Paper review on game user churn prediction

User churn prediction models have improved with the advancement of artificial intelligence and computing systems. We conducted a review to understand the techniques or models used in various studies, key features, and utilization of social interaction data for churn prediction as shown in Table 1.

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Table 1. Summary of related works on game user churn prediction.

https://doi.org/10.1371/journal.pone.0321560.t001

Kawale et al. [17] applied social network analysis to networks created from user party records in the gaming domain. They generated centrality features from these networks and used an AdaBoost model to classify churn and retention. The model was trained using the centrality features derived from party networks and conventional personal features such as the playtime, login frequency, and payment records. Kim et al. [26] applied social network analysis to perform community detection and calculate centrality. They classified churn and retention using a model with custom-defined learning methods and structures. The model was trained using network centrality metrics, community metrics, and conventional personal features. Tamassia et al. [18] applied social network analysis to networks generated from user party records to create and use centrality features. They performed time-series classification using a hidden markov model. The model was trained using centrality features generated from the party network and conventional personal features. Kim et al. [19] performed churn and retention classification using an LSTM model, which was effective for modeling complex relationships in time-series datasets. The model was trained using conventional personal features. Lee et al. [23] and Oskarsdottir et al. [24] applied social network analysis to networks generated from party, trade, and friend interactions to create centrality features. They utilized models such as random forests to classify churn and retention. The models were trained using centrality features derived from social network analysis and conventional personal features. Moon et al. [21] investigated the impact of social activities in MMORPGs on user churn using actual game data and features extracted from prechurn activity logs to develop an efficient churn prediction model with reduced feature dimensions. Seo et al. [22] classified MMORPG users based on their social activity tendencies within guilds, analyzed churn rates and reasons for churn among categorized groups, and proposed a framework to predict churn by measuring gameplay engagement trends among these groups. Their framework used data from Aion, which is a flagship MMORPG by NCSOFT, and achieved an average precision of approximately 75%. Tao et al. [25] classified churn and retention by applying a static GCN to networks generated from friend and chat records. The feature matrix consisted of conventional personal features.

In summary, studies on user churn prediction have focused on identifying patterns of changes in user behavior over time. Across various domains, churn has been predicted on the basis of social activities by utilizing the principle of homophily, where contact among similar individuals occurs at a higher rate than that among dissimilar individuals [27]. In the gaming domain, studies have actively incorporated social activities such as friend interactions, trading, and chatting within games. This is mainly achieved by applying social network analysis to networks formed based on specific activities and deriving centrality features. Recent works have used GCNs, where embeddings are generated based on relationships between users, thus moving beyond simply indicating relative positions within a graph.

However, static graph models aggregate user interactions over a fixed period, resulting in a loss of temporal information. Static GCNs have inherent limitations in dynamic environments, as node states and edge connections remain fixed throughout the observation period, disregarding the temporal dynamics of user behavior. For instance, interactions between users (edges) that exist at one timestamp may disappear at the next, reflecting changes in social engagement. By collapsing these interactions into a single graph, static models overlook such fluctuations, leading to incomplete representations of user relationships. This static representation fails to capture the evolving nature of user interactions, which is crucial for predicting churn in dynamic environments such as MMORPGs.

