspondence bias, subjects are on average willing to pay to receive the dictator givings from a player with whom they played the benign game. We show, further, that experiencing both games oneself, as opposed to playing one and observing the other, reduces the bias, and receiving information about how each of the players behaved in both games, eliminates it.
∗Han: Department of Economics, University of Pittsburgh, yi.han@pitt.edu; Liu: Humboldt University of Berlin, WZB Berlin Social Science Center, yiming.liu@wzb.eu; Loewenstein: Social and Decision Sciences, Carnegie Mellon University, gl20@andrew.cmu.edu. We thank Kareem Haggag, David Huffman, Lise Vesterlund, Alistair Wilson for helpful comments.
1 Introduction
When drawing inferences about a person’s enduring characteristics from their behaviors, the cor- respondence bias (Jones and Harris, 1967; Ross, 1977; Gilbert and Malone, 1995) is the tendency to overestimate the influence of the person’s enduring characteristics on decisions they make, and to underestimate the impact of situational factors, such as social pressures. The situational factor of greatest interest to economists is the incentives that an individual faces. One setting in which incentives matter is in decisions to cooperate or defect in interpersonal in- teractions. In economic games for which defection is a dominant strategy, prior research has found that people cooperate more when the payoff from mutual cooperation is higher (Charness, Rigotti and Rustichini, 2016), when “punishment” from cooperating unilaterally is smaller, and when the payoff from defecting against a cooperator is lower (Mengel, 2018). Correspondence bias, in such situations, would predict that observers will underestimate the impact of the incentives that players face, and so, in games that incentivize defection, attribute other’s uncooperative behaviors to their negative traits such as selfishness. Perhaps reflecting such an effect, a common belief is that the rich are more selfish than the poor. This belief most likely stems from the observation that they avoid taxes more often than others (Chris- tian, 1994; Alstadsæter, Johannesen and Zucman, 2019; Saez and Zucman, 2019), and break traffic laws more often (Piff, Stancato, Cˆot´e, Mendoza-Denton and Keltner, 2012). However, Andreoni, Nikiforakis and Stoop (2017) argue that the differences in behaviors can be fully explained by differ- ences in incentives. The rich have greater incentive and ability to protect their income from taxation, and paying traffic tickets is less painful for them due to the diminishing marginal utility of money. The rich may actually be similarly generous as the poor (Andreoni, Nikiforakis and Stoop, 2017), but correspondence bias will lead people to attribute their behaviors to negative character traits. Correspondence bias, which was previously overlooked by economists, has important implica- tions for everyday life. Consider two regions (countries, neighborhoods, etc.) or ethnic groups where social norms (or institutions) are starkly different. Person A is from region/group 1 where unethical behaviors are harshly punished and everyone finds it optimal to be trustworthy. Person B is from region/group 2 where legal enforcement is weak and sabotaging others is common. Now a person C needs to choose one of the two to work with or hire. She observes that A behaved more ethically in the past than person B. If she is correspondence-biased, then she may jump to the conclusion that A
game is the classic prisoner’s dilemma game in which the dominant strategy is to defect, while the benign game is the Harmony Game (Dal B´o, Dal B´o and Eyster, 2018) in which the dominant strategy is to cooperate. At the end of the second stage, subjects are able to see the actions of one or more players, and to obtain information about the payoff structure of the games they played. Based on this information, in the third stage, they choose which of two players to receive the dictator givings from, and we use a multiple price list to elicit their willingness to pay (WTP) for their preferred player. We address the Bayesian updating confound by randomly assigning players to the two games. This randomization ensures that the benign-game players and malign-game players are equally likely to be the Good type ex ante. The Martingale property of Bayesian beliefs then implies that the expected posterior beliefs are the same; a Bayesian model predicts that the individual will be in expectation indifferent between receiving the dictator offerings of