Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data

We consider learning, from strictly behavioral data, the structure and parameters of linear influence games (LIGs), a class of parametric graphical games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic inference (CSI): Making inferences from causal interventions on stable behavior in strategic settings. Applications include the identification of the most influential individuals in large (social) networks. Such tasks can also support policy-making analysis. Motivated by the computational work on LIGs, we cast the learning problem as maximum-likelihood estimation (MLE) of a generative model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation uncovers the fundamental interplay between goodness-of-fit and model complexity: good models capture equilibrium behavior within the data while controlling the true number of equilibria, including those unobserved. We provide a generalization bound establishing the sample complexity for MLE in our framework. We propose several algorithms including convex loss minimization (CLM) and sigmoidal approximations. We prove that the number of exact PSNE in LIGs is small, with high probability; thus, CLM is sound. We illustrate our approach on synthetic data and real-world U.S. congressional voting records. We briefly discuss our learning framework's generality and potential applicability to general graphical games.Comment: Journal of Machine Learning Research. (accepted, pending publication.) Last conference version: submitted March 30, 2012 to UAI 2012. First conference version: entitled, Learning Influence Games, initially submitted on June 1, 2010 to NIPS 201

Learning Sparse Polymatrix Games in Polynomial Time and Sample Complexity

We consider the problem of learning sparse polymatrix games from observations of strategic interactions. We show that a polynomial time method based on $\ell_{1,2}$-group regularized logistic regression recovers a game, whose Nash equilibria are the $\epsilon$-Nash equilibria of the game from which the data was generated (true game), in $\mathcal{O}(m^4 d^4 \log (pd))$ samples of strategy profiles --- where $m$ is the maximum number of pure strategies of a player, $p$ is the number of players, and $d$ is the maximum degree of the game graph. Under slightly more stringent separability conditions on the payoff matrices of the true game, we show that our method learns a game with the exact same Nash equilibria as the true game. We also show that $\Omega(d \log (pm))$ samples are necessary for any method to consistently recover a game, with the same Nash-equilibria as the true game, from observations of strategic interactions. We verify our theoretical results through simulation experiments

Iterated Prisoner's Dilemma with Choice and Refusal of Partners

This article extends the traditional iterated prisoner's dilemma (IPD) with round-robin partner matching by permitting players to choose and refuse partners in each iteration on the basis of continually updated expected payoffs. Comparative computer experiments are reported that indicate the introduction of partner choice and refusal accelerates the emergence of mutual cooperation in the IPD relative to round-robin partner matching. Moreover, in contrast to findings for round-robin partner matching (in which the average payoffs of the players tend to be either clustered around the mutual cooperation payoff or widely scattered), the average payoff scores of the players with choice and refusal of partners tend to cluster into two or more distinct narrow bands. Preliminary analytical and computational sensitivity studies are also reported for several key parameters. Related work can be accessed here: http://www.econ.iastate.edu/tesfatsi/tnghome.htmiterated prisoner's dilemma; preferential partner selection; evolutionary game theory

Citizen Social Lab: A digital platform for human behaviour experimentation within a citizen science framework

Cooperation is one of the behavioral traits that define human beings, however we are still trying to understand why humans cooperate. Behavioral experiments have been largely conducted to shed light into the mechanisms behind cooperation and other behavioral traits. However, most of these experiments have been conducted in laboratories with highly controlled experimental protocols but with varied limitations which limits the reproducibility and the generalization of the results obtained. In an attempt to overcome these limitations, some experimental approaches have moved human behavior experimentation from laboratories to public spaces, where behaviors occur naturally, and have opened the participation to the general public within the citizen science framework. Given the open nature of these environments, it is critical to establish the appropriate protocols to maintain the same data quality that one can obtain in the laboratories. Here, we introduce Citizen Social Lab, a software platform designed to be used in the wild using citizen science practices. The platform allows researchers to collect data in a more realistic context while maintaining the scientific rigour, and it is structured in a modular and scalable way so it can also be easily adapted for online or brick-and-mortar experimental laboratories. Following citizen science guidelines, the platform is designed to motivate a more general population into participation, but also to promote engaging and learning of the scientific research process. We also review the main results of the experiments performed using the platform up to now, and the set of games that each experiment includes. Finally, we evaluate some properties of the platform, such as the heterogeneity of the samples of the experiments and their satisfaction level, and the parameters that demonstrate the robustness of the platform and the quality of the data collected.Comment: 17 pages, 11 figures and 4 table