149 research outputs found
The Complexity of Admissibility in Omega-Regular Games
Iterated admissibility is a well-known and important concept in classical
game theory, e.g. to determine rational behaviors in multi-player matrix games.
As recently shown by Berwanger, this concept can be soundly extended to
infinite games played on graphs with omega-regular objectives. In this paper,
we study the algorithmic properties of this concept for such games. We settle
the exact complexity of natural decision problems on the set of strategies that
survive iterated elimination of dominated strategies. As a byproduct of our
construction, we obtain automata which recognize all the possible outcomes of
such strategies
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
On Relevant Equilibria in Reachability Games
We study multiplayer reachability games played on a finite directed graph
equipped with target sets, one for each player. In those reachability games, it
is known that there always exists a Nash equilibrium (NE) and a subgame perfect
equilibrium (SPE). But sometimes several equilibria may coexist such that in
one equilibrium no player reaches his target set whereas in another one several
players reach it. It is thus very natural to identify "relevant" equilibria. In
this paper, we consider different notions of relevant equilibria including
Pareto optimal equilibria and equilibria with high social welfare. We provide
complexity results for various related decision problems
The Complexity of Nash Equilibria in Stochastic Multiplayer Games
We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with -regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game~, does there exist a pure-strategy Nash equilibrium of~ where player 0 wins with probability~. Moreover, this problem remains undecidable if it is restricted to strategies with (unbounded) finite memory. However, if randomised strategies are allowed, decidability remains an open problem; we can only prove NP-hardness in this case. One way to obtain a provably decidable variant of the problem is to restrict the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively. Finally, we single out a special case of the general problem that, in many cases, admits an efficient solution. In particular, we prove that deciding the existence of an equilibrium in which each player either wins or loses with probability~ can be done in polynomial time for games where, for instance, the objective of each player is given by a parity condition with a bounded number of priorities
Decision Problems for Nash Equilibria in Stochastic Games
We analyse the computational complexity of finding Nash equilibria in
stochastic multiplayer games with -regular objectives. While the
existence of an equilibrium whose payoff falls into a certain interval may be
undecidable, we single out several decidable restrictions of the problem.
First, restricting the search space to stationary, or pure stationary,
equilibria results in problems that are typically contained in PSPACE and NP,
respectively. Second, we show that the existence of an equilibrium with a
binary payoff (i.e. an equilibrium where each player either wins or loses with
probability 1) is decidable. We also establish that the existence of a Nash
equilibrium with a certain binary payoff entails the existence of an
equilibrium with the same payoff in pure, finite-state strategies.Comment: 22 pages, revised versio
The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games
We analyse the computational complexity of finding Nash equilibria in simple
stochastic multiplayer games. We show that restricting the search space to
equilibria whose payoffs fall into a certain interval may lead to
undecidability. In particular, we prove that the following problem is
undecidable: Given a game G, does there exist a pure-strategy Nash equilibrium
of G where player 0 wins with probability 1. Moreover, this problem remains
undecidable if it is restricted to strategies with (unbounded) finite memory.
However, if mixed strategies are allowed, decidability remains an open problem.
One way to obtain a provably decidable variant of the problem is restricting
the strategies to be positional or stationary. For the complexity of these two
problems, we obtain a common lower bound of NP and upper bounds of NP and
PSPACE respectively.Comment: 23 pages; revised versio
Parametric LTL on Markov Chains
This paper is concerned with the verification of finite Markov chains against
parametrized LTL (pLTL) formulas. In pLTL, the until-modality is equipped with
a bound that contains variables; e.g., asserts that
holds within time steps, where is a variable on natural
numbers. The central problem studied in this paper is to determine the set of
parameter valuations for which the probability to
satisfy pLTL-formula in a Markov chain meets a given threshold , where is a comparison on reals and a probability. As for pLTL
determining the emptiness of is undecidable, we consider
several logic fragments. We consider parametric reachability properties, a
sub-logic of pLTL restricted to next and , parametric B\"uchi
properties and finally, a maximal subclass of pLTL for which emptiness of is decidable.Comment: TCS Track B 201
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
Modification of a PE/PPE substrate pair reroutes an Esx substrate pair from the mycobacterial ESX-1 type VII secretion system to the ESX-5 system
Bacterial type VII secretion systems secrete a wide range of extracellular proteins that play important roles in bacterial viability and in interactions of pathogenic mycobacteria with their hosts. Mycobacterial type VII secretion systems consist of five subtypes, ESX-1-5, and have four substrate classes, namely, Esx, PE, PPE, and Esp proteins. At least some of these substrates are secreted as heterodimers. Each ESX system mediates the secretion of a specific set of Esx, PE, and PPE proteins, raising the question of how these substrates are recognized in a system-specific fashion. For the PE/PPE heterodimers, it has been shown that they interact with their cognate EspG chaperone and that this chaperone determines the designated secretion pathway. However, both structural and pulldown analyses have suggested that EspG cannot interact with the Esx proteins. Therefore, the determining factor for system specificity of the Esx proteins remains unknown. Here, we investigated the secretion specificity of the ESX-1 substrate pair EsxB_1/EsxA_1 in Mycobacterium marinum Although this substrate pair was hardly secreted when homologously expressed, it was secreted when co-expressed together with the PE35/PPE68_1 pair, indicating that this pair could stimulate secretion of the EsxB_1/EsxA_1 pair. Surprisingly, co-expression of EsxB_1/EsxA_1 with a modified PE35/PPE68_1 version that carried the EspG5 chaperone-binding domain, previously shown to redirect this substrate pair to the ESX-5 system, also resulted in redirection and co-secretion of the Esx pair via ESX-5. Our results suggest a secretion model in which PE35/PPE68_1 determines the system-specific secretion of EsxB_1/EsxA_1
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