the two players. However, our model predicts that a correspondence-biased individual will be (in expectation) willing to pay a positive amount to be matched with the benign-game player. Our design avoids the possibility that reciprocity could drive the results by using a dictator game in which there are no actions that the receiver can take; thus, there is no way to reciprocate the benign-game player’s cooperation in the follow-up game. Finally, we avoid the potential for participation in the benign or malign game to shape the player’s prosociality by sequencing the dictator decision so it occurs before stage 2. Even if individuals be- come more prosocial after playing the benign game, the dictator decision will have already been made in Stage 1, and cannot be altered by the game. To better understand correspondence bias, and to explore potential methods to reduce it, we uti- lize a 4-Treatment design. The treatments differ in how many games subjects play, and how much information they receive. In Treatment 1, subjects only play one game and are completely unaware of the other game. In Stage 3 they choose whether to obtain the dictator givings of the person they played either the benign or malign game with or those from a randomly chosen other player. In Treatment 2, subjects still only play one game as in Treatment 1, but those who played the benign (malign) game also learn about the action of a malign-game (benign-game) player at the end of Stage 2. In this treatment they are informed about the payoffs of the game played by the other player, as well as the other player’s action, but they do not experience the game themselves. In Stage
3 they choose between the player they played with in Stage 2 and the player who they only received information about. In Treatment 3, subjects actually play each of the games with two different partners in Stage 2. In Stage 3, they then choose whether to obtain the dictator givings of their Stage 2 benign- or malign-game partner. The setup of Treatment 4 is the same as in Treatment 3, with the exception that subjects are also informed of both of their partners’ actions in the other game (benign for the malign-game partner and malign for the benign-game partner) that each of their partners plays with someone else. Our results show, first, that correspondence bias exists and influences Stage 3 decisions. We measure the impact of correspondence bias through the benign premium – the extra amount a subject, in stage 3, is willing to pay for the dictator game givings of a benign-game player compared to the dictator game givings of a malign-game player, which the players had decided upon in Stage 1. While the rational Bayesian model predicts the benign premium to be 0, we find that the benign premium is 11.67 cents on average in Treatment 2, the baseline treatment, which is significantly different from 0 at the 1% level. To receive the dictator game givings of the player who is randomly assigned to the benign game, subjects are on average willing to give up 6% of the $2.00 divided by the dictator (which is the largest possible difference between the two potential dictators), or 12% of the $1. (half of the ‘pie’ is the typical modal amount given in the dictator game; only 11 out of 817 subjects, or 1 percent of subjects, in our experiment gave more than $1.00). Second, and consistent with the predictions of our model, we find that correspondence bias is driven by both overestimation of the prosociality of the benign-game player and by underestimation of the prosociality of the malign-game player. In Treatment 1, when choosing between a stranger and a benign/malign-game player, subjects are willing to pay more for dictator givings of a benign-game player compared to a stranger, and willing to pay more for dictator givings of a stranger compared to a malign-game player. We also test two potential methods to reduce or even eliminate correspondence bias. First, we test whether experiencing instead of observing the games can help to reduce the bias. Given that they are likely to behave differently in the two games, themselves, experiencing both games in Treatment 3, as opposed to only learning about it in Treatment 2, should help people to understand that actions are likely to be game-contingent, and they should take the games into account when inferring from the actions. Consistent with such an effect, we find that the benign premium in Treatment 3 is smaller