Backgrounds

In the early stages of deep learning, Deep neural networks(DNNs) were developed to handle regular types of data effectively. Later, Recurrent neural networks(RNNs)-based models emerged, specializing in sequential data with inherent order. RNNs shows significant potential in various machine learning tasks for time-series data. The RNN processes the data iteratively, maintaining a state that evolves by transforming prior sequences. This state acts as a memory, capturing how earlier values influence the prediction system. The input to the RNN is represented as a 2D tensor with dimensions corresponding to timesteps and input features. At each timestep, the current input is fed into the RNN, which updates its state by combining the current input with the previously retained state. This updated state is then used to process the subsequent input, enabling the network to dynamically learn from the sequence over time. A simple RNN model combines the current input and the previous hidden state directly, so in the long-time series data, former input data is forgotten. To overcome this drawback, the Long Short-Term Memory (LSTM) [32] introduces a memory cell that maintains earlier inputs in their original form and supplies them to the RNN node when necessary. Additionally, the input is selectively passed to the hidden state, which connects to the input in the next iteration. This selective memory and state mechanism allows LSTMs to effectively capture long-term dependencies in sequential data. Bi-LSTM (Bidirectional Long Short-Term Memory) processes sequential input data in the backward direction as well as the forward direction. It enables the model to capture context from both the past and the future within the input sequence. DNNs and RNNs are not suitable for graph data that involves relational structures. This is because graph data represents relationships between nodes, a characteristic that DNNs cannot effectively capture. Moreover, graph data lacks a meaningful order among its data, making RNNs unsuitable since they process data sequentially. Graph neural networks (GNN) are specialized neural networks that are designed for graph-form data. GNN learns from nodes, edge, and graph structure. Basic GNN uses the message passing method where graph nodes iteratively update their representations by exchanging information with their neighbors [35]. However, early GNNs has a drawback in iterative message passing because it has proper optimization technique in aggregating node information. This led to computational inefficiency and difficulty in scaling to large graphs [34]. Graph convolution network (GCN) introduces the convolution calculation in the node information aggregation. GCN adopts a simple calculation of the adjacency matrix and node features to aggregate information from neighbors to represent the node [33].

Social graph construction

We generate graphs based on various user interactions within the game, such as trade records, guild membership, party records, and raid records. A trade involves the exchange of goods, such as gold or items, between users. A guild refers to a group of individuals who gather for camaraderie or to share common goals or interests. A party is when up to 6 users form a single group to complete quests or engage in hunting activities. A raid extends this concept, where up to 4 parties systematically form a single group to handle high-difficulty dungeons.

In the trade graph, an edge is formed between two users when a transaction occurs between them. In the guild, party, and raid graphs, edges are formed between users who belonged to the same guild, party, or raid, respectively, during the data collection period. We add the following conditions for the three networks that can consider the weight of an edge to construct a strong edge.

• For creating edges in the trade graph, we exclude one-time transactions by considering only those instances where the same user IDs have conducted transactions at least twice on the same day and both user IDs belong to the sample of 10,000 users collected for the experiment.
• To exclude random party matching in the party graph, we consider only those instances where users have been in the same party at least twice on the same day or where the party’s duration from creation to disbandment is at least 60 min.
• To exclude random party matching in the raid graph, we consider only those instances where users have been in the same party at least twice on the same day and have entered a raid dungeon at the same time.

TempGraphNet

Our model applies a GCN to strengthen the influence among users who frequently interact and weaken it among those who do not. Similar to how convolutional neural networks (CNNs), widely used for image recognition, identify patterns by analyzing small, local regions of an image, GCNs analyze the local neighborhoods within a social network graph. In CNNs, a "kernel" (or filter) slides across the image, looking at small groups of pixels at a time and combining their values to detect features like edges or textures. This process creates "feature maps" that highlight these detected features. GCNs perform a similar process, but instead of pixels on a grid, they operate on nodes in a graph. Each node represents a user, and the connections (edges) represent their relationships. A GCN layer gathers information from a user’s direct connections (friends, followers, etc.) and combines it to create a new representation for that user, capturing the influence of their social connections. Like CNNs emphasize local visual patterns, GCNs emphasize local social patterns within the network.

The mathematical operation of GCNs is as follows: Given a graph, , where is the set of nodes and E is the set of edges, each node, , has a feature vector, . A GCN layer uses the input feature vector, , (N is the number of nodes and F is the number of features) and the adjacency matrix, A, of the graph to generate the output feature vector, H. This process is generally expressed as follows:

(1)

Here, is the adjacency matrix with added self-loops and is the diagonal node degree matrix of . W is a trainable weight matrix, and is an activation function. We utilize trade, guild, party, and raid graphs, each of which passes through a GCN layer. Each graph represents a specific type of interaction among users, and the convolution operations on each graph generate embeddings that reflect the interaction information among users. Specifically, for each graph, G_k (k denotes the type of graph), we perform the following steps:

1. Prepare adjacency matrix A_k and feature matrix X_k for G_k.
2. Generate new feature matrix H_k from A_k and X_k through the GCN layer.
3. Concatenate the generated feature matrices, H_k, across channels to create composite embedding H for each user.

