3,036 research outputs found
On the robustness of learning in games with stochastically perturbed payoff observations
Motivated by the scarcity of accurate payoff feedback in practical
applications of game theory, we examine a class of learning dynamics where
players adjust their choices based on past payoff observations that are subject
to noise and random disturbances. First, in the single-player case
(corresponding to an agent trying to adapt to an arbitrarily changing
environment), we show that the stochastic dynamics under study lead to no
regret almost surely, irrespective of the noise level in the player's
observations. In the multi-player case, we find that dominated strategies
become extinct and we show that strict Nash equilibria are stochastically
stable and attracting; conversely, if a state is stable or attracting with
positive probability, then it is a Nash equilibrium. Finally, we provide an
averaging principle for 2-player games, and we show that in zero-sum games with
an interior equilibrium, time averages converge to Nash equilibrium for any
noise level.Comment: 36 pages, 4 figure
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
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