605 research outputs found
Multiplayer Cost Games with Simple Nash Equilibria
Multiplayer games with selfish agents naturally occur in the design of
distributed and embedded systems. As the goals of selfish agents are usually
neither equivalent nor antagonistic to each other, such games are non zero-sum
games. We study such games and show that a large class of these games,
including games where the individual objectives are mean- or discounted-payoff,
or quantitative reachability, and show that they do not only have a solution,
but a simple solution. We establish the existence of Nash equilibria that are
composed of k memoryless strategies for each agent in a setting with k agents,
one main and k-1 minor strategies. The main strategy describes what happens
when all agents comply, whereas the minor strategies ensure that all other
agents immediately start to co-operate against the agent who first deviates
from the plan. This simplicity is important, as rational agents are an
idealisation. Realistically, agents have to decide on their moves with very
limited resources, and complicated strategies that require exponential--or even
non-elementary--implementations cannot realistically be implemented. The
existence of simple strategies that we prove in this paper therefore holds a
promise of implementability.Comment: 23 page
On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games
We study turn-based quantitative multiplayer non zero-sum games played on
finite graphs with reachability objectives. In such games, each player aims at
reaching his own goal set of states as soon as possible. A previous work on
this model showed that Nash equilibria (resp. secure equilibria) are guaranteed
to exist in the multiplayer (resp. two-player) case. The existence of secure
equilibria in the multiplayer case remained and is still an open problem. In
this paper, we focus our study on the concept of subgame perfect equilibrium, a
refinement of Nash equilibrium well-suited in the framework of games played on
graphs. We also introduce the new concept of subgame perfect secure
equilibrium. We prove the existence of subgame perfect equilibria (resp.
subgame perfect secure equilibria) in multiplayer (resp. two-player)
quantitative reachability games. Moreover, we provide an algorithm deciding the
existence of secure equilibria in the multiplayer case.Comment: 32 pages. Full version of the FoSSaCS 2012 proceedings pape
Payoff-Based Dynamics for Multiplayer Weakly Acyclic Games
We consider repeated multiplayer games in which players repeatedly and simultaneously choose strategies from a finite set of available strategies according to some strategy adjustment process. We focus on the specific class of weakly acyclic games, which is particularly relevant for multiagent cooperative control problems. A strategy adjustment process determines how players select their strategies at any stage as a function of the information gathered over previous stages. Of particular interest are âpayoff-basedâ processes in which, at any stage, players know only their own actions and (noise corrupted) payoffs from previous stages. In particular, players do not know the actions taken by other players and do not know the structural form of payoff functions. We introduce three different payoff-based processes for increasingly general scenarios and prove that, after a sufficiently large number of stages, player actions constitute a Nash equilibrium at any stage with arbitrarily high probability. We also show how to modify player utility functions through tolls and incentives in so-called congestion games, a special class of weakly acyclic games, to guarantee that a centralized objective can be realized as a Nash equilibrium. We illustrate the methods with a simulation of distributed routing over a network
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Chris Cannings: A Life in Games
Chris Cannings was one of the pioneers of evolutionary game theory. His early work was inspired by the formulations of John Maynard Smith, Geoff Parker and Geoff Price; Chris recognized the need for a strong mathematical foundation both to validate stated results and to give a basis for extensions of the models. He was responsible for fundamental results on matrix games, as well as much of the theory of the important war of attrition game, patterns of evolutionarily stable strategies, multiplayer games and games on networks. In this paper we describe his work, key insights and their influence on research by others in this increasingly important field. Chris made substantial contributions to other areas such as population genetics and segregation analysis, but it was to games that he always returned. This review is written by three of his students from different stages of his career
Learning Convex Partitions and Computing Game-theoretic Equilibria from Best Response Queries
Suppose that an -simplex is partitioned into convex regions having
disjoint interiors and distinct labels, and we may learn the label of any point
by querying it. The learning objective is to know, for any point in the
simplex, a label that occurs within some distance from that point.
We present two algorithms for this task: Constant-Dimension Generalised Binary
Search (CD-GBS), which for constant uses queries, and Constant-Region Generalised Binary
Search (CR-GBS), which uses CD-GBS as a subroutine and for constant uses
queries.
We show via Kakutani's fixed-point theorem that these algorithms provide
bounds on the best-response query complexity of computing approximate
well-supported equilibria of bimatrix games in which one of the players has a
constant number of pure strategies. We also partially extend our results to
games with multiple players, establishing further query complexity bounds for
computing approximate well-supported equilibria in this setting.Comment: 38 pages, 7 figures, second version strengthens lower bound in
Theorem 6, adds footnotes with additional comments and fixes typo
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
Rational Verification in Iterated Electric Boolean Games
Electric boolean games are compact representations of games where the players
have qualitative objectives described by LTL formulae and have limited
resources. We study the complexity of several decision problems related to the
analysis of rationality in electric boolean games with LTL objectives. In
particular, we report that the problem of deciding whether a profile is a Nash
equilibrium in an iterated electric boolean game is no harder than in iterated
boolean games without resource bounds. We show that it is a PSPACE-complete
problem. As a corollary, we obtain that both rational elimination and rational
construction of Nash equilibria by a supervising authority are PSPACE-complete
problems.Comment: In Proceedings SR 2016, arXiv:1607.0269
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