2,322 research outputs found
Efficient Markov perfect Nash equilibria: theory and application to dynamic fishery games
In this paper, we present a method for the characterization of Markov perfect Nash equilibria being Pareto efficient in non-linear differential games. For that purpose, we use a new method for computing Nash equilibria with Markov strategies by means of a system of quasilinear partial differential equations. We apply the necessary and sufficient conditions derived to characterize efficient Markov perfect Nash equilibria to dynamic fishery games.We are grateful to the editor Kenneth L. Judd and an anonymous referee for
helpful comments. The research of the first author was supported by MCYT under
project BEC2002-02361 and JCYL under project VA51/03, cofinanced by FEDER
funds. The research of the second author was supported by MCYT under project
BFM2002–00425 and JCYL under project VA099/04 cofinanced by FEDER funds.Publicad
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
Finding Any Nontrivial Coarse Correlated Equilibrium Is Hard
One of the most appealing aspects of the (coarse) correlated equilibrium
concept is that natural dynamics quickly arrive at approximations of such
equilibria, even in games with many players. In addition, there exist
polynomial-time algorithms that compute exact (coarse) correlated equilibria.
In light of these results, a natural question is how good are the (coarse)
correlated equilibria that can arise from any efficient algorithm or dynamics.
In this paper we address this question, and establish strong negative
results. In particular, we show that in multiplayer games that have a succinct
representation, it is NP-hard to compute any coarse correlated equilibrium (or
approximate coarse correlated equilibrium) with welfare strictly better than
the worst possible. The focus on succinct games ensures that the underlying
complexity question is interesting; many multiplayer games of interest are in
fact succinct. Our results imply that, while one can efficiently compute a
coarse correlated equilibrium, one cannot provide any nontrivial welfare
guarantee for the resulting equilibrium, unless P=NP. We show that analogous
hardness results hold for correlated equilibria, and persist under the
egalitarian objective or Pareto optimality.
To complement the hardness results, we develop an algorithmic framework that
identifies settings in which we can efficiently compute an approximate
correlated equilibrium with near-optimal welfare. We use this framework to
develop an efficient algorithm for computing an approximate correlated
equilibrium with near-optimal welfare in aggregative games.Comment: 21 page
Efficient computation of approximate pure Nash equilibria in congestion games
Congestion games constitute an important class of games in which computing an
exact or even approximate pure Nash equilibrium is in general {\sf
PLS}-complete. We present a surprisingly simple polynomial-time algorithm that
computes O(1)-approximate Nash equilibria in these games. In particular, for
congestion games with linear latency functions, our algorithm computes
-approximate pure Nash equilibria in time polynomial in the
number of players, the number of resources and . It also applies to
games with polynomial latency functions with constant maximum degree ;
there, the approximation guarantee is . The algorithm essentially
identifies a polynomially long sequence of best-response moves that lead to an
approximate equilibrium; the existence of such short sequences is interesting
in itself. These are the first positive algorithmic results for approximate
equilibria in non-symmetric congestion games. We strengthen them further by
proving that, for congestion games that deviate from our mild assumptions,
computing -approximate equilibria is {\sf PLS}-complete for any
polynomial-time computable
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