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Agent-based models (ABMs) are used to simulate human-subject experiments. A comprehensive understanding of these human systems often requires executing large numbers of simulations, but these requirements are constrained by computational and other resources. In this work, we build a framework of digital twins for modeling human-subject experiments. The framework has three modules: ABMs of player behaviors built from game data; extensions of these models to represent virtual assistants (agents that are exogenously manipulated to create controlled environments for human agents); and an uncertainty quantification module composed of functional ANOVA and a Gaussian process-based emulator. The emulator is built from the extended ABM; we focus on emulator validation. By incorporating experimental data and agent-based simulation data, our proposed framework enhances the virtual representation of the dynamics in human-subject word formation experiments, which we consider a digital twin. Networked anagram experiments are used as an exemplar to demonstrate the methods. 

Researchers have modeled contagion processes on social networks for wide ranging applications, including spreading of epidemics, financial defaults, actions such as joining social media sites, and rumors. So, too, researchers have developed a host of intervention methods to control harmful contagions on networks; among these approaches are node and edge removal, separating network communities, altering contagion properties, and introducing a second competing contagion. In this work, minimum dominating sets are used to identify blocking nodes—nodes that do not contract a contagion and therefore also do not assist in transmitting it. A novel, generalized method that utilizes integer linear programming to determine exact minimum dominating sets (which is an NP-hard problem) has been developed for a subgraph of any social network for any combination of covering distance and coverage requirement. Three social networks are used to understand and evaluate (i) the method itself and (ii) the efficacy of the blocking nodes that the method produces to stop contagion spread. 

Common knowledge (CK) is a phenomenon where a group of individuals each knows some collection of information, and, in essence, everyone knows that everyone knows the information. There are many applications involving CK, including business decision making, protests and rebellions, and online advertising. CK can lead to contagion and collective action but in ways that are fundamentally different from classic (e.g., Granovetter) threshold models used in the social sciences. Researchers developed CK models to enable the computation of contagion in networked populations. But these models have largely not been investigated using experiments with human subjects. In this work, we conduct a successive analysis of online CK experiments. We devise a flexible and interpretable statistical method to investigate the effects of significant factors, such as network structure and communication type. Among our findings, we demonstrate a phase change in group payout in the games that is caused by prohibiting player communication. 

In a networked anagram game, players are provided letters with possible actions of requesting letters from their neighbours, replying to letter requests, or forming words. The objective is to form as many words as possible as a team. The experimental data show that behaviours among players can vary significantly. However, simulations using agent-based models (ABM) in the literature often have not incorporated proper uncertainty quantification methods to characterise diverse behaviours of players. In this work, we propose an uncertainty quantification framework to build, exercise, and evaluate agent behaviour models and simulations for networked group anagram games. Specifically, using the data of game experiments, the proposed framework considers the clustering of game players based on their performance to reflect players’ heterogeneity. Moreover, we also quantify uncertainty within each cluster through statistical modelling and inference. Numerical studies of networked game configurations are conducted to demonstrate the merits of the proposed framework. 

Common knowledge (CK) is a phenomenon where each individual within a group knows the same information and everyone knows that everyone knows the information, infinitely recursively. CK spreads information as a contagion through social networks in ways different from other models like susceptible-infectious-recovered (SIR) model. In a model of CK on Facebook, the biclique serves as the characterizing graph substructure for generating CK, as all nodes within a biclique share CK through their walls. To understand the effects of network structure on CK-based contagion, it is necessary to control the numbers and sizes of bicliques in networks. Thus, learning how to generate these CK networks (CKNs) is important. Consequently, we develop an exponential random graph model (ERGM) that constructs networks while controlling for bicliques. Our method offers powerful prediction and inference, reduces computational costs significantly, and has proven its merit in contagion dynamics through numerical experiments. 

Experiments that are games played among a network of players are widely used to study human behavior. Furthermore, bots or intelligent systems can be used in these games to produce contexts that elicit particular types of human responses. Bot behaviors could be specified solely based on experimental data. In this work, we take a different perspective, called the Probability Calibration (PC) approach, to simulate networked group anagram games with certain players having bot-like behaviors. The proposed method starts with data-driven models and calibrates in principled ways the parameters that alter player behaviors. It can alter the performance of each type of agent (e.g., bot) in group anagram games. Further, statistical methods are used to test whether the PC models produce results that are statistically different from those of the original models. Case studies demonstrate the merits of the proposed method. 

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. 

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. 

Heterogeneous player behaviors are commonly observed in games. It is important to quantify and visualize these heterogeneities in order to understand collective behaviors. Our work focuses on developing a Bayesian approach for uncertainty visualization in a model of networked anagram games. In these games, team members collectively form as many words as possible by sharing letters with their neighbors in a network. Heterogeneous player behaviors include great differences in numbers of words formed and the amount of cooperation among networked neighbors. Our Bayesian approach provides meaningful insights for inferring worst, average, and best player performance within behavioral clusters, overcoming previous model shortcomings. These inferences are integrated into a simulation framework to understand the implications of model uncertainty and players' heterogeneous behaviors.