M samples, we mostly observe a unique outcome of the model. This outcome may be either a bank run or a no-run outcome depending on the parameter values. The probability of bank run weakly increases with the share of impatient depositors (), and weakly decreases with the sample size (N) and the decision threshold (o), ceteris paribus.PLOS ONE | DOI:10.1371/journal.pone.0147268 April 1,19 /Correlated Observations, the Law of Small Numbers and Bank RunsFig 3. The GSK-1605786 price long-run theoretical share of depositors who do not withdraw (k) in the case of random sampling and Scenario 3. The black line represents the left-hand side of Eq (13) (i.e. the 45-degree line), the colored lines represent the right-hand side of Eq (13) for different parameter values as shown in the legend. The long-run share of depositors who do not withdraw is given by the largest (rightmost) crossing point of the 45-degree line and a given colored line. The parameter values are as in Scenario 3 (R = 1.5, = 4). And on the first Panel: N = 85, is varied as = 0.1 (blue line), = 0.5 (red line), = 0.9 (green line). On the second Panel: = 0.5, N is varied as N = 10 (blue line), N = 85 (red line), N = 160 (green line). doi:10.1371/journal.pone.0147268.gPLOS ONE | DOI:10.1371/journal.pone.0147268 April 1,20 /Correlated Observations, the Law of Small Numbers and Bank RunsTable 3. The probability of bank run in the case of random sampling as computed from the simulations. Scenario 1 N 10 35 60 85 110 135 160 jir.2012.0140 185 210 N 10 35 60 85 110 135 160 185 210 N 10 35 60 85 110 135 160 185 210 = 0.1 0 0 0 0 0 0 0 0 0 = 0.1 0 0 0 0 0 0 0 0 0 = 0.1 1 0 0 0 0 0 0 0 0 = 0.3 0 0 0 0 0 0 0 0 0 Scenario 2 = 0.3 0 0 0 0 0 0 0 0 0 Scenario 3 = 0.3 1 1 0 0 0 0 0 0 0 = 0.5 1 1 1 0 0 0 0 0 0 = 0.7 1 1 1 1 1 1 1 0 0 = 0.9 0.88 1 1 1 1 1 1 1 1 = 0.5 1 0 0 0 0 0 0 0 0 = 0.7 0 0 0 0 0 0 0 0 0 = 0.9 0.93 1 0.65 0 0 0 0 0 0 = 0.5 0 0 0 0 0 0 0 0 0 = 0.7 0 0 0 0 0 0 0 0 0 = 0.9 0.9 0 0 0 0 0 0 0The probability of bank run is computed as the percentage of simulation runs where a bank run occurred (out of 100 simulation runs). A bank run occurs in a given simulation run if less than 3 of the last 20000 depositors in the line keep their money in the bank. The order JNJ-26481585 population consists of 107 depositors. The first panel shows the results for Scenario 1 (R = 1.1, = 1.5), the second panel for Scenario 2 (R = 1.3, = 2.5), the third panel for Scenario 3 (R = 1.5, = 4). The journal.pone.0158910 values of N and are varied as shown in the first column and first row of each panel, respectively. The underlined entries can be directly compared to the outcomes represented on Figs 1?. doi:10.1371/journal.pone.0147268.tDiscussion. Remember that the bank in our model is assumed to be fundamentally healthy, so bank runs are clearly suboptimal. However, they still occur in the random setting as well, but they are considerably less likely to happen than in the overlapping case. As indicated earlier, in real life good banks also suffer bank runs and in many occasions one of the driver of the bank run is that depositors observe other depositors rushing to the bank. Our resultsPLOS ONE | DOI:10.1371/journal.pone.0147268 April 1,21 /Correlated Observations, the Law of Small Numbers and Bank Runssuggest that there is some room for preventing runs on good banks by making samples less correlated. More precisely, when massive withdrawals are observed by depositors (for instance through a TV broadcast showing long queues in front