94,770 research outputs found
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
A cognitive hierarchy model of learning in networks
This paper proposes a method for estimating a hierarchical model of bounded rationality in games of learning in networks. A cognitive hierarchy comprises a set of cognitive types whose behavior ranges from random to substantively rational. SpeciÖcally, each cognitive type in the model corresponds to the number of periods in which economic agents process new information. Using experimental data, we estimate type distributions in a variety of task environments and show how estimated distributions depend on the structural properties of the environments. The estimation results identify signiÖcant levels of behavioral hetero-geneity in the experimental data and overall conÖrm comparative static conjectures on type distributions across task environments. Surprisingly, the model replicates the aggregate pat-terns of the behavior in the data quite well. Finally, we found that the dominant type in the data is closely related to Bayes-rational behavior
On Similarities between Inference in Game Theory and Machine Learning
In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifically, we consider the analogies between smooth best responses in fictitious play and Bayesian inference methods. Initially, we use these insights to develop and demonstrate an improved algorithm for learning in games based on probabilistic moderation. That is, by integrating over the distribution of opponent strategies (a Bayesian approach within machine learning) rather than taking a simple empirical average (the approach used in standard fictitious play) we derive a novel moderated fictitious play algorithm and show that it is more likely than standard fictitious play to converge to a payoff-dominant but risk-dominated Nash equilibrium in a simple coordination game. Furthermore we consider the converse case, and show how insights from game theory can be used to derive two improved mean field variational learning algorithms. We first show that the standard update rule of mean field variational learning is analogous to a Cournot adjustment within game theory. By analogy with fictitious play, we then suggest an improved update rule, and show that this results in fictitious variational play, an improved mean field variational learning algorithm that exhibits better convergence in highly or strongly connected graphical models. Second, we use a recent advance in fictitious play, namely dynamic fictitious play, to derive a derivative action variational learning algorithm, that exhibits superior convergence properties on a canonical machine learning problem (clustering a mixture distribution)
Quality-Of-Service Provisioning in Decentralized Networks: A Satisfaction Equilibrium Approach
This paper introduces a particular game formulation and its corresponding
notion of equilibrium, namely the satisfaction form (SF) and the satisfaction
equilibrium (SE). A game in SF models the case where players are uniquely
interested in the satisfaction of some individual performance constraints,
instead of individual performance optimization. Under this formulation, the
notion of equilibrium corresponds to the situation where all players can
simultaneously satisfy their individual constraints. The notion of SE, models
the problem of QoS provisioning in decentralized self-configuring networks.
Here, radio devices are satisfied if they are able to provide the requested
QoS. Within this framework, the concept of SE is formalized for both pure and
mixed strategies considering finite sets of players and actions. In both cases,
sufficient conditions for the existence and uniqueness of the SE are presented.
When multiple SE exist, we introduce the idea of effort or cost of satisfaction
and we propose a refinement of the SE, namely the efficient SE (ESE). At the
ESE, all players adopt the action which requires the lowest effort for
satisfaction. A learning method that allows radio devices to achieve a SE in
pure strategies in finite time and requiring only one-bit feedback is also
presented. Finally, a power control game in the interference channel is used to
highlight the advantages of modeling QoS problems following the notion of SE
rather than other equilibrium concepts, e.g., generalized Nash equilibrium.Comment: Article accepted for publication in IEEE Journal on Selected Topics
in Signal Processing, special issue in Game Theory in Signal Processing. 16
pages, 6 figure
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