So far, we have focused on the case of substitutes in whichwH <2 wM. In this section we vary the strategic setting and consider the opposite case, i.e. wH >2 wM, to check whether our results still hold when agents’contributions are complements. We invited 130 additional individuals in order to run our four treatments withwM = 110 instead ofwM = 172. All other parameters of the game remained the same. Table 2.7 presents our additional treatments that are indicated byX.
Table 2.7: Additional treatments of the team production setting
Treatment Signal Number of participants T-NOX no signal 18 T-IMPX e1 36 T-PX b 1 38 T-PPlusX e 1 and b1 38
As described in Section 2.3, e¤orts are strategic complements in T-NOX and the second mover’s reaction is predicted to increase in the signals in T-IMPX, T-PX, and
T-PPlusX.34 Furthermore, the self-interest model predicts the …rst mover to not work less but more when informative signals are available. Similar to the case of substi- tutes, no treatment di¤erences are predicted between T-PX and T-PPlusX. Table 2.8 summarizes the predictions of the self-interest model for our additional treatments.35
Table 2.8: Behavioral predictions for the additional treatments
Treatment e1 e2 T-NOX 61.05 61.05 T-IMPX 77.61 46.40 + 0.240 * e 1 = 65.02 T-PX 73.28 68.00 if b1 = 1 44.00 if b1 = 0 T-PPlusX 73.28 68.00 if b 1 = 1 44.00 if b1 = 0
The predictions are rounded to two digits after the decimal point.
Based on these predictions we formulate the following hypotheses.
Hypothesis 2.4: Increasing reaction of the second mover when signals are infor-
mative and wM = 110:
(i) In T-IMPX the second mover exerts more e¤ort the higher the …rst mover’s
e¤ort.
(ii) In T-PX and T-PPlusX the second mover exerts more e¤ort when the …rst
mover’s contribution is high than when it is low.
If wH > 2 wM, the second mover faces higher incentives to work when the …rst mover works more in T-IMPX, or when the …rst mover’s contribution is high rather than low in T-PX and T-PPlusX.
Hypothesis 2.5: Higher e¤ort of the …rst mover when signals are informative and
wM = 110: The …rst mover’s e¤ort is higher in T-IMPX, T-PX, and T-PPlusX than
in T-NOX.
34In T-PPlusX the increasing reaction only refers to the …rst mover’s contribution and not to his
e¤ort. This is analogous to T-PPlus.
The …rst mover anticipates that the second mover positively reacts to the informa- tive signals and that he can, therefore, induce the second mover to exert a high e¤ort by working a lot in T-IMPX, T-PX, and T-PPlusX.
Hypothesis 2.6: No e¤ect of the additional information on the …rst mover’s e¤ort
when the …rst mover’s contribution is known and wM = 110: E¤orts in T-PX and T-
PPlusX are the same.
Table 2.9 reports the average behavior of both agents in our additional treatments.
Table 2.9: Mean of e1 and e2 in the additional treatments
Treatment Mean of e1 Mean of e2 Number of
observations T-NOX 45.37 46.53 126 T-NOX* 45.95 45.95 252 T-IMPX 62.27 59.67 252 T-PX 61.05 61.88 266 if b1 = 1 61.60 199 if b1 = 0 62.70 67 T-PPlusX 55.54 55.82 266 if b1 = 1 62.94 155 if b1 = 0 45.88 111
*: e1and e2 are considered.
In T-NOX agents work on average about 46 which is lower than the prediction of about 61.05. AswM is smaller than in the case of substitutes (andwH andwLremained the same), agents may be less motivated to exert e¤ort. Similar to the previous section, both agents work more on average when the second mover receives an informative signal. The second mover’s reaction to the …rst mover’s contribution di¤ers, however, compared to what we observed for substitutes: In T-PX the second mover’s average e¤ort does not vary with the …rst mover’s contribution, while in T-PPlusX the second mover on average works more when the …rst mover’s contribution is high than when it is low.