(2)

The reasons for concatenating the embeddings from each graph are as follows: First, each graph is generated based on different types of social activities, thereby enabling them to be processed independently. This ensures that each graph captures the unique patterns of social interactions through the independent application of GCNs.

Second, this method enables multimodal integration. Each graph represents different modalities, and a unified embedding is created by concatenating the graphs. This enables the model to comprehensively utilize diverse interaction information, thus facilitating a nuanced understanding of complex relationships and interaction patterns among customers.

Last, individual characteristics can be clearly represented by concatenating the embeddings from each graph. Each customer engages in various social activities, resulting in distinct interaction patterns. The model can accurately capture and model diverse relationships among customers by integrating the embeddings from multiple graphs, thereby enhancing the predictive performance of customer churn.

Therefore, the concatenation of the embeddings from each graph plays a crucial role in enhancing the accuracy and explanatory capability of the model through the independent processing and integration of multimodal interaction information.

Our model incorporates a Bi-LSTM layer based on two factors. First, we incorporate the Bi-LSTM layer to effectively learn the change patterns in user social graphs over time. Bidirectional Long Short-Term Memory networks (Bi-LSTMs) are a specialized type of recurrent neural network (RNN) designed for processing sequential data, such as time series. Unlike traditional RNNs, which process information in a single direction, Bi-LSTMs process input sequences in both forward and backward directions. This bidirectional processing enables the network to capture contextual information from both preceding and subsequent elements in the sequence. In the context of social network analysis, this means the Bi-LSTM can consider both past interactions and potential future trends to better understand the evolution of user behavior. This capability is crucial for accurately predicting user churn, as user behavior is influenced by both past actions and anticipated future interactions. Research on user churn prediction has highlighted the crucial role of capturing the evolution of user behavior over time [28, 29]. Despite the necessity of designing domain-specific churn prediction models, the temporal evolution of user behavior remains a key factor in predicting user churn. The proposed model uses the Bi-LSTM layer to effectively capture the behavior change patterns of retained and churned users.

The Bi-LSTM layer processes sequences bidirectionally by simultaneously utilizing forward and backward LSTM. A Bi-LSTM consists of two LSTM networks: a forward LSTM and a backward LSTM. The forward LSTM processes the input sequence from the beginning to the end, while the backward LSTM processes the same sequence in reverse order. At each time step, the outputs from both the forward and backward LSTMs are combined, typically through concatenation. This combined output represents a more comprehensive understanding of the current element in the sequence, as it incorporates information from both its past and its future context. In our model, the input sequence to the Bi-LSTM is the series of user social graph embeddings generated by the GCN layers. By processing this sequence bidirectionally, the Bi-LSTM captures the dynamic changes in user relationships and behaviors over time. Specifically, for a given input sequence, , the forward LSTM computes and the backward LSTM computes , which are concatenated to form the final output, . This enables the model to learn the complex features of user behavior patterns at each timestamp.

Second, in contrast to previous studies that aggregated all interactions that occurred during the data collection period into a single graph, our approach considers the dynamic nature of trade targets, party members, guild affiliations, and other features within online games. These attributes can vary with timestamps. Therefore, we generate graphs at each time step to capture these dynamics, thus creating inputs in the form of dynamic graphs. This strengthens the influence among customers who interact with each other and incorporates temporal changes.

At each time step, the generated graphs pass through GCN layers, and the concatenated embeddings are used as inputs to the Bi-LSTM layer. This approach enables us to effectively model and analyze temporal changes while leveraging the aggregated influence among interacting users.

This approach consists of the following steps:

1. At each timestamp, T_t, the graph data are passed through GCN layers to generate embeddings for each node.
2. The generated embeddings are concatenated across channels to obtain a comprehensive embedding for that timestamp.
3. This sequence of comprehensive embeddings over time is used as the input to the Bi-LSTM layer to learn the changes in user behavior patterns.

Through this method, the proposed model effectively integrates the graph embeddings that reflect relationships among users at each timestamp while capturing temporal changes to enhance the accuracy of user churn prediction. Ultimately, the output of the Bi-LSTM layers is fed into the ODE segment to obtain refined predictions.

