Joint modeling of playing time and purchase propensity in massively multiplayer online role-playing games using crossed random effects

Massively Multiplayer Online Role Playing Games (MMORPGs) offer a unique blend of a personalized gaming experience and a platform for forging social connections. Managers of these digital products usually rely on predictions of key player responses, such as playing time and purchase propensity, to design timely interventions for promoting, engaging and monetizing their playing base. However, the longitudinal data associated with these MMORPGs not only exhibit a large set of potential predictors to choose from but often present several other distinctive characteristics that pose significant challenges in developing flexible statistical algorithms that can generate efficient predictions of future player activities. For instance, the existence of virtual communities or guilds in these games complicate prediction since players who are part of the same guild have correlated behaviors and the guilds themselves evolve over time and, thus, have a dynamic effect on the future playing behavior of its members. In this paper, we develop a Crossed Random Effects Joint Modeling (CREJM) framework for analyzing correlated player responses in MMORPGs. Contrary to existing methods that assume player independence, CREJM is flexible enough to incorporate both player dependence as well as time varying guild effects on the future playing behavior of the guild members. On a large-scale data from a popular MMORPG, CREJM conducts simultaneous selection of fixed and random effects in high-dimensional penalized multivariate mixed models. We study the asymptotic properties of the variable selection procedure in CREJM and establish its selection consistency. Besides providing superior predictions of daily playing time and purchase propensity over competing methods, CREJM also predicts player correlations within each guild which are valuable for optimizing future promotional and reward policies for these virtual communities.