spite being informed about the random assignment to position, subjects still rate speakers who speak in favor of the opinion as more supportive of it. The most common explanation that psychologists offer for the correspondence bias is that, when attempting to make sense of a person’s behavior, the characteristics of the person are typically more “salient” than their situation, resulting in an overestimation of the influence of the former, and an underestimation of the latter. We formulate the bias in a different way. We are less focused on the salience of other people’s characteristics, but more on assessments of their stability. In our formulation in the following section of the paper, it is people’s failure to fully account for the incentive-contingent nature of other’s actions that leads them to under-attribute actions to incentives. The current study augments the existing psychology research on correspondence bias in three ways. First, the standard experimental paradigm for studying correspondence bias in psychology suffers from the potential confound that subjects may believe that the randomly assigned positions can potentially shape the speakers’ attitudes. As we discussed, our design rules this out. Second, in an environment that closely mimics real-life interpersonal interactions, our design clearly shows that correspondence bias is welfare-reducing. Third, we provide a suggestion for how to reduce or eliminate correspondence bias by providing counterfactual information. We also contribute to the literature on people’s belief updating relative to Bayesian updating. Pre- vious evidence suggests that people generally infer less from evidence than Bayes’ Theorem predicts (Phillips and Edwards, 1966; Edwards, 1968; M¨obius, Niederle, Niehaus and Rosenblat, 2014; Am- buehl and Li, 2018). However, as pointed out by Kahneman, this finding is in contrast to the everyday experience that people often jump to conclusions based on little information. We provide another rea- son, in addition to the Law of Small Numbers (Kahneman and Tversky, 1972) and base-rate neglect (Kahneman and Tversky, 1973), for why people may draw overly extreme conclusions from small samples.^1 In our case, people jump from observations of others’ actions in narrow contexts to con- clusions about those people’s underlying qualities, without paying sufficient attention to the transient incentives they are facing. The paper proceeds as follows: Section 2 describes a simple model of correspondence bias. Sec-
(^1) For more discussion on over-inference, see Benjamin (2019).
tion 3 introduces our experimental design and the predictions it tests. Section 4 presents results, and Section 5 concludes and discusses policy implications.
2 Model
In this section, we build a simple model of correspondence bias that is in a similar spirit to the cursed equilibrium of Eyster and Rabin (2005). In our model, the individual does not fully take into account the fact that other people’s actions depend on the incentives they face (or the game they play); they are aware of the distributions of others’ actions, but underestimate the correlation between actions and the game structure when they try to interpret those actions. Consider two games τ ∈ {b, m}, the benign game b and the malign game m. In each complete information game, there are two actions to take: {C, D}. There are two types of agent, the Good type G and the Bad type B. Let the probability of being the Good type be P(ti = G) = p 0. In the benign game τb, both the Good type and the Bad type choose C; in the malign game τm, the Good type chooses C and the Bad type chooses D. Half of the players are assigned to play the benign game, and the other half are assigned to play the malign game. After observing player i’s action in the benign game abi and player j’s action in the malign game amj , player k needs to choose between i and j to play a follow-up game. k’s payoff in the follow-up game is defined by the type of the partner of her choosing. If we standardize the payoff of choosing type B to 0 and choosing type G to 1, then player k’s expected payoff for choosing i to play the follow-up game with is given by
Uki = P(ti = G) − P(t (^) j = G). (1)
Without loss, the payoff for choosing j is standardized to 0.^2 Define p(·) as the true probability and π(·) as a person’s potentially biased belief. For a Bayesian agent, as both types choose C in the benign game, the posterior π(ti = G | abi ) = p(ti = G | abi ) is
(^2) By formulating the expected payoff in this way, we assume that the decision maker is risk neutral. However, our main results remain unchanged by assuming risk aversion.
