*3.6. Implementation in NetLogo*

Four types of agents (see Section 3.2) have been created in NetLogo 6.0.4, belonging to either class A (in red), B (in green), C (in cyan), or D (in orange), as presented in Figure 3. Additionally, four monitors are available for each type of members, where one can easily observe how the number of the members in each category is changing in real-time. Additionally, we have offered the agents the possibility to return to group D, by setting the switch "Group-C-Can-Return-To-Group-D" to "on". The agents passing from group C to group D will be highlighted by coloring them in yellow, while their number, in real-time, will be counted in the "Group-D-Returned-Members" monitor. The NetLogo code is provided in Appendix A.

**Figure 3.** The types of agents created in NetLogo 6.0.4.

A series of variables have been considered in accordance with the model description presented above. The visual interface created in NetLogo 6.0.4. offers the possibility of setting some of these

<sup>16</sup> We have considered a normal distribution, and not a fat-tail one (e.g., McGroarty et al. 2019) for this variable due to the NetLogo limitations.

variables' values at the beginning of the simulation, while the presence of monitors and graphs depicts their evolution in real-time (see Figure 4).

**Figure 4.** A snapshot of the NetLogo 6.0.4. model's interface at *t* = 20 ticks.

The simulation is stopping when the total number of members in groups A and D is smaller or equal than 50%. The "time interval" monitor depicts the number of ticks needed in order to change the power, where the tick is the time unit in NetLogo.

## **4. Numerical Results: Discussion**

We have considered two main situations, described in Section 3.2, respectively: (i) Situation S1: group D members cannot return to their initial status (once they decide to enter in group C, they remain in this one); (ii) Situation S2: group D members can change their group (becoming member of group C if the performance of the company is changing in worse, but also re-becoming a member of D group if the performance of the company is changing in better). The first situation can be considered more optimistic (as it is easier to be followed), but the second one seems to be more connected to reality. For this reason, the DSMBD estimated in Situation S2 is the indicator which should be taken into account when a prudent approach is required.

For S1, different levels for "the tolerance for the manager's performance" (τ) and "the impact of making bad decisions" (*bd*) have been considered (see Tables 6 and 7). For each situation (S1-1 to S1-13) the model has been run 400 times and the average DSMBD in ticks has been extracted.


**Table 6.** Simulation's results for S1 when *bd* = 0.1.


**Table 7.** Simulation's results for S1 when τ = 0.5.

For the (S1-1)–(S1-7) situations, we have kept the value of *bd* constant at the level of 0.1 and we have changed the tolerance for the manager's performance from 0 to 1. A level of *bd* = 0.1 can be interpreted as a systematic bad decision, but having a minor impact on financial performance. As a result, it has been observed that the average time (years) needed in order to stop the process of making bad decisions ranges between [12.29, 43.52], depending on the various values of the tolerance for the manager's decision variable (see Figure 5). Obviously, a systematic bad decision with minor impact can remain unobserved for a longer period.

**Figure 5.** Average DSMBD versus the tolerance for manager's performance, when *bd* = 0.1 and S1 is considered.

As observation, even in the case of τ = 0, DSMBD can reach 10–14 years (iterations). Looking closer to the S1-1 situation in which we encounter zero tolerance for the manager's performance, an average DSMBD of 12.29 years results. Comparing this to the case in which 10% tolerance is considered, the average DSMBD of 12.54 years is recorded. Considering the individual values obtained from the simulations, it can be observed that the most frequent recorded value is 11 years (in 26% of the cases), the amount of time needed for making bad decisions being in [10, 16] (see Figure 6).

Additionally, from simulations, 32.75% of the cases in S1-2 have reached a DSMBD of 13 units, being also the most frequent value. On the other hand, no particular distribution can be determined for S1-3 average time, as there were a series of most frequent values encountered through simulations, such as: 13, 18, 22, and 26. This situation also occurs for all the other cases starting with S1-4 until S1-7.

Now, considering the two extreme cases: no tolerance (S1-1) and total tolerance for the manager's performance (S1-7), the average DSMBD difference is of 31.23 years, almost three and a half times more than in the no tolerance case. As expected, for the intermediate situations (S1-2 until S1-6), as the tolerance for manager's performance is increasing, while the impact of making bad decisions is not changing, the average DSMBD increases.

**Figure 6.** DSMBD—situation S1-1.

Considering the S1-4, S1-8 until S1-13 cases, it can be observed that when the deciders have over-confidence in the values of the expected IRR, DSMBD is longer, even though the time difference among the situations with the smallest and the largest average time amount is of only 4.22 time units (see Table 7). All the other average DSMBD values range smoothly among the values recorded for the extreme cases (see Figure 7).

