2,836 research outputs found
Privacy and Truthful Equilibrium Selection for Aggregative Games
We study a very general class of games --- multi-dimensional aggregative
games --- which in particular generalize both anonymous games and weighted
congestion games. For any such game that is also large, we solve the
equilibrium selection problem in a strong sense. In particular, we give an
efficient weak mediator: a mechanism which has only the power to listen to
reported types and provide non-binding suggested actions, such that (a) it is
an asymptotic Nash equilibrium for every player to truthfully report their type
to the mediator, and then follow its suggested action; and (b) that when
players do so, they end up coordinating on a particular asymptotic pure
strategy Nash equilibrium of the induced complete information game. In fact,
truthful reporting is an ex-post Nash equilibrium of the mediated game, so our
solution applies even in settings of incomplete information, and even when
player types are arbitrary or worst-case (i.e. not drawn from a common prior).
We achieve this by giving an efficient differentially private algorithm for
computing a Nash equilibrium in such games. The rates of convergence to
equilibrium in all of our results are inverse polynomial in the number of
players . We also apply our main results to a multi-dimensional market game.
Our results can be viewed as giving, for a rich class of games, a more robust
version of the Revelation Principle, in that we work with weaker informational
assumptions (no common prior), yet provide a stronger solution concept (ex-post
Nash versus Bayes Nash equilibrium). In comparison to previous work, our main
conceptual contribution is showing that weak mediators are a game theoretic
object that exist in a wide variety of games -- previously, they were only
known to exist in traffic routing games
Pure Nash Equilibria: Hard and Easy Games
We investigate complexity issues related to pure Nash equilibria of strategic
games. We show that, even in very restrictive settings, determining whether a
game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has
a strong Nash equilibrium is SigmaP2-complete. We then study practically
relevant restrictions that lower the complexity. In particular, we are
interested in quantitative and qualitative restrictions of the way each players
payoff depends on moves of other players. We say that a game has small
neighborhood if the utility function for each player depends only on (the
actions of) a logarithmically small number of other players. The dependency
structure of a game G can be expressed by a graph DG(G) or by a hypergraph
H(G). By relating Nash equilibrium problems to constraint satisfaction problems
(CSPs), we show that if G has small neighborhood and if H(G) has bounded
hypertree width (or if DG(G) has bounded treewidth), then finding pure Nash and
Pareto equilibria is feasible in polynomial time. If the game is graphical,
then these problems are LOGCFL-complete and thus in the class NC2 of highly
parallelizable problems
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 mean-field game economic growth model
Here, we examine a mean-field game (MFG) that models the economic growth of a
population of non-cooperative rational agents. In this MFG, agents are
described by two state variables - the capital and consumer goods they own.
Each agent seeks to maximize their utility by taking into account statistical
data of the total population. The individual actions drive the evolution of the
players, and a market-clearing condition determines the relative price of
capital and consumer goods. We study the existence and uniqueness of optimal
strategies of the agents and develop numerical methods to compute these
strategies and the equilibrium price
Mean-Field-Type Games in Engineering
A mean-field-type game is a game in which the instantaneous payoffs and/or
the state dynamics functions involve not only the state and the action profile
but also the joint distributions of state-action pairs. This article presents
some engineering applications of mean-field-type games including road traffic
networks, multi-level building evacuation, millimeter wave wireless
communications, distributed power networks, virus spread over networks, virtual
machine resource management in cloud networks, synchronization of oscillators,
energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201
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