However, the correspondence-biased agent would believe that the expected payoff of choosing i, ˜Uki, is U˜ki = π˜Cb − π˜Dm. (5) As ˜πCb > πCb and ˜πDm = πDm , ˜Uki > Uki. Similarly, when abi = C and amj = C, as ˜πCb > πCb and ˜πCm < πCm , U˜ki is also larger than Uki. As U˜ki is larger than Uki in both cases, we conclude that the perceived payoff for choosing the benign-game player is larger for the correspondence-biased agent. For a Bayesian agent, the expected benefit of choosing i is 0. The Martingale property of Bayesian updating implies that E[π | τ = b] = E[π | τ = m] = E[π] = p 0. (6) Intuitively, as whether one is assigned to the benign game or the malign game is completely deter- mined by chance, i and j are equally likely to be the Good type ex ante. As the expected posterior is equal to the prior, they are equally likely to be the Good type in expectation ex post. However, for a correspondence-biased agent, the expected benefit of choosing i is larger than 0. As ˜πCb > πCb = p 0 for the biased agent, E[ π˜ | τ = b] > p 0. As πDm = π˜Dm and ˜πCm < πCm , E[ π˜ | τ = m] < E[π | τ = m] = p 0. Therefore, for a correspondence-biased agent
E[π ˜ | τ = m] < p 0 < E[ π˜ | τ = b] (7)
Definition. We define a correspondence-biased agent’s benign premium as her expected payoff of choosing the benign-game player over the malign game player, namely E[ π˜ | τ = b] − E[ π˜ | τ = m]. We summarize our main results in the following proposition. Proposition 1. i) A Bayesian is in expectation indifferent between a benign-game player and a malign-game player to play the follow-up game with, and is expected to pay E[π | τ = b] − E[π | τ = m] = 0 for the benign-game player. ii) For any χ ∈ ( 0 , 1 ], a χ-biased individual’s benign premium E[ π˜ | τ = b] − E[ π˜ | τ = m] is larger than 0. iii) For any χ ∈ ( 0 , 1 ], a χ-biased individual is willing to pay E[ π˜ | τ = b] − p 0 > 0 in expectation for a benign-game player when choosing between the benign-game player and a stranger, and is willing to pay p 0 − E[ π˜ | τ = m] > 0 for a stranger when choosing between the stranger and a malign-game player. While a Bayesian is in expectation indifferent between a benign-game player, a malign game
player, and a stranger.
3 Design
The experiment has three stages. In the first stage, all subjects make a decision as the dictator in the dictator game. In the second stage, they are randomly matched into groups of 4 to play the benign game and the malign game. The benign game was chosen to encourage players to cooperate with their partners, while the malign game was chosen to motivate selfish behavior. Lastly, they are asked, as the receiver, to choose between receiving the dictator givings of two players from the first stage. Our model predicts that there exists a benign premium: subjects are, on average, willing to pay to be matched with the benign-game player.
First Stage
The experiment was conducted online, and subjects were recruited through Amazon Mechanical Turk (Mturk). Upon arriving at the study website, each subject was instructed to play a dictator game as the dictator. They divided 200 cents between themselves and a random receiver. As in a standard dictator game, the receiver had no influence over the outcome of the game, and both the receiver and the dictator receive 50 cents of endowment prior to the split decision. Subjects were also informed that, although everyone needed to make the decision, only half of those decisions would be implemented later. At this stage, they had no idea of the existence or nature of the future stages of the experiment or of the identity of the potential random receiver. This dictator decision serves as our measure of each subject’s prosociality.
Second Stage
In the second stage, subjects were randomly matched into four-player groups. Everyone was randomly assigned a role. There were four roles in each four-player group. We name them A, B, C and D. Then, the participants played the benign and/or the malign games with individuals in their own group. Depending on the treatment, a subject interacted with one or two individuals at this stage. The two games are defined as follows. The malign game is a two-player one-shot prisoner’s dilemma, see left panel in Table 1. Partic-
sure that they had the time to understand the game structure and make inferences about the types of their partners based on their actions.
