Fig. 17. Effect of limited rationality on convergence.Figure optionsDownload full-size imageDownload as PowerPoint slide
Fig. 17 shows that STA9090 the convergence speed is faster when sdsd is higher if the decision makers have limited rationality. However, the results shown in Fig. 17 do not satisfy (15), so herding does not occur. In particular, when sd=1sd=1, the percentage waiting is close to zero after the 15th15th decision maker and the probability of correct decisions is 79%; when sd=0.2sd=0.2, the probability of waiting approaches zero after the 55th55th decision maker and the percentage of correct decisions is 93%; when sd=0.1sd=0.1, the percentage of waiting is close to zero after the 90th90th decision maker and the probability of a correct decision is 94%; and when sd=0.05sd=0.05 or 0.01, there is no clear trend in the convergence for 100 decision makers.
Next, we consider two extreme situations. First, sdsd is extremely high and g(βt)g(βt) comes from a uniform distribution that varies from negative infinity to positive infinity. Second, sdsd is zero and g(βt)g(βt) is no longer a random variable, but instead resolution is a constant with a value of 1. We have performed simulations where sd=0.0001sd=0.0001 and sd=1000sd=1000, and the results are shown in Fig. 18.
Fig. 17 shows that STA9090 the convergence speed is faster when sdsd is higher if the decision makers have limited rationality. However, the results shown in Fig. 17 do not satisfy (15), so herding does not occur. In particular, when sd=1sd=1, the percentage waiting is close to zero after the 15th15th decision maker and the probability of correct decisions is 79%; when sd=0.2sd=0.2, the probability of waiting approaches zero after the 55th55th decision maker and the percentage of correct decisions is 93%; when sd=0.1sd=0.1, the percentage of waiting is close to zero after the 90th90th decision maker and the probability of a correct decision is 94%; and when sd=0.05sd=0.05 or 0.01, there is no clear trend in the convergence for 100 decision makers.
Next, we consider two extreme situations. First, sdsd is extremely high and g(βt)g(βt) comes from a uniform distribution that varies from negative infinity to positive infinity. Second, sdsd is zero and g(βt)g(βt) is no longer a random variable, but instead resolution is a constant with a value of 1. We have performed simulations where sd=0.0001sd=0.0001 and sd=1000sd=1000, and the results are shown in Fig. 18.