8 research outputs found
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
-group regularized logistic regression recovers a game, whose Nash
equilibria are the -Nash equilibria of the game from which the data
was generated (true game), in samples of
strategy profiles --- where is the maximum number of pure strategies of a
player, is the number of players, and 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
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
Provable Sample Complexity Guarantees for Learning of Continuous-Action Graphical Games with Nonparametric Utilities
In this paper, we study the problem of learning the exact structure of
continuous-action games with non-parametric utility functions. We propose an
regularized method which encourages sparsity of the coefficients of
the Fourier transform of the recovered utilities. Our method works by accessing
very few Nash equilibria and their noisy utilities. Under certain technical
conditions, our method also recovers the exact structure of these utility
functions, and thus, the exact structure of the game. Furthermore, our method
only needs a logarithmic number of samples in terms of the number of players
and runs in polynomial time. We follow the primal-dual witness framework to
provide provable theoretical guarantees.Comment: arXiv admin note: text overlap with arXiv:1911.0422
Design and Analysis of Strategic Behavior in Networks
Networks permeate every aspect of our social and professional life.A networked system with strategic individuals can represent a variety of real-world scenarios with socioeconomic origins. In such a system, the individuals\u27 utilities are interdependent---one individual\u27s decision influences the decisions of others and vice versa. In order to gain insights into the system, the highly complicated interactions necessitate some level of abstraction. To capture the otherwise complex interactions, I use a game theoretic model called Networked Public Goods (NPG) game. I develop a computational framework based on NPGs to understand strategic individuals\u27 behavior in networked systems. The framework consists of three components that represent different but complementary angles to the understanding. The first part is learning, which aims to produce quantitative and interpretable models of individuals\u27 behavior. The second part focuses on analyzing the individuals\u27 equilibrium behavior, providing guidance on what a rational individual would do when facing other individuals\u27 strategic behavior. The individuals\u27 equilibrium behavior may not be socially preferable, motivating the third part to investigate designing their behavior through network modifications
Learning Tree Structured Potential Games
© 2016 NIPS Foundation - All Rights Reserved. Many real phenomena, including behaviors, involve strategic interactions that can be learned from data. We focus on learning tree structured potential games where equilibria are represented by local maxima of an underlying potential function. We cast the learning problem within a max margin setting and show that the problem is NP-hard even when the strategic interactions form a tree. We develop a variant of dual decomposition to estimate the underlying game and demonstrate with synthetic and real decision/voting data that the game theoretic perspective (carving out local maxima) enables meaningful recovery