Third Stage
In the third stage, every subject had the opportunity to choose whether to receive the dictator transfer from the first stage either from a malign-game player and a benign-game player. In this second condition, one of them was the player they had played with, and the other was the player whose play they only learned about. The two candidates are those two whose actions in Stage 2 were shown to the subject in the information provision phase. For example, A played the benign game with B and observed D’s action in the malign game. Then in Stage 3, A chose between B and D’s dictator transfers in the first-stage dictator game. Therefore, the only source of information that the subject had to go on when choosing between the two candidates was the action that each had taken in the game they played in Stage 2 (as well as the payoffs for these games). After reading the instructions for Stage 3 and before making any decisions, subjects were asked three comprehension questions. Only those who answer all three questions correctly could proceed to make their choices in this stage; those who answered at least one question incorrectly were required to re-do all three questions until they get them all right.^4 After a subject made the choice between the two candidates, we used a multiple price list to elicit her WTP to be matched with the partner of her choosing. The list shown to A if she chooses B over D in the first choice is displayed in Table 2 as an example. In total, subjects made 10 choices, excluding the first one. In each choice, there were two options. D+(x cents) means if in this choice A chooses D, and this is the choice selected at random to count, then she will then get an extra reward of x cents. But if she chooses B, there is no extra reward. The point where A switches from option 1 to option 2 defines A’s WTP to get B. One of these 11 choices (including the one between B and D with no extra
(^4) Please see Appendix A1 for the comprehension questions. As one cannot proceed to the decision stage of Stage 3 without answering all 3 questions correctly, some subjects dropped out in this stage. Out of 1,008 subjects who signed up for the experiment, 151 of them finished Stage 2 but dropped out in Stage 3. As Stage 3 is not interactive, the dropouts of those subjects have no impact on the use of data from others in the same group. Moreover, there is no significant difference in attrition rate across treatments.
rewards) was randomly selected as the choice-that-counts, and the instructions made this clear. We then implement one of the four choice-that-counts with a designated matching protocol. Our matching protocol in stage 3 was designed to deal with a potential confound of correspon- dence bias. One way to reciprocate the benign-game player is to choose her as the dictator in the stage 3 as dictators are expected to earn more than receivers. The protocol can be divided into 4 steps. In the first step, we randomly chose 1 player from the 4. Let us name her the chosen player and assume it was A. Second, both the chosen player’s (A) benign- and malign-game partners (B and D) got the dictator role. Therefore who played as the dictator and who played as the receiver in the first stage dictator game were determined at the second step. The next steps only affected the matching between the two dictators and the two receivers. In the third step, we implemented the chosen player’s (A) choice-that-counts. Suppose A chose B’s dictator offerings in that choice, then A and B were matched with B as the dictator. Fourth, the partner whom was not picked by the chosen player A, D in our example, was matched with the remaining player C. D’s dictator transfer decision was carried out, and C received D’s offerings as the receiver. The fact that D was the dictator but not C was determined in step 2. Therefore, who got dictator roles was completely determined by whom was randomly selected to be the chosen player in the matching protocol, choosing a player as the dictator in stage 3 did not raise her chances of being the dictator in the dictator game. The dictator’s decisions made in Stage 1 were then carried out. For example, suppose B chose to give x cents to the random receiver in the first stage, and if A and B are matched with B being the dictator, then A gets x cents and B gets (200 − x) cents. Putting the dictator decision ahead of the second-stage games solves the institution shaping people’s prosociality confound. The idea is that, at the third stage, the dictators had already made their decisions about how much to transfer in the first stage. Therefore, what happened at the second stage could not have an impact on them. Even if the benign-game player became a nicer person after playing the game, her choice in the first stage remained the same.
Treatments
There are four treatments in the experiment and they only differ in the second stage. What sep- arates them from each other is how many games each subject plays and how much information they are given.
Prediction 2. In Treatment 1, when choosing between a benign-game player and a random stranger, subjects are on average willing to pay more for the benign-game player; when choosing between a malign-game player and a stranger, they are on average willingness to pay more for the stranger. Treatment 1 aims to decompose the benign premium. As no information is provided on the stranger, the chance of her being the Good type is equal to the prior, p 0. Thus, Treatment 1 helps us separate the benign premium E[ π˜ | τ = b] − E[ π˜ | τ = m] into two parts: underestimation of the chance of the malign-game player being the Good type p 0 − E[ π˜ | τ = m] and overestimation of the chance of the benign-game player being the Good type E[ π˜ | τ = b] − p 0. While Bayesian inference predicts that E[π | τ = m] = E[π | τ = b] = p 0 , we predict that for correspondence-biased agents E[ π˜ | τ = m] < p 0 < E[ π˜ | τ = b].
