PROPUESTA ECONÓMICA

In the previous subsection we concluded that imitating oneself is faster than imitating others. Decisions where a player imitates him- or herself are in line with both imitation and inertia, because the previous action is repeated. It is hence legitimate to ask whether the results regarding positive reinforce- ment are just due to the involvement of a further behavioral rule, namely inertia. Alós-Ferrer et al. (2016b) recently found that decision inertia causes error-rate asymmetries in the belief-updating task of Achtziger and Alós- Ferrer (2014), but the process is considerably weaker than reinforcement and is washed away by the latter. Hence, we will exploratively test for the ef- fects of inertia in the cases where it is not aligned with imitation, because the alignment of imitation and inertia corresponds to positive reinforcement. That is, we restrict the tests to decisions not aligned with imitation. In case of conflict between imitation and myopic best reply, this means that we test within correct decisions, i.e. decisions following myopic best replies. In case of alignment between imitation and myopic best reply, it means we test within errors.

Figure 4.9 shows the response times of decisions that are in line with in- ertia (“stay” decisions) and those that are not (“shift” decisions). The figure displays those response times for three subsets of our data, i.e. the pooled data for Experiment 1 (left-hand side) and both treatments (NoLoad and Load) for Experiment 2 (right-hand side). Within each subset the left-hand side corresponds to response times of correct decisions which are differenti- ated according to whether the decision followed inertia, resulting in a “stay” best reply, or not, resulting in a “shift” best reply.

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While it is often useful to think of decision processes in dichotomous terms as “auto- matic” or “controlled,” this is just a simplification. The automaticity dimension is best conceived of as a continuum, and all that can be concluded when comparing different processes is whether one is more automatic than another one or not.

*** ** ** Experiment 1 Experiment 2 0 2 4 6 8 10 12 14 16 18

Average Response Time (s)

Conflict Alignment Conflict Alignment Conflict Alignment Pooled Data No Cognitive Load Cognitive Load

Inertia Decisions Non−Inertia

Figure 4.9: Average response times of of stay and shift correct decisions and errors.

Notes. _{Left-hand side: Experiment 1. Right-hand side: Experiment 2 separated by the} cognitive load treatment. Each subset shows stay and shift correct (myopic best reply) decisions in case myopic best reply and imitation were in conflict and stay and shift errors in case myopic best reply and imitation were aligned. ⋆_{p < 0.1,}⋆⋆ _{p < 0.05,}⋆⋆⋆_{p < 0.01,}

WSR test.

In Experiment 1, stay best replies averaged 12.10 s compared to 12.24 s for shift best replies, and the difference is not significant (WSR, N = 79, z = −0.117, p = 0.9066). Hence, there is no evidence for an involvement of pure inertia in the correct decisions in Experiment 1. Now consider the case of errors, for which the right-hand side within each subset shows the response times of errors, i.e. non-best replies, in the case where myopic best reply and imitation were aligned. In Experiment 1, stay (inertia) errors were significantly faster (mean 12.41 s) than shift errors (mean 14.62 s; WSR, N = 50, z = −2.833, p = 0.0046). This difference is interesting. In case of alignment between imitation and myopic best reply, errors do not follow from imitation, and shift errors do not follow from inertia either. Although this is

a post hoc interpretation, this result might point out that the shift errors in this case possibly include some decisions following higher-order reasoning, as in the case of the noise errors discussed in the regression analysis of Section 4.3. This suggests even more behavioral rules are at work than we focused on in this work.

The results of the NoLoad treatment in Experiment 2 obtains the same conclusions as in Experiment 1, as expected since it is a replication. In the NoLoad treatment, stay best replies averaged 14.31 s compared to 14.58 s for shift best replies, and the difference is not significant (WSR, N = 43, z = −0.169, p = 0.8658). In the case of alignment, stay (inertia) errors were significantly faster (mean 13.36 s) than shift errors (mean 16.08 s; WSR, N = 21, z = −1.964, p = 0.0496). Hence, there is no strong evidence for an involvement of a pure inertia process for the correct decisions while shift errors might following higher-order reasoning in the NoLoad treatment.

In the cognitive Load treatment we find the opposite to be true. In the case of conflict, the response times of stay best replies (mean 9.81 s) were significantly faster than shift best replies (mean 11.43 s), in contrast to the findings in Experiment 1 and the NoLoad treatment (WSR, N = 40, z = −2.554, p = 0.0107). Hence, there is evidence for an involvement of pure inertia in the correct decisions. We also find a different result for stay and shift errors in case myopic best reply and imitation were aligned. Stay (inertia) errors were not significantly faster (mean 11.17 s) than shift errors (mean 12.59 s), contrary to the findings in Experiment 1 and the NoLoad treatment (WSR, N = 17, z = −1.112, p = 0.2659).23

The influence of inertia on decisions is affected by the cognitive load ma- nipulation. In Experiment 1 and the NoLoad treatment there is no significant difference for stay and shift best replies but there is one in the Load treat-

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Conservative tests at the block level generally obtain the same results and conclusions. Only the comparison of stay and shift best replies in conflict situations in the Load treat- ment yields a different conclusion on the block level and is non-significant (stay best replies, mean 9.83 s; shift best replies, mean 11.14 s; WSR, N = 6, z = −0.943, p = 0.3454). Note that the non-significant result for stay and shift errors in the Load treatment are not due to the low number of observations. We also find a non-significant result when not requir- ing at least two observations per individual (mean stay errors 11.43 s; mean shift errors 11.92 s; WSR, N = 50, z = −0.729, p = 0.4661).

