Replication and Robustness

Experiment 2 manipulates cognitive resources but also serves as a replica- tion of the FullInfo treatment of Experiment 1 and a robustness check of Hypotheses H1 and H2 under cognitive load. We follow the same steps as in Experiment 1 and analyze the data for each treatment, NoLoad and Load, separately. We calculated the average response times for each subject when she made a correct response or error when myopic best reply and imitation are in conflict or in alignment. Recall, H1 predicts faster errors in conflict situations and H2 predicts slower errors in alignment situations.

The left-hand side of Figure 4.6 shows the response times for conflict and alignment situations for the NoLoad treatment. As predicted by H1, imita- tion errors (11.79 s) are significantly faster than correct responses (14.67 s) in conflict situations. The difference is highly significant according to a Wilcoxon Signed-Rank test (N = 71, z = −4.991, p < 0.0001).16

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The correct responses in case of conflict are also not significantly across treatments (NoLoad, 23.81% correct responses; Load 23.87% correct responses; MWW, N = 144, z = 0.210, p = 0.8338).

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The analysis conditioning only on responses when the cognitive load task was recalled correctly yields the same conclusion.

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The final number of observations deviates from 72 because not all subjects had at least two decisions following imitation and myopic best reply.

0 .1 .2 .3 .4 .5 Relative Frequency

Errors Correct Correct

Alignment

Conflict No Cognitive Load Cognitive Load

Figure 4.5: Experiment 2, Relative frequency of errors and correct responses for NoLoad and Load treatments.

Notes. _{Left-hand side: Correct responses and imitation errors in case of conflict. Right-} hand side: Correct responses in case of alignment.

As predicted by H2, errors (14.79 s) are slower than correct responses (13.08 s) when myopic best reply and imitation are aligned. The difference is significant according to a WSR test despite fewer observations (N = 44, z = 1.926, p = 0.0542).17

In summary, we replicate the results of Experiment 1 in the NoLoad treatment with fewer numbers of observations.

The right-hand side of Figure 4.6 shows the response times in conflict and alignment situations for the Load treatment. As predicted by H1, imitation errors (8.27 s) are significantly faster than correct responses (10.75 s) in con- flict situations. The difference is highly significant according to a Wilcoxon Signed-Rank test (N = 70, z = −4.878, p < 0.0001). As predicted by H2,

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If we do not require at least two observation to create an individual’s average the resulting test yields only a non-significantly trend (mean errors 14.47 s, mean correct responses 13.17 s; WSR, N = 61, z = 1.512, p = 0.1305).

*** * *** ** 0 2 4 6 8 10 12 14 16 18

Average Response Time (s)

Conflict Alignment Conflict Alignment No Cognitive Load Cognitive Load

Error Correct

Figure 4.6: Experiment 2, Average response times of correct responses and errors.

Notes. _{Left-hand side: Average response times of correct responses and errors in case of} conflict and alignment in the NoLoad treatment. Right-hand side: Average response times of correct responses and errors in case of conflict and alignment for the Load treatment.

⋆ _{p < 0.1,}⋆⋆ _{p < 0.05,}⋆⋆⋆ _{p < 0.01, WSR test.}

errors (11.65 s) are significantly slower than correct responses (9.67 s) in align- ment. The difference is significant (WSR, N = 35, z = 2.375, p = 0.0176). In summary, we also confirm H1 and H2 in the Load treatment serving as a robustness check. The evidence presented above shows that the interac- tion of two behavioral rules, imitation being more automatic and myopic best reply being more controlled, is robust to cognitive load manipulations and codetermines behavior in a complex, dynamic setting such as Cournot oligopolies.

Before we turn to the regression models as in Experiment 1, we want to point out an interesting finding regarding the response times between the two treatments. Figure 4.7 simply reorders the average response times as shown

in Figure 4.6 and put for each decision the NoLoad and Load treatments next to each other. The picture clearly shows that participants made their decisions significantly faster in the Load than in the NoLoad treatment. A MWW test confirms that response times are significantly faster in the Load than in the NoLoad treatment.18

*** *** ** *** 0 2 4 6 8 10 12 14 16 18

Average Response Time (s)

Error Correct Error Correct

Conflict Alignment

No Cognitive Load Cognitive Load

Figure 4.7: Experiment 2, Average response times for the NoLoad and Load treat- ments.