TempODEGraphNet

Our model employs a neural ODE to enhance the consistency of model performance [30]. A neural ODE combines neural networks with differential equations; this makes it particularly useful for modeling time-series data or continuous dynamic systems. Conventional neural networks are used to learn complex relationships between inputs and outputs. They are composed of multiple layers of neurons that adjust weights and apply activation functions to generate outputs as data pass through a network. In contrast, a neural ODE models dynamic systems where the network output varies discretely, unlike conventional neural networks that generate fixed outputs for given inputs. This dynamic system is represented by the following differential equation:

(3)

Here, x(t) represents a function of time t and defines the rate of change in . The function is modeled by a neural network for given input and time t to determine as a function of time in the network output. The model trained using the neural ODE starts from given initial conditions, and it predicts the state of the system over time through differential equations. Thus, it can be used to model dynamic systems.

The core idea of the neural ODE is to find the solution to the differential equation rather than directly update network parameters. For this purpose, differential equations are solved using numerical methods such as the Runge–Kutta method. The Dopri-5 method used in this study is a high-order Runge–Kutta method that provides high accuracy while considering computational efficiency. This method computes one 5th order approximation and another 4th order approximation, estimates the error by comparing them, and accordingly adjusts the step size. It is represented by the following formula:

(4)

• y_n + 1: the approximated solution at the next time step.
• y_n: the current solution.
• : the weighted sum of the gradients used to compute the next value of y, where s is the number of stages in the Runge-Kutta method.
• k_i: the gradients calculated at each stage of the step, used to estimate the slope (derivative) of the solution curve at different points within the current step.
• h: the step size.
• t_n: the current time.
• c_i: the coefficients that determine the points within the interval at which the function evaluations are to be made.
• a_ij: the coefficients used to weigh the gradients from previous stages for calculating each subsequent gradient k_i.

Here, represents the gradient at each step, and it is calculated as follows:

(5)

The Dopri-5 method efficiently solves differential equations within specified error tolerances by dynamically adjusting step sizes using the 5th and 4th order approximations at each step. This method enables neural ODEs to simultaneously maintain high accuracy and stability. Conventional neural networks directly learn the mapping between inputs and outputs. The gradient descent method is used to update the weight that connects inputs and outputs in the direction that reduces the loss. The gradients required to calculate the weight update are obtained using backpropagation. In contrast, neural ODEs find solutions to differential equations starting from given initial conditions, thereby modeling the dynamic changes in systems. This enables neural ODEs to approximate primitive functions more effectively compared with conventional methods. Neural ODEs achieve sophisticated predictions while maintaining model coherence. This is particularly beneficial for addressing dynamic and complex patterns such as customer churn prediction.

Experimental results

The performance of the model is measured as the average of the F1 scores for both test sets, and the F1 scores are defined as follows:

(6)

The performance of the proposed model is compared with that of the top-performing participant in Track 1 of the GDMC 2017 competition using the same dataset [31]. The Yokozuma Data team, which achieved the highest ranking in GDMC 2017 Track 1, addressed the data imbalance issue through cost sensitive learning and adjusted label strategies. They utilized nonlinear modeling to determine temporal patterns. For structural modeling based on decision trees, they employed preprocessing techniques, such as linear discriminant analysis and PCA, to extract an optimal feature set. They optimized their model using the XGBoost algorithm and hyperopt and achieved an average F1 score of 0.62 across Test1 and Test2. The performance comparison evaluates the impact of considering social interaction on various models, including TempODEGraphNet , tempGraphNet (TGN) trained using standard methods, Yokozuma Data’s model, decision trees, random forests, and static GCN models. The results are presented in Table 5.

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Table 5. Performance comparison.

https://doi.org/10.1371/journal.pone.0321560.t005

To ensure consistency in model training, tempODEGraphNet and TGN are input in chronological order rather than random order. The Adam optimizer with a learning rate of 0.001 is used. Training is performed for 1000 epochs with early stopping.

