User activity fluctuations reflect the performance of online society. We investigate the statistical properties of 1-min user activity time series of simultaneously online users inhabited in 95 independent virtual worlds. The number of online users e
xhibits clear intraday and weekly patterns due to humans circadian rhythms and week cycles. Statistical analysis shows that the distribution of absolute activity fluctuations has a power-law tail for 44 virtual worlds with an average tail exponent close to 2.15. The partition function approach unveils that the absolute activity fluctuations possess multifractal features for all the 95 virtual worlds. For the sample of 44 virtual worlds with power-law tailed distributions of the absolute activity fluctuations, the width of singularity $Deltaalpha$ is negatively correlated with the maximum activity ($p$-value=0.070) and the time to the maximum activity ($p$-value=0.010). The negative correlations are not observed for neither the other 51 virtual worlds nor the whole sample of the 95 virtual worlds. In addition, numerical experiments indicate that both temporal structure and large fluctuations have influence on the multifractal spectrum. We also find that the temporal structure has stronger impact on the singularity width than large fluctuations.
Similar to charitable giving in real world, donation behaviors play an important role in the complex interactions among individuals in virtual worlds. However, it is not clear if the donation process is random or not. We investigate this problem usin
g detailed data from parallel virtual worlds adhered to a massively multiplayer online role-playing game. We find that the inter-donation durations follow power-law-tailed distributions distributed with an average tail exponent close to 1.91, have strong long-range correlations, and possess multifractal features. These findings indicate that the donation process is non-Poissonian, which has potential worth in modeling the complicated individuals behaviors in virtual worlds.
The availability of big data recorded from massively multiplayer online role-playing games (MMORPGs) allows us to gain a deeper understanding of the potential connection between individuals network positions and their economic outputs. We use a stati
stical filtering method to construct dependence networks from weighted friendship networks of individuals. We investigate the 30 distinct motif positions in the 13 directed triadic motifs which represent microscopic dependences among individuals. Based on the structural similarity of motif positions, we further classify individuals into different groups. The node position diversity of individuals is found to be positively correlated with their economic outputs. We also find that the economic outputs of leaf nodes are significantly lower than that of the other nodes in the same motif. Our findings shed light on understanding the influence of network structure on economic activities and outputs in socioeconomic system.
Mutually interacting components form complex systems and the outputs of these components are usually long-range cross-correlated. Using wavelet leaders, we propose a method of characterizing the joint multifractal nature of these long-range cross cor
relations, a method we call joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable to detect the cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to the pairs of series from financial markets (returns and volatilities) and online worlds (online numbers of different genders and different societies) and find an intriguing joint multifractal behavior.