ment. This suggests that under cognitive load the alignment with inertia promoted the use of the shortcut of the very fast heuristic and made deci- sions significantly faster. For stay and shift errors it is the opposite case, i.e. there is a significant difference for stay and shift errors in Experiment 1 and the NoLoad treatment but there is none in the Load treatment suggesting that cognitive load reduced the complexity of some behavior leading to shift errors. Hence, we find another difference between the behavioral rules of imitation and myopic best reply. The alignment with inertia (whether it is a “stay” or a “shift” decision) affects imitative decisions in a different way than myopic best reply decisions. With our cognitive load manipulation, we do find a difference between the more automatic and intuitive behavioral rule of imitation and the more controlled one of myopic best reply. This finding provides further evidence that these processes are different and codetermine behavior in Cournot oligopolies.

In any case, this is evidence that the interaction with inertia (whether a decision is a “stay” or a “shift”) affects imitative decisions in a different way than myopic best replies. Hence, we aim to conduct a robustness test of our results regarding Hypotheses H1 and H2 controlling for the effects of inertia. Figure 4.10 shows the average response times for Experiment 1 and both treatments of Experiment 2 while excluding all observations which were additionally aligned with inertia. Let us start with H1, which concerns the case of conflict between imitation and myopic best reply. We compare shift best replies to imitating-others errors. The comparison is shown for Experi- ment 1 in the left-hand side of Figure 4.10. Again, errors (mean 12.04 s) are significantly faster than correct responses (mean 12.61 s; WSR, N = 118, z = −2.029, p = 0.0425), confirming H1 even when all inertia decisions are excluded from the analysis. Hypothesis H2 concerns the case of alignment between imitation and myopic best reply. We are hence comparing shift best replies (which were also imitating-others decisions) to shift errors. The com- parison is shown in the right-hand side of the subset for Experiment 1 in Figure 4.10. This time, errors (mean 15.20 s) are not significantly different from correct responses (mean 13.82 s; WSR, N = 25, z = 1.063, p = 0.2879), not confirming H2 when all inertia decisions are excluded from the analy-

** *** *** Experiment 1 Experiment 2 0 2 4 6 8 10 12 14 16 18

Average Response Time

Conflict Alignment Conflict Alignment Conflict Alignment Pooled Data No Cognitive Load Cognitive Load

Error Correct

Figure 4.10: Average response times of correct decisions and errors excluding inertia decisions.

Notes. _{Left-hand side: Experiment 1. Right-hand side: Experiment 2 separated by the} cognitive load treatment. Each subset shows correct decisions and errors in case myopic best reply and imitation were in conflict and in alignment. ⋆ _{p < 0.1,} ⋆⋆ _{p < 0.05,} ⋆⋆⋆ _{p < 0.01, WSR test.}

sis.24

Hence, the predictions of the DPDM (Achtziger and Alós-Ferrer, 2014; Alós-Ferrer, 2018) are confirmed.

Also in the NoLoad treatment of Experiment 2 we find that in conflict situations, errors (mean 12.41 s) are significantly faster than correct responses (mean 14.84 s; WSR, N = 68, z = −3.605, p = 0.0003), confirming H1 even when all inertia decisions are excluded from the analysis and replicating the results of Experiment 1 with fewer observations. Regarding H2, we do

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Testing at the block level shows significantly faster errors than correct response in conflict situations and significantly slower errors than correct responses in alignment sit- uations. Also, the test on the individual level not requiring at least two observations per subject yields significantly slower errors (mean 14.51 s) than correct responses (mean 12.88 s; WSR, N = 71, z = 2.131, p = 0.0330).

not obtain significant results and cannot confirm the prediction. Shift errors (mean 14.76 s) are not significantly slower than shift best-replies in alignment (mean 16.24 s; WSR, N = 13, z = −0.943, p = 0.3454).25

For cases of conflict in the cognitive load treatment, we find that errors (mean 9.35 s) are significantly faster than correct responses (mean 10.70 s; WSR, N = 62, z = −3.130, p = 0.0017). As in all the other conflict situations we confirm prediction H1. However, as before we do not obtain significant results for H2 in the Load treatment for alignment situations. Errors (mean 9.97 s) are not significantly slower than correct responses (mean 8.51 s; WSR, N = 10, z = 1.376, p = 0.1688), not confirming H2 when all inertia decisions are excluded from the analysis.26

One obvious explanation for not obtaining significant results for Hypoth- esis 2 is the strongly reduced amount of observations after excluding all stay decisions. In case of alignment the number of overall decisions is already rel- atively low compared to conflict situations and is further split into errors and correct response. When excluding all decisions which are additionally aligned with inertia the overall number of errors and correct response is very low (Ex- periment 1: 491 errors and 121 correct responses out of 6,144 observations; Experiment 2, NoLoad treatment: 227 errors and 70 correct responses out of 3,456 observations; Experiment 2, Load treatment: 185 errors and 74 correct responses out of 3,456 observations). Not only are there few observations left, there are also only few individuals who have more than one observation for creating the average response times. We cannot confirm the predictions of H2, however, we confirmed the predictions of H1 even when excluding inertia decisions from the analysis in Experiment 1 and both treatments in Experiment 2.

25

The same conclusion obtains testing the block level.

26

Tests at the block level yield the same conclusion for conflict situations and obtain significant slower errors (mean 11.81 s) than correct responses (mean 9.87 s; WSR, N = 6, z = 1.782, p = 0.0747) in contrast to the results on the individual level.