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In network games, individuals interact strategically within network environments to maximize their utilities. However, obtaining network structures is challenging. In this work, we propose an unsupervised learning model, called data-dependent gated-prior graph variational autoencoder (GPGVAE), that infers the underlying latent interaction type (strategic complement vs. substitute) among individuals and the latent network structure based on their observed actions. Specially, we propose a spectral graph neural network (GNN) based encoder to predict the interaction type and a data-dependent gated prior that models network structures conditioned on the interaction type. We further propose a Transformer based mixture of Bernoulli encoder of network structures and a GNN based decoder of game actions. We systematically study the Monte Carlo gradient estimation methods and effectively train our model in a stage-wise fashion. Extensive experiments across various synthetic and real-world network games demonstrate that our model achieves state-of-the-art performances in inferring network structures and well captures interaction types. 

Machine learning is commonly used to estimate the heterogeneous treatment effects (HTEs) in randomized experiments. Using large-scale randomized experiments on the Facebook and Criteo platforms, we observe substantial discrepancies between machine learning-based treatment effect estimates and difference-in-means estimates directly from the randomized experiment. This paper provides a two-step framework for practitioners and researchers to diagnose and rectify this discrepancy. We first introduce a diagnostic tool to assess whether bias exists in the model-based estimates from machine learning. If bias exists, we then offer a model-agnostic method to calibrate any HTE estimates to known, unbiased, subgroup difference-in-means estimates, ensuring that the sign and magnitude of the subgroup estimates approximate the model-free benchmarks. This calibration method requires no additional data and can be scaled for large data sets. To highlight potential sources of bias, we theoretically show that this bias can result from regularization and further use synthetic simulation to show biases result from misspecification and high-dimensional features. We demonstrate the efficacy of our calibration method using extensive synthetic simulations and two real-world randomized experiments. We further demonstrate the practical value of this calibration in three typical policy-making settings: a prescriptive, budget-constrained optimization framework; a setting seeking to maximize multiple performance indicators; and a multitreatment uplift modeling setting. 

In this paper, we develop distributed computation algorithms for Nash equilibriums of linear quadratic network games with proven differential privacy guarantees. In a network game with each player's payoff being a quadratic function, the dependencies of the decisions in the payoff function naturally encode a network structure governing the players' inter-personal influences. Such social influence structure and the individual marginal payoffs of the players indicate economic spillovers and individual preferences, and thus they are subject to privacy concerns. For distributed computing of the Nash equilibrium, the players are interconnected by a public communication graph, over which dynamical states are shared among neighboring nodes. When the players' marginal payoffs are considered to be private knowledge, we propose a distributed randomized gradient descent algorithm, in which each player adds a Laplacian random noise to her marginal payoff in the recursive updates. It is proven that the algorithm can guarantee differential privacy and convergence in expectation to the Nash equilibrium of the network game at each player's state. Moreover, the mean-square error between the players' states and the Nash equilibrium is shown to be bounded by a constant related to the differential privacy level. Next, when both the players' marginal payoffs and the influence graph are private information, we propose two distributed algorithms by randomized communication and randomized projection, respectively, for privacy preservation. The differential privacy and convergence guarantees are also established for such algorithms. 

We use high-resolution mobile phone data with geolocation information and propose a novel technical framework to study how social influence propagates within a phone communication network and affects the offline decision to attend a performance event. Our fine-grained data are based on the universe of phone calls made in a European country between January and July 2016. We isolate social influence from observed and latent homophily by taking advantage of the rich spatial-temporal information and the social interactions available from the longitudinal behavioral data. We find that influence stemming from phone communication is significant and persists up to four degrees of separation in the communication network. Building on this finding, we introduce a new “influence” centrality measure that captures the empirical pattern of influence decay over successive connections. A validation test shows that the average influence centrality of the adopters at the beginning of each observational period can strongly predict the number of eventual adopters and has a stronger predictive power than other prevailing centrality measures such as the eigenvector centrality and state-of-the-art measures such as diffusion centrality. Our centrality measure can be used to improve optimal seeding strategies in contexts with influence over phone calls, such as targeted or viral marketing campaigns. Finally, we quantitatively demonstrate how raising the communication probability over each connection, as well as the number of initial seeds, can significantly amplify the expected adoption in the network and raise net revenue after taking into account the cost of these interventions. History: Sam Ransbotham, Senior Editor; Yan Huang, Associate Editor. Funding: Y. Leng acknowledges the support provided by the National Science Foundation [Grant IIS-2153468]. E. Moro acknowledges the support provided by the National Science Foundation [Grant 2218748]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/isre.2023.1231 . 

Decision-making on networks can be explained by both homophily and social influences. While homophily drives the formation of communities with similar characteristics, social influences occur both within and between communities. Social influences can be reasoned through role theory, which indicates that the influences among individuals depending on their roles and the behavior of interest. To operationalize these social science theories, we empirically identify the homophilous communities and use the community structures to capture such “roles”, affecting particular decision-making processes. We propose a generative model named the Stochastic Block influences Model and jointly analyzed both network formation and behavioral influences within and between different empirically-identified communities. To evaluate the performance and demonstrate the interpretability of our method, we study the adoption decisions for a microfinance product in Indian villages. We show that although individuals tend to form links within communities, there are strongly positive and negative social influences between communities, supporting the weak ties theory. Moreover, communities with shared characteristics are associated with positive influences. In contrast, communities that do not overlap are associated with negative influences. Our framework facilitates the quantification of the influences underlying decision communities and is thus a helpful tool for driving information diffusion, viral marketing, and technology adoption. 

Strategic interactions between a group of individuals or organisations can be modelled as games played on networks, where a player’s payoff depends not only on their actions but also on those of their neighbours. Inferring the network structure from observed game outcomes (equilibrium actions) is an important problem with numerous potential applications in economics and social sciences. Existing methods mostly require the knowledge of the utility function associated with the game, which is often unrealistic to obtain in real-world scenarios. We adopt a transformer-like architecture which correctly accounts for the symmetries of the problem and learns a mapping from the equilibrium actions to the network structure of the game without explicit knowledge of the utility function. We test our method on three different types of network games using both synthetic and real-world data, and demonstrate its effectiveness in network structure inference and superior performance over existing methods.