2,960 research outputs found
Games with Delays. A Frankenstein Approach
We investigate infinite games on finite graphs where the information flow is
perturbed by nondeterministic signalling delays. It is known that such
perturbations make synthesis problems virtually unsolvable, in the general
case. On the classical model where signals are attached to states, tractable
cases are rare and difficult to identify.
Here, we propose a model where signals are detached from control states, and
we identify a subclass on which equilibrium outcomes can be preserved, even if
signals are delivered with a delay that is finitely bounded. To offset the
perturbation, our solution procedure combines responses from a collection of
virtual plays following an equilibrium strategy in the instant- signalling game
to synthesise, in a Frankenstein manner, an equivalent equilibrium strategy for
the delayed-signalling game
Games on graphs with a public signal monitoring
We study pure Nash equilibria in games on graphs with an imperfect monitoring
based on a public signal. In such games, deviations and players responsible for
those deviations can be hard to detect and track. We propose a generic
epistemic game abstraction, which conveniently allows to represent the
knowledge of the players about these deviations, and give a characterization of
Nash equilibria in terms of winning strategies in the abstraction. We then use
the abstraction to develop algorithms for some payoff functions.Comment: 28 page
Pure Nash Equilibria in Concurrent Deterministic Games
We study pure-strategy Nash equilibria in multi-player concurrent
deterministic games, for a variety of preference relations. We provide a novel
construction, called the suspect game, which transforms a multi-player
concurrent game into a two-player turn-based game which turns Nash equilibria
into winning strategies (for some objective that depends on the preference
relations of the players in the original game). We use that transformation to
design algorithms for computing Nash equilibria in finite games, which in most
cases have optimal worst-case complexity, for large classes of preference
relations. This includes the purely qualitative framework, where each player
has a single omega-regular objective that she wants to satisfy, but also the
larger class of semi-quantitative objectives, where each player has several
omega-regular objectives equipped with a preorder (for instance, a player may
want to satisfy all her objectives, or to maximise the number of objectives
that she achieves.)Comment: 72 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
Computer aided synthesis: a game theoretic approach
In this invited contribution, we propose a comprehensive introduction to game
theory applied in computer aided synthesis. In this context, we give some
classical results on two-player zero-sum games and then on multi-player non
zero-sum games. The simple case of one-player games is strongly related to
automata theory on infinite words. All along the article, we focus on general
approaches to solve the studied problems, and we provide several illustrative
examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language
Theory" (DLT 2017
Evolutionary Tournament-Based Comparison of Learning and Non-Learning Algorithms for Iterated Games
Evolutionary tournaments have been used effectively as a tool for comparing game-playing algorithms. For instance, in the late 1970's, Axelrod organized tournaments to compare algorithms for playing the iterated prisoner's dilemma (PD) game. These tournaments capture the dynamics in a population of agents that periodically adopt relatively successful algorithms in the environment. While these tournaments have provided us with a better understanding of the relative merits of algorithms for iterated PD, our understanding is less clear about algorithms for playing iterated versions of arbitrary single-stage games in an environment of heterogeneous agents. While the Nash equilibrium solution concept has been used to recommend using Nash equilibrium strategies for rational players playing general-sum games, learning algorithms like fictitious play may be preferred for playing against sub-rational players. In this paper, we study the relative performance of learning and non-learning algorithms in an evolutionary tournament where agents periodically adopt relatively successful algorithms in the population. The tournament is played over a testbed composed of all possible structurally distinct 2Ă—2 conflicted games with ordinal payoffs: a baseline, neutral testbed for comparing algorithms. Before analyzing results from the evolutionary tournament, we discuss the testbed, our choice of representative learning and non-learning algorithms and relative rankings of these algorithms in a round-robin competition. The results from the tournament highlight the advantage of learning algorithms over players using static equilibrium strategies for repeated plays of arbitrary single-stage games. The results are likely to be of more benefit compared to work on static analysis of equilibrium strategies for choosing decision procedures for open, adapting agent society consisting of a variety of competitors.Repeated Games, Evolution, Simulation
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