Notes. _{Left-hand side: Conflict situations for the NoLoad and Load treatments. Right-} hand side: Alignment situations for the NoLoad and Load treatments. ⋆⋆ _{p < 0.05,} ⋆⋆⋆ _{p < 0.01, MWW test.}

These response time results in combination with the findings of non- significant differences in (choice) behavior show that the additional cognitive load task made the participants faster while not changing their behavior. This finding has also been explored in a series of cognitive load studies in

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Conflict situations: errors (p < 0.0001) and correct responses (p < 0.0001); Alignment situations: errors (p = 0.0291) and correct responses (p = 0.0018).

Achtziger et al. (2019), who also offer an explanation and propose it as a test of a successful cognitive load manipulation. The cognitive load, i.e. the additional task of maintaining a number in the working memory, did not slow down the participants but sped up the decision while not changing the choice behavior.

We now turn to a more detailed regression analysis as in Experiment 1 and look at the random effects panel regressions on the log-response times while clustering the standard errors at the block level. We consider the same regression models as in Experiment 1 with the one exception of a different treatment dummy. Starting with regression model 2, the Cognitive Load dummy, i.e. being 1 in the Load treatment and 0 otherwise, is introduced to the regressions.

Model 1 in Table 4.5 tests for the basic effects. The coefficient for Error × Conflict directly represents the difference between imitation errors and correct decisions in case of conflict. The coefficient is negative and highly significant, confirming Hypothesis H1. The coefficient for Error × Alignment directly represents the difference between errors and correct decisions in case of alignment. The coefficient is positive and highly significant, confirming Hypothesis H2. The coefficient for Conflict is positive and highly significant. This shows that correct decisions are slower in case of conflict than in case of alignment.

The Noise coefficient is also positive and highly significant showing that noise errors are slower than the imitation errors. As in Experiment 1, we take this as an indication that the category of noise errors is capturing higher cognitive, more complex decision processes or behavioral rules.

Models 2 and 3 add further controls and show that the results just re- ported are robust. The dummy called Cognitive Load is negative and highly significant showing that the decisions in the Load treatment are signifi- cantly faster than the decisions in the NoLoad treatment as seen in the non-parametric analysis. We find a significant time trend, i.e. the partici- pants become faster the longer they play reflected by the variable Normalized Time and dummies for parts 2 and 3. As in Experiment 1, we interpret this as familiarity with the interface or other learning effects, however, our main

Table 4.5: Experiment 2, Random effects panel regressions for ln(ResponseTimes).

ln(ResponseTimes) Model 1 Model 2 Model 3

Conflict 0.1691∗∗∗ _0.1621∗∗∗ _0.1627∗∗∗ (0.0304) (0.0251) (0.0250) Error × Conflict −0.2548∗∗∗ _−0.2060∗∗∗ _−0.2060∗∗∗ (0.0296) (0.0112) (0.0113) Error × Aligned 0.2068∗∗∗ _0.1717∗∗∗ _0.1718∗∗∗ (0.0347) (0.0313) (0.0307) Noise (in Conflict) 0.2407∗∗∗ _0.1939∗∗∗ _0.1946∗∗∗

(0.0312) (0.0158) (0.0155) Cognitive Load _−0.3452∗∗∗ _−0.3446∗∗∗ (0.0770) (0.0772) Normalized Time _−0.3116∗∗∗ _−0.3117∗∗∗ (0.0308) (0.0308) Part 2 _−0.1701∗∗∗ _−0.1701∗∗∗ (0.0249) (0.0209) Part 3 _−0.3054∗∗∗ _−0.3046∗∗∗ (0.0328) (0.0313) Payoff Table 2 0.0245 (0.0278) Payoff Table 3 0.0431∗∗ (0.0174) Collusion _−0.7449∗∗∗ _−0.7759∗∗∗ (0.0253) (0.0344) Constant 2.1329∗∗∗ _2.6304∗∗∗ _2.6067∗∗∗ (0.0757) (0.0675) (0.0693) R2 _{0.0467 0.1836 0.1840}

Notes. _{Standard errors, clustered by 6 matching blocks, in parentheses.} ∗ _{p < 0.1,} ∗∗ _{p < 0.05,}∗∗∗ _{p < 0.01.}

results remain robust. The collusion dummy is negative and highly signifi- cant, but the previous results and conclusions are not affected. A post-hoc linear combination test shows no significant difference between Payoff Table 2 and Payoff Table 3 (Linear Combination test, Payoff Table 3 - Payoff Table 2, coefficient= 0.0186, z = 0.732, p = 0.4639.)19

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Additional regressions controlling for demographics and psychological characteristics yielded the same qualitative results and conclusions.

In summary, we find strong evidence in our data suggesting multiple behavioral rules codetermine behavior in Cournot oligopolies. In particular, we find evidence for imitation, a more automatic and intuitive behavioral rule, and myopic best reply, a more controlled and rational behavioral rule.