The proposed model demonstrates the best performance in terms of the average F1 score, regardless of whether the neural ODE is applied. The performance gap between TempODEGraphNet and static graph models highlights the limitations of static approaches in dynamic settings. Static Graph Convolutional Networks has limitations in that they aggregate user interactions over the entire data collection period without accounting for temporal changes. This approach fixes node states and edge connections, ignoring the dynamic nature of user behavior. Interactions (edges) between users that exist at one point in time may disappear or reemerge at another, reflecting fluctuations in graph data. These temporal variations are important for detecting early signals of user churn. By reducing these interactions into a single static graph, important temporal patterns are smoothed out or lost, which can result in delayed churn detection or the misclassification of active users as retained. TempODEGraphNet addresses this limitation by constructing dynamic graphs at each timestamp, allowing the model to track changes in node states and edge connections over time. This ensures that short-term fluctuations and evolving user relationships are effectively captured, providing a more comprehensive representation of user behavior in dynamic environments. In addition, the performance of the static GCN is better than that of random forests for the same feature matrix. This suggests that considering interactions between customers positively improves the model performance for predicting customer churn, particularly in the domain of MMORPGs. To further analyze the model performance, confusion matrices for ours and Yokozuma’s models are presented in Table 6.

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Table 6. Confusion Matrices for Ours and Yokozuma’s Model on Test1 and Test2.

https://doi.org/10.1371/journal.pone.0321560.t006

The confusion matrices highlight key differences in the models’ predictive capabilities. TempODEGraphNet demonstrates consistently lower false positive (FP) and false negative (FN) rates across both datasets, indicating superior model stability and reliability. Specifically, TempODEGraphNet achieves lower FP rates compared to Yokozuma’s model. This suggests that TempODEGraphNet is more conservative in predicting churn, resulting in fewer incorrect churn predictions for users who were actually retained. Moreover, TempODEGraphNet records higher true positive values in Test1 compared to Yokozuma’s model, demonstrating improved sensitivity to churn cases. However, Yokozuma’s model achieves slightly higher TP values in Test2 compared to TempODEGraphNet, indicating that while Yokozuma’s model may capture more churn users, it does so at the cost of increased false alarms (FP). These findings suggest that TempODEGraphNet offers a more balanced approach, effectively capturing churn cases while minimizing false positives, which can be critical in applications where overestimating churn could lead to unnecessary interventions or resource misallocations.

To compare the model performance based on the application of the neural ODE, we measure the performance by randomly removing 10 days from the 6 week training dataset and varying the random seed. The results are shown in Table 7.

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Table 7. Performance comparison based on the application of neural ODE in terms of F1 score.

https://doi.org/10.1371/journal.pone.0321560.t007

The model with the neural ODE achieves an average F1 score of 0.60, which is comparable to the F1 score of the conventional model (0.59). However, the standard deviation (Std.) of the model with the neural ODE is smaller (0.011 for Test1, 0.015 for Test2, and 0.007 overall) than that of the conventional model (0.044 for Test1, 0.033 for Test2, and 0.035 overall). This indicates that the neural ODE enhances the consistency and stability of the model.

To statistically assess whether there is a difference in the consistency and stability of the models with and without the neural ODE, an F-test is conducted to verify if the variances between the two groups differ significantly. Performance metrics are recorded up to trial 20 for the models with the neural ODE and conventional models on the Test1 and Test2 datasets. Separate F-tests are performed for comparing the performances of the models for the Test1 and Test2 datasets. The results are presented in Table 8. The F-test results reveal that the p-values for Test1 () and Test2 (0.0021714) are both below the 0.05 significance threshold. This indicates that the variances between the two groups are significantly different, implying that the model incorporating the neural ODE demonstrates significantly lower variability compared to the conventional model. The reduced variance reflects that the neural ODE enhances the stability and consistency of the model across different trials. While this analysis focuses on the stability of the model’s performance, it supports the argument that the neural ODE contributes to more reliable and robust predictions by minimizing fluctuations in performance. This is particularly critical in dynamic environments where consistent outputs are essential for reliable churn prediction. The significant difference in variance suggests that the neural ODE’s integration leads to a model that is less sensitive to variations in the data, reinforcing its advantage over conventional approaches.

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Table 8. Performance comparison results.

https://doi.org/10.1371/journal.pone.0321560.t008