Prediction 3. The benign premium is smaller in Treatment 3 than in Treatment 2. Treatment 3 is set to test whether inattention to strategic motives is a cause of correspondence bias. As participants play both games in this treatment, they have a better understanding of the incentives in the two games. In Treatment 2, the subject may only pay attention to behaviors without understanding the incentives behind them. Consequently, she tends to treat cooperation in the two games equally even though it is a much stronger signal of the Good type to cooperate in the malign game. When she plays both games herself in Treatment 3, she is more likely to know that choosing cooperation does not mean the same thing across the two games.
Prediction 4. The benign premium is smaller in Treatment 4 than in Treatment 3. In Treatment 4, we test whether providing counterfactual information reduces correspondence bias. In treatments 2 and 3, the participant was not able to know how the benign-game player per- formed in the malign game, and vise versa. However, in Treatment 4, such information was available, and subjects could clearly see how other’s actions changed according to the incentives. If corre- spondence bias is caused by failing to fully account for the impact of the incentives on actions, then enabling people to compare opponents’ behaviors in the same game with the same incentives should
those people’s behavior in other environments. Second, Treatment 2 is directly comparable to Treatment 3 and 4, as in all three of these treatments subjects chose, in stage 3, between a benign-game player and a malign-game player. In Treatment 1, in contrast, they chose between a benign or malign player and a stranger.
reduce the bias significantly.
Implementation
The experiment was conducted on Amazon Mechanical Turk between October 12, 2018 and De- cember 7, 2018. As our experiment is rather complicated, we only recruited subjects who had at least a two-year associate degree. We also restricted participation to residents of the United States who had completed at least 100 tasks prior to our study and had an approval rating of at least 95%. We advertised the experiment as a 20-minutes academic decision-making study with an average payment of 2.5 dollars. On average, the experiment lasted 20.1 minutes and subjects earned 2.77 dollars. Overall, we recruited 817 subjects in our online experiment, with 121 in Treatment 1, 246 in Treatment 2, 223 in Treatment 3, and 227 in Treatment 4.^6 We randomly assign fewer subjects to Treatment 1 based on a power calculation. We need more subjects in the other 3 treatments because we need to test whether the benign premium is significantly different between two treatments, whereas in Treatment 1, we only need to test whether the average WTP is significantly different from 0 or not. Table 3 shows summary statistics both in aggregate and across treatment conditions. All of the non-outcome behaviors and demographics are balanced. On average subjects shared 67 cents in the dictator game. 95.2% of subjects chose to cooperate in the benign game and 38.9% defected in the malign game. A natural concern is that subjects may behave differently in Treatment 2 and in treatments 3 and 4 as the number of games they play is different. Reassuringly, the cooperation rate in the malign game in Treatment 2 is not significantly different from the average cooperation rate in treatments 3 and 4 (p-value=0.486). We collected subjects’ demographic information in a voluntary follow-up survey. 735 out of 817 subjects (90%) completed the survey, and there is no significant difference in the take-up rates across treatments. Survey respondents have an average age of 38, 57% are female, and 80% have jobs (either employed or self-employed).