**Figure 7.** Average DSMBD versus the impact of making bad decisions, when τ = 0.5 and S1 is considered.

Thus, among the two considered variables (the tolerance for the manager's performance and the impact of making bad decisions), the tolerance for manager's decisions has a greater impact, recording an average of 31.23 years (time units) when comparing the extreme cases with zero and total tolerance, while for the impact of making bad decisions considering the extreme cases, a time difference of only 4.22 years (time units) have been recorded. This result can suggest the important role of good monitoring processes, in accordance with Campbell et al. (2009).

We have made the same measurements for the S2 situation, in which the deciders can decide to return to group D. The results are summarized in Tables 8 and 9 below.


**Table 8.** Simulation's results for S2 when *bd* = 0.1.

**Table 9.** Simulation's results for S2 when τ = 0.5.


Obviously, the greater the tolerance for the manager's performance, the longer the average DSMBD is. However, it can be observed that, as the tolerance is higher, DSMBD can take extremely long periods of time until a normal situation is reached (see the S2-7 situation). This length (in years) substantially exceeds the normal life of companies which are in existence at this moment17.

Figure 8 depicts the evolution of the average DSMBD when considering different values for the tolerance for manager's decision, ranging between zero tolerance (S2-1) and full tolerance (S2-7). It can easily be observed that a tolerance greater than 0.5 can have dramatic results on the DSMBD value.

In the extreme case of total tolerance (S2-7), the negative effects can perpetuate as much as possible, as people are continually changing their mind and switching groups, making DSMBD very long (supposing that the company can function in these conditions for such a long period).

Considering a low-tolerance situation (case S2-1), which can be plausible in some real-life situations, the average of such bad decisions' time is 17.92 years, which can be characterized as a double time for not creating major problems within the analyzed economic entity. Moreover, as the tolerance for manager's performance increases, DSMBD continues to increase, and it can be observed that, after a 0.5 tolerance, it is critically high, reaching, on average, more than 59.14 years (time units).

Comparing (S1-1)–(S1-7) with (S2-1)–(S2-7), it can be observed that for small values of tolerance for the manager's decisions (τ), DSMBD has comparable values. For example, the time difference between S1-1 and S2-1 is of only 0.43 (practically, 0) years (time units), while for 0.1 tolerance is 5.38 years (cases S1-2 and S2-2), and for 0.3 tolerance is of 10.24 years (cases S1-3 and S2-3). Starting with 0.5 tolerance, differences for DSMBD become notable: 39.97 years for τ = 0.5, 236.29 for τ = 0.7. Higher

<sup>17</sup> According to Wikipedia (https://en.wikipedia.org/wiki/List\_of\_oldest\_companies, accessed on 23 July 2019), the oldest company still in function is Nishiyama Onsen Keiunkan (founded in 705 AD, so with an age less than 1400 years). Of course, such a long period of existence can be explained by making good decisions. From this perspective, it is implausible that, for a company to function for so many years, making systematically bad decisions, large levels of DSMBD can be interpreted as a failure before the change of the decider.

levels of tolerance make the difference extremely high: 1172.28 years (time units) for 0.9 tolerance and 4512.34 years for total tolerance (τ = 1). Once more, the significant effect the degree of tolerance has on the average DSMBD can be underlined.

**Figure 8.** Average DSMBD versus the tolerance for manager's performance, when *bd* = 0.1 and S2 is considered.

As for the impact of making bad decisions, the data in Table 9, shows, as in the previous cases (S2-8 until S2-13), that *bd* has only a reduced influence over the overall average bad decisions time, making only a 17.49-time units (years) difference.

Figure 9 presents the evolution of DSMBD for various values of the impact of making bad decisions. It can be observed that the decrease of the average DSMBD values is smooth as it was also in Figure 7. The only difference is that in this case the values of DSMBD are higher than in the (S1-8)–(S1-13) situations and the difference among the extreme values is higher in this case.

**Figure 9.** Average DSMBD versus the impact of making bad decisions, when τ = 0.5 and S2 is considered.

Comparing the two situations (S1 and S2), it can be seen that in both of them, the deciders' tolerance to manager's bad decisions can make a difference, having a significant contribution to the overall average decision-making time.

Based on these simulations, we can conclude that the length of the DSMBD can be very long, probably exceeding the lifetime of the company. In some cases, the dominant group (class A in our model) can impose their viewpoint until the end of the company, while the group of rational shareholders (class B in our model) cannot impose theirs. Thus, in the absence of the improving the quality of making judgments and making better decisions, the existence of informed and rational investors is useless.