In order to analyze behavior more closely and to test our hypotheses for the ad- ditional treatments, we regress the second mover’s e¤ort on treatment dummies, in-
teractions of treatments dummies with available signals, and control variables and we regress the …rst mover’s e¤ort on treatment dummies, and control variables.36 Table 2.10 reports our regression results.
Table 2.10: Regression results on e2 and e1 in the additional treatments
Dependent variable: e2 e2 e1 e1
Panel (re) Panel (re) Panel (re) Panel (re) (Tobit) (Tobit) Intercept +46.08 +44.79 +43.52 +42.56 (0.000) (0.000) (0.000) (0.000) T-IMPX - 09.85 - 13.09 +17.23 +20.58 (0.083) (0.076) (0.001) (0.001) T-PX +14.96 +20.67 +14.08 +19.09 (0.000) (0.000) (0.005) (0.003) T-PPlusX - 12.64 - 14.38 +09.15 +11.75 (0.003) (0.010) (0.066) (0.064) T-IMPX * e1 +00.37 +00.48 (0.000) (0.000) T-PPlusX * e1 +00.30 +00.34 (0.000) (0.000) T-PX * b 1 +00.41 +00.72 (0.863) (0.814) T-PPlusX * b1 +09.22 +11.08 (0.000) (0.000) Sex +01.02 +02.73 +05.46 +06.48 (1 if male, 0 else) (0.680) (0.421) (0.133) (0.162) Number of observations 1036 1036 1036 1036 (Pseudo) R-squared 0.173 0.106
(re): random e¤ects
In all four regressions e1 and e2in T-NOX are considered.
Numbers in brackets represent the p-values of the coe¢ cients.
Similar to the results for substitutes, the second mover’s e¤ort signi…cantly increases in the …rst mover’s e¤ort in T-IMPX. The coe¢ cient of the interaction of T-IMPX with the …rst mover’s e¤ort is even signi…cantly larger than the predicted 0.24. In contrast to Hypothesis 2.4(ii) and the results for substitutes, the second mover’s e¤ort does not increase in the …rst mover’s contribution in T-PX. In T-PPlusX, however, the second mover’s e¤ort signi…cantly increases in both the …rst mover’s e¤ort and his contribution. Hence, the …rst mover’s e¤ort, again, is a very stimulating signal for the second mover, while the …rst mover’s contribution signi…cantly a¤ects the second
36In our regressions we again consider the …rst and the second mover’s decisions in T-NOX. Our
results do not change considerably if we separately consider the …rst mover’s and the second mover’s decisions in T-NOX.
mover’s e¤ort only if also the …rst mover’s e¤ort is observable. With respect to the …rst mover’s behavior we …nd that in all treatments with informative signals the …rst mover works signi…cantly more than in our benchmark treatment. On the basis of these results, we reject Hypothesis 2.4(ii) with respect to T-PX. We also reject Hypothesis 2.6 regarding the second mover’s behavior as his e¤ort in T-PPlusX varies with the …rst mover’s e¤ort and contribution, while it is independent of both in T-PX. We summarize our …ndings in the following results.
Result 2.6: Higher average e¤ort in T-IMPX, T-PX, and T-PPlusX than in T-
NOX: On average, the …rst and the second mover exert more e¤ort when informative
signals are available.
Result 2.7: Increasing reaction of the second mover in T-IMPX and T-PPlusX:
In line with Hypotheses 2.4(i) and 2.4(ii), the second mover works more the higher the
…rst mover’s e¤ort in T-IMPX, and the higher the …rst mover’s contribution in T-
PPlusX. In T-PX the …rst mover’s contribution does not signi…cantly a¤ect the second
mover’s e¤ort.
Result 2.8: Increasing e¤ect of informative signals on the …rst mover’s e¤ort when wM = 110: The …rst mover works signi…cantly more in T-IMPX, T-PX, and
T-PPlusX than in T-NOX.
Result 2.9: E¤ect of the additional information on the …rst mover’s e¤ort on the
second mover’s behavior when wM = 110: In contrast to Hypothesis 2.6, the second
mover’s e¤ort increases in the …rst mover’s e¤ort in T-PPlusX. The …rst mover’s
behavior does, however, not di¤er between T-PX and T-PPlusX.