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1. Uncertainty Visualization for Characterizing Heterogeneous Human Behaviors in Discrete Dynamical System Models

   Liu, Xueying ; Hu, Zhihao ; Deng, Xinwei ; Kuhlman, Chris J. ( August 2023 , Advances in complex systems)

   When modeling human behavior in multi-player games, it is important to understand heterogeneous aspects of player behaviors. By leveraging experimental data and agent-based simulations, various data-driven modeling methods can be applied. This provides a great opportunity to quantify and visualize the uncertainty associated with these methods, allowing for a more comprehensive understanding of the individual and collective behaviors among players. For networked anagram games, player behaviors can be heterogeneous in terms of the number of words formed and the amount of cooperation among networked neighbors. Based on game data, these games can be modeled as discrete dynamical systems characterized by probabilistic state transitions. In this work, we present both Frequentist and Bayesian approaches for visualizing uncertainty in networked anagram games. These approaches help to elaborate how players individually and collectively form words by sharing letters with their neighbors in a network. Both approaches provide valuable insights into inferring the worst, average, and best player performance within and between behavioral clusters. Moreover, interesting contrasts between the Frequentist and Bayesian approaches can be observed. The knowledge and inferences gained from these approaches are incorporated into an agent-based simulation framework to further demonstrate model uncertainty and players’ heterogeneous behaviors. 

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2. Versatile Uncertainty Quantification of Contrastive Behaviors for Modeling Networked Anagram Games

   https://doi.org/10.1007/978-3-030-93409-5_53  

   Hu, Zhihao ; Deng, Xinwei ; Kuhlman, Chris J ( January 2021 , Complex Networks and their Applications)

   In a networked anagram game, each team member is given a set of letters and members collectively form as many words as possible. They can share letters through a communication network in assisting their neighbors in forming words. There is variability in behaviors of players, e.g., there can be large differences in numbers of letter requests, of replies to letter requests, and of words formed among players. Therefore, it is of great importance to understand uncertainty and variability in player behaviors. In this work, we propose versatile uncertainty quantification (VUQ) of behaviors for modeling the networked anagram game. Specifically, the proposed methods focus on building contrastive models of game player behaviors that quantify player actions in terms of worst, average, and best performance. Moreover, we construct agent-based models and perform agent-based simulations using these VUQ methods to evaluate the model building methodology and understand the impact of uncertainty. We believe that this approach is applicable to other networked games. 

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3. A Bayesian Uncertainty Quantification Approach for Agent-Based Modeling of Networked Anagram Games

   Liu, Xueying ; Hu, Zhihao ; Deng, Xinwei ; Kuhlman, Chris J. ( December 2022 , Proceedings Winter Simulation Conference)

   In group anagram games, players cooperate to form words by sharing letters that they are initially given. The aim is to form as many words as possible as a group, within five minutes. Players take several different actions: requesting letters from their neighbors, replying to letter requests, and forming words. Agent-based models (ABMs) for the game compute likelihoods of each player’s next action, which contain uncertainty, as they are estimated from experimental data. We adopt a Bayesian approach as a natural means of quantifying uncertainty, to enhance the ABM for the group anagram game. Specifically, a Bayesian nonparametric clustering method is used to group player behaviors into different clusters without pre-specifying the number of clusters. Bayesian multi nominal regression is adopted to model the transition probabilities among different actions of the players in the ABM. We describe the methodology and the benefits of it, and perform agent-based simulations of the game. 

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4. Approaches to Uncertainty Quantification in Building Models of Human Behavior

   Hu, Zhihao ; Deng, Xinwei ; Kuhlman, Chris J ( January 2021 , Winter Simulation Conference)

   In a group anagram game, players are provided letters to form as many words as possible. They can also request letters from their neighbors and reply to letter requests. Currently, a single agent-based model is produced from all experimental data, with dependence only on number of neighbors. In this work, we build, exercise, and evaluate enhanced agent behavior models for networked group anagram games under an uncertainty quantification framework. Specifically, we cluster game data for players based on their skill levels (forming words, requesting letters, and replying to requests), perform multinomial logistic regression for transition probabilities, and quantify uncertainty within each cluster. The result of this process is a model where players are assigned different numbers of neighbors and different skill levels in the game. We conduct simulations of ego agents with neighbors to demonstrate the efficacy of our proposed methods. 

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5. Modeling Player Engagement with Bayesian Hierarchical Models

   Sawyer, R. ; Rowe, J. ; Azevedo, R. ; Lester, J. ( January 2018 , Proceedings of the Fourteenth AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment)

   Modeling player engagement is a key challenge in games. However, the gameplay signatures of engaged players can be highly context-sensitive, varying based on where the game is used or what population of players is using it. Traditionally, models of player engagement are investigated in a particular context, and it is unclear how effectively these models generalize to other settings and populations. In this work, we investigate a Bayesian hierarchical linear model for multi-task learning to devise a model of player engagement from a pair of datasets that were gathered in two complementary contexts: a Classroom Study with middle school students and a Laboratory Study with undergraduate students. Both groups of players used similar versions of Crystal Island, an educational interactive narrative game for science learning. Results indicate that the Bayesian hierarchical model outperforms both pooled and context-specific models in cross-validation measures of predicting player motivation from in-game behaviors, particularly for the smaller Classroom Study group. Further, we find that the posterior distributions of model parameters indicate that the coefficient for a measure of gameplay performance significantly differs between groups. Drawing upon their capacity to share information across groups, hierarchical Bayesian methods provide an effective approach for modeling player engagement with data from similar, but different, contexts. 

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