How does blind trust emerge? – Dynamics of second mover

upper panel of figure 5.3 depicts aggregate second mover behavior splitted up by ter-minal and non-terter-minal periods, and figure 5.8 depicts the full aggregate dynamics of second mover’s behavior. The left-hand column of figure 5.8 depict the results for the costless monitoring condition. The time trend of the reciprocation rate is non-monotone since reciprocation is always contingent on first mover cooperation. Thus, a sorting effect tends to increase reciprocation rates over time, since exploiters are no longer trusted (at least for some time), while the strategic reciprocation incentive diminishes towards the terminal period, inducing a trend tendency into the oppo-site direction. Consistent with a strategically reciprocal strategy, cooperation rates

are clearly higher in non-terminal rounds than in terminal rounds. In non-terminal rounds, second movers reciprocated in 71.4 percent (50 out of 70) of the time, while in in terminal rounds, they returned cooperation in 50.0 percent (1 out of 2) of the time. As a result, overall second mover reciprocation rates were 70.8 percent (51 out of 72).

Consider now the costly monitoring condition depicted in the right-hand column of figure 5.8. As in the costly monitoring condition, cooperation rates are clearly higher in non-terminal rounds than in terminal rounds. In non-terminal rounds, sec-ond movers reciprocated in 82.7 percent (91 out of 110) of the time, while in in ter-minal rounds, they returned cooperation in 50.0 percent (3 out of 6) of the time. As a result, overall second mover reciprocation rates were 81.0 percent (94 out of 116), which is somewhat higher than under costless monitoring. Figure 5.8 illustrates why:

while reciprocation rates are similar in both treatment conditions towards the terminal period, they are clearly higher in the costly monitoring condition than in the costless monitoring condition over the initial rounds, in fact at remarkable 100 percent in pe-riod 1 through 3. In addition, reciprocation rates have a markedly decreasing trend over time in the costly monitoring condition.

Result 5.6. In both the costless and the costly monitoring condition the majority of first mover cooperation is reciprocated. However, reciprocation is markedly more frequent in the initial rounds of the latter compared to the former, and there is a more pronounced decreasing trend if monitoring is costly.

The latter fact is quite consistent with the average second mover’s belief about being monitored in the current period. The circles connected with the hatched line in figure 5.8 depict this belief. Evidently, the average second mover anticipates the average first mover’s monitoring pattern (as summarized in result 5.5) remarkably closely.¹² While the average second mover’s belief about being monitored is approx-imately stable close to unity in the costless monitoring condition, it exhibits a clearly decreasing pattern under costly monitoring. Thus, while the average second mover believes to be monitored with almost-certainty throughout the whole match in the costless monitoring condition, (s)he expects to be monitored predominantly at the beginning of a match, less so towards the end, under costly monitoring.

Result 5.7. The average second mover anticipates the average first mover’s monitor-ing pattern quite accurately. Specifically, while the average second mover believes to be monitored with almost-certainty throughout the whole match in the costless mon-itoring condition, (s)he expects to be monitored predominantly at the beginning of a match, less so towards the end, under costly monitoring.

Did the average second mover responded consistently to this belief? Conven-tional economic theory suggests that the temptation to cheat is decreasing in the per-ceived likelihood of being detected, and vice versa. The belief and behavior patterns

12Recall that we deliberately kept them uninformed about whether they are currently monitored or not.

depicted in figure 5.8 are consistent with this intuition: while second movers re-spond in a standard way to their belief of being constantly monitored in the costless monitoring condition, reciprocation rates diminish with the belief of being moni-tored towards the end in the costly monitoring condition. In both conditions, the average cooperating second mover had a stronger belief of being monitored (.945 in the costless monitoring condition, .652 in the costly monitoring condition) than the average defecting second mover (.880 in the costless monitoring condition, .471 in the costly monitoring condition), where the difference is significant in the costly (Mann-Whitney, p= .039) but not in the costless monitoring condition (p = .260).

Rank correlation between beliefs of being monitored and reciprocation is positive and significant when monitoring is costly (Kendall’s τb= 0.168, p = .040).

While this accounts neatly for the increasing trend of cheating in the costly mon-itoring condition, a simple response to the belief of being monitored in the current period cannot, however, account for result 5.6, namely that reciprocation is markedly more frequent in the initial rounds if monitoring is costly compared to the costless monitoring condition. Although speculative at this point, a possible explanation of this fact is that the active and costly nature of monitoring gives rise to a «higher or-der» of reputation building. In standard repeated games with perfect monitoring (but incomplete information), strategically acting second movers can build a favorable reputation in order to induce the first mover to cooperate until close to termination (Kreps et al., 1982). In our game, second movers can induce the first movers not only to cooperate, but also to refrain from monitoring. We suspect that the incentive for the latter («second-order reputation building») is much stronger than the former («first-order reputation building»), because under perfect monitoring the maximum number of periods in which a strategically acting second mover can exploit the first mover is equal to one (assuming that the first mover will not cooperate again once cheated), while in our game there is the possibility of cheating over multiple periods once the first mover trusts blindly. This is a possible explanation why reciprocation rates are initially so much higher under costly monitoring. Intuitively, (some) second movers deliberately try to «earn» a reputation in the initial periods in which they are likely to be monitored, favorable enough to be trusted blindly later on. Strategically acting subjects may do so in order to exploit their coplayers more easily and perhaps over multiple periods. This strategic incentive is missing in the costless monitoring condition, since second movers do not believe in blind trust anyway (and this belief is justified). Thus, we have the following conjecture

Conjecture 5.1. Some second movers try to strategically exploit the costliness of monitoring by investing in a sufficiently favorable reputation in the initial periods in which they are likely to be monitored in order induce blind trust and reap larger gains from exploitation in later periods.

We leave a direct test of this conjecture for future research, but the facts presented below already lend some preliminary support.

5.4.5 How does blind trust emerge? – Strategic reputation building and first