#### **5. Conclusions**

Bad decisions have an impact on the company's performance. However, their impact is not instant. For this reason, the process of making bad decisions can be very persistent, especially if no agreement about the best solution is existent. In this paper, we propose a model in which shareholders are not instantly aware about a bad decision made by the shareholders that dominate the annual general meeting of shareholders (AGM). This paper analyzes the case in which, for different reasons, the deciders systematically make bad decisions regarding dividend payout. We use this model for the estimation of the DSMBD in setting one dividend policy. We have started from Dragotă (2016), as a general case, and we have made some adjustments in order to adapt this model for the case of financial management, respectively, for dividend policy. We use NetLogo 6.0.4 for modelling, which offers a graphical interface, where the changes in the simulated environment can be observed in real-time.

This paper considers the case in which, in voting one dividend policy or another, individuals are following different objectives based on different values. Unfortunately, the democratic vote and the good intentions are not sufficient for guaranteeing the avoidance of systematically making bad decisions (Dragotă 2016). Since the deciders are convinced that their decisions are right, they have no reason to change them until the results of their actions significantly affect themselves. However, as long as their wealth is determined by other factors, too, they can hardly differentiate between the effect of their decisions and the impact of these other factors. As an effect, they can still be convinced that they are making good decisions. Moreover, even if the outputs are not acceptable, these results can be explained not as the effect of some bad decisions, but as the effect of some nonsystematic, external effects.

Our paper analyzes the conditions in which making bad decisions can become a systematic phenomenon and proposes a model presented both mathematically and numerically on a small example in order to increase its understanding and readability. Using the advantages provided by the agent-based modelling and NetLogo 6.0.4, a model is created and numerically simulated in order to make a proper estimation of DSMBD. In our model, we consider four classes of shareholders, each of them with a specific behavior. We propose an algorithm that can be used in modelling their interaction and for predicting this duration. Thus, the changes in voting structure can be followed in real-time. As far as we know, this approach has not been used in the financial literature concerning dividend policy.

Some cases have been considered, depending on whether hat the deciders can change their groups or not. Additionally, different values for the involved variables have been considered and simulated 400 times each. It has been observed that the deciders' tolerance to a manager's bad decisions can make a difference in terms of time.

We prove that, in some circumstances, DSMBD can be very long. Its length can reach a very large number of years, exceeding in some conditions a human lifetime and the maximal age of existing companies on Earth at this moment. Moreover, it can be possible for DSMBD to increase dramatically if the shareholders have a great level of trust in the management's decisions. Practically, in some conditions, the dominant group (controlling shareholders) can impose their viewpoint until the end of the company, while the group of rational shareholders cannot impose theirs. As a principal implication, an increase of the quality of financial education for top-management and shareholders, and, from here, more performant instruments for controlling the power's decisions are required. After all, Campbell et al. (2009) warn that "Given the way the brain works, we can't rely on leaders to spot and safeguard against their own errors in judgment. [ ... ] So rather than rely on the wisdom of experienced chairmen, the humility of CEOs, or the standard organizational checks and balances, we urge all involved in important decisions to explicitly consider whether red flags exist and, if they do, to lobby for appropriate safeguards."

Of course, simulations provide only an artificial environment and our study and their findings can be easily attacked from this perspective. New directions for study can be related to two proposed inputs—the coefficient of impact of bad decisions (*bd*) and the coefficient of intolerance for the manager's performance (τ). However, most of the parameters required in our model can be relatively easily imported in real-life, company level context.

Further, one interesting development of the study is to consider the agency problems which occur in dividend payment decision (Dragotă et al. 2009). In this case, multiple objective functions (Lovric et al. 2010), adaptable for different classes of shareholders, could be used. The manner in which the dividend payout is fixed can be a fruitful field of study, especially if the asymmetrical information, the power in negotiation, and the skills required for persuading other individuals to vote somehow are considered. In the same context, valuation the impact of combining financial and non-financial (e.g., ethical objectives) (Ballestero et al. 2012; Mallin 2016) can be another direction for study.

**Author Contributions:** Conceptualization: V.D.; formal analysis: V.D. and C.D.; investigation: V.D. and C.D.; methodology: V.D. and C.D.; software: C.D.; supervision: V.D.; validation: V.D. and C.D.; visualization: V.D. and C.D.; writing—original draft: V.D. and C.D.; writing—review and editing: V.D. and C.D.

**Funding:** This research received no external funding.

**Acknowledgments:** We wish to thank the participants of the 29th European Conference on Operational Research (Valencia, 8–11 July 2018) for their remarks. The remaining errors are ours.

**Conflicts of Interest:** The authors declare no conflict of interest.