(^6) We received a total of 857 responses, but dropped 40 subjects (4.67%) who exhibited multiple switching points in the multiple price-list questions at the third stage.
of WTP, we use the mid-point of the interval as the WTP for the benign-game player.^7 For example, if subject A chooses B’s (the benign-game player) transfers over D’s (the malign-game player) transfers plus 10 cents bonus, and switches to D’s transfers plus 20 cents when choosing between it and B’s transfers, then A’s WTP for the benign-game player is coded as 15 cents. As shown in Figure 3, the average WTP for the benign-game player’s dictator givings is 11. cents higher than that for the malign-game player’s givings in Treatment 2, which is significantly larger than 0 at the 1% level. The Bayesian model is rejected. One way to interpret this result is that subjects believe that the benign-game player on average transferred 11.67 cents more in Stage 1 than the malign-game player. To put those numbers into perspective, one can compare them with the maximum plausible benign premium of 100 cents. A completely selfish individual transfers 0 in Stage 1, while an altruistic individual who weights other’s utility exactly as much as her own transfers 100 cents in Stage 1. Therefore, although larger values are possible (up to 200 cents), the largest plausible difference between the two potential opponents’ transfer is 100 cents. The benign premium can also be interpreted as a measure of the welfare loss caused by corre- spondence bias. To see this, consider the case when the expected dictator givings of the malign-game player are higher than that of the benign-game player from a Bayesian’s perspective but the difference between the two is smaller than the benign premium. While a risk-neutral Bayesian would choose the malign-game player, a risk-neutral correspondence-biased agent would still choose the benign- game player, leading to an expected welfare loss. The larger the benign premium, the more likely a correspondence-biased agent would forfeit a gain from choosing the malign-game player’s givings. On the aggregate level we confirm that subjects are correspondence-biased, a natural next question is how many subjects are correspondence-biased. This question is hard to answer when the malign- game player chooses to defect. Both the Bayesian model and our model predict that in this situation subjects should choose the benign-game player, and the only difference is that our model predicts a larger WTP towards the benign-game player. However, the case when the malign-game player chooses to cooperate is clear-cut. While a Bayesian subject should choose the malign-game player,
(^7) The results are robust if we use the lower or upper bound of the interval as the WTP for the benign-game player (Appendix Figure A1).
regardless of her prior, our model predicts that a fully correspondence-biased subject is indifferent between the two players and may choose the benign-game player. Our data show that 52% of subjects choose the benign-game player over the malign-game player when the latter choose to cooperate in Treatment 2 (Panel A of Table 6).
Result 2. Evidence suggests that correspondence bias is caused by both an overestimation of the prosociality of the benign-game player and an underestimation of the prosociality of the malign-game player.
In Treatment 1, subjects only play one game, and are asked to choose between receiving the dictator givings of the person they play this one game with, and those from a random participant. As predicted by the model, a Bayesian subject should be indifferent between her partner and a stranger in expectation regardless of which game she is assigned to play. However, the game an individual plays does have an impact on her WTP towards her partner. Treatment 1 is more comparable to previous studies in psychology on correspondence bias. We randomly assigned subjects to interact with someone in a benign environment (corresponding to the “against an opinion” condition in the psychology literature) or a malign environment (corresponding to the “in favor of an opinion” condition), and we test whether this randomly assigned environment had an impact on a subject’s evaluation of their partner or not (corresponding to asking subjects to rate the attitudes of the speaker towards that opinion). Our results show that the orthogonal environment has a strong effect on a subject’s WTP towards her partner. When the game played together is the benign game, the average WTP for partners over strangers is 12.62 cents; when it is the malign game, the average WTP for the partner is -7.24 cents, meaning subjects are willing to pay to receive the dic- tator givings from random strangers, rather than from their partners. The two WTPs are significantly different from each other (p-value<0.01, Wilcoxon rank-sum test), which serves as another piece of evidence of correspondence bias. Treatment 1 also serves as a test of the formulation of correspondence bias. If the bias is caused by people’s failure to fully account for the degrees to which incentives affect actions, then we would predict a preference for the benign-game player to the stranger and a preference for the stranger rather than the malign-game player. The results are consistent with this prediction. As shown above, the average WTP for the benign-game player is positive and is significantly different from 0, with a p- value of 0.025. Meanwhile, the average WTP for the malign-game player is negative (p-value=0.155).