of a bank), then.M samples, we mostly observe a unique outcome of the model. This outcome may be either a bank run or a no-run outcome depending on the parameter values. The probability of bank run weakly increases with the share of impatient depositors (), and weakly decreases with the sample size (N) and the decision threshold (o), ceteris paribus.PLOS ONE | DOI:10.1371/journal.pone.0147268 April 1,19 /Correlated Observations, the Law of Small Numbers and Bank RunsFig 3. The long-run theoretical share of depositors who do not withdraw (k) in the case of random sampling and Scenario 3. The black line represents the left-hand side of Eq (13) (i.e. the 45-degree line), the colored lines represent the right-hand side of Eq (13) for different parameter values as shown in the legend. The long-run share of depositors who do not withdraw is given by the largest (rightmost) crossing point of the 45-degree line and a given colored line. The parameter values are as in Scenario 3 (R = 1.5, = 4). And on the first Panel: N = 85, is varied as = 0.1 (blue line), = 0.5 (red line), = 0.9 (green line). On the second Panel: = 0.5, N is varied as N = 10 (blue line), N = 85 (red line), N = 160 (green line). doi:10.1371/journal.pone.0147268.gPLOS ONE | DOI:10.1371/journal.pone.0147268 April 1,20 /Correlated Observations, the Law of Small Numbers and Bank RunsTable 3. The probability of bank run in the case of random sampling as computed from the simulations. Scenario 1 N 10 35 60 85 110 135 160 jir.2012.0140 185 210 N 10 35 60 85 110 135 160 185 210 N 10 35 60 85 110 135 160 185 210 = 0.1 0 0 0 0 0 0 0 0 0 = 0.1 0 0 0 0 0 0 0 0 0 = 0.1 1 0 0 0 0 0 0 0 0 = 0.3 0 0 0 0 0 0 0 0 0 Scenario 2 = 0.3 0 0 0 0 0 0 0 0 0 Scenario 3 = 0.3 1 1 0 0 0 0 0 0 0 = 0.5 1 1 1 0 0 0 0 0 0 = 0.7 1 1 1 1 1 1 1 0 0 = 0.9 0.88 1 1 1 1 1 1 1 1 = 0.5 1 0 0 0 0 0 0 0 0 = 0.7 0 0 0 0 0 0 0 0 0 = 0.9 0.93 1 0.65 0 0 0 0 0 0 = 0.5 0 0 0 0 0 0 0 0 0 = 0.7 0 0 0 0 0 0 0 0 0 = 0.9 0.9 0 0 0 0 0 0 0The probability of bank run is computed as the percentage of simulation runs where a bank run occurred (out of 100 simulation runs). A bank run occurs in a given simulation run if less than 3 of the last 20000 depositors in the line keep their money in the bank. The population consists of 107 depositors. The first panel shows the results for Scenario 1 (R = 1.1, = 1.5), the second panel for Scenario 2 (R = 1.3, = 2.5), the third panel for Scenario 3 (R = 1.5, = 4). The journal.pone.0158910 values of N and are varied as shown in the first column and first row of each panel, respectively. The underlined entries can be directly compared to the outcomes represented on Figs 1?. doi:10.1371/journal.pone.0147268.tDiscussion. Remember that the bank in our model is assumed to be fundamentally healthy, so bank runs are clearly suboptimal. However, they still occur in the random setting as well, but they are considerably less likely to happen than in the overlapping case. As indicated earlier, in real life good banks also suffer bank runs and in many occasions one of the driver of the bank run is that depositors observe other depositors rushing to the bank. Our resultsPLOS ONE | DOI:10.1371/journal.pone.0147268 April 1,21 /Correlated Observations, the Law of Small Numbers and Bank Runssuggest that there is some room for preventing runs on good banks by making samples less correlated. More precisely, when massive withdrawals are observed by depositors (for instance through a TV broadcast showing long queues in front of a bank), then.