1,939 research outputs found
Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games
Probabilistic model checking for stochastic games enables formal verification
of systems that comprise competing or collaborating entities operating in a
stochastic environment. Despite good progress in the area, existing approaches
focus on zero-sum goals and cannot reason about scenarios where entities are
endowed with different objectives. In this paper, we propose probabilistic
model checking techniques for concurrent stochastic games based on Nash
equilibria. We extend the temporal logic rPATL (probabilistic alternating-time
temporal logic with rewards) to allow reasoning about players with distinct
quantitative goals, which capture either the probability of an event occurring
or a reward measure. We present algorithms to synthesise strategies that are
subgame perfect social welfare optimal Nash equilibria, i.e., where there is no
incentive for any players to unilaterally change their strategy in any state of
the game, whilst the combined probabilities or rewards are maximised. We
implement our techniques in the PRISM-games tool and apply them to several case
studies, including network protocols and robot navigation, showing the benefits
compared to existing approaches
Efficient Energy Distribution in a Smart Grid using Multi-Player Games
Algorithms and models based on game theory have nowadays become prominent
techniques for the design of digital controllers for critical systems. Indeed,
such techniques enable automatic synthesis: given a model of the environment
and a property that the controller must enforce, those techniques automatically
produce a correct controller, when it exists. In the present paper, we consider
a class of concurrent, weighted, multi-player games that are well-suited to
model and study the interactions of several agents who are competing for some
measurable resources like energy. We prove that a subclass of those games
always admit a Nash equilibrium, i.e. a situation in which all players play in
such a way that they have no incentive to deviate. Moreover, the strategies
yielding those Nash equilibria have a special structure: when one of the agents
deviate from the equilibrium, all the others form a coalition that will enforce
a retaliation mechanism that punishes the deviant agent. We apply those results
to a real-life case study in which several smart houses that produce their own
energy with solar panels, and can share this energy among them in micro-grid,
must distribute the use of this energy along the day in order to avoid
consuming electricity that must be bought from the global grid. We demonstrate
that our theory allows one to synthesise an efficient controller for these
houses: using penalties to be paid in the utility bill as an incentive, we
force the houses to follow a pre-computed schedule that maximises the
proportion of the locally produced energy that is consumed.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
Maximizing Welfare in Social Networks under a Utility Driven Influence Diffusion Model
Motivated by applications such as viral marketing, the problem of influence
maximization (IM) has been extensively studied in the literature. The goal is
to select a small number of users to adopt an item such that it results in a
large cascade of adoptions by others. Existing works have three key
limitations. (1) They do not account for economic considerations of a user in
buying/adopting items. (2) Most studies on multiple items focus on competition,
with complementary items receiving limited attention. (3) For the network
owner, maximizing social welfare is important to ensure customer loyalty, which
is not addressed in prior work in the IM literature. In this paper, we address
all three limitations and propose a novel model called UIC that combines
utility-driven item adoption with influence propagation over networks. Focusing
on the mutually complementary setting, we formulate the problem of social
welfare maximization in this novel setting. We show that while the objective
function is neither submodular nor supermodular, surprisingly a simple greedy
allocation algorithm achieves a factor of of the optimum
expected social welfare. We develop \textsf{bundleGRD}, a scalable version of
this approximation algorithm, and demonstrate, with comprehensive experiments
on real and synthetic datasets, that it significantly outperforms all
baselines.Comment: 33 page
Verification and Control of Turn-Based Probabilistic Real-Time Games
Quantitative verification techniques have been developed for the formal analysis of a variety of probabilistic models, such as Markov chains, Markov decision process and their variants. They can be used to produce guarantees on quantitative aspects of system behaviour, for example safety, reliability and performance, or to help synthesise controllers that ensure such guarantees are met. We propose the model of turn-based probabilistic timed multi-player games, which incorporates probabilistic choice, real-time clocks and nondeterministic behaviour across multiple players. Building on the digital clocks approach for the simpler model of probabilistic timed automata, we show how to compute the key measures that underlie quantitative verification, namely the probability and expected cumulative price to reach a target. We illustrate this on case studies from computer security and task scheduling
Strategic Network Formation with Attack and Immunization
Strategic network formation arises where agents receive benefit from
connections to other agents, but also incur costs for forming links. We
consider a new network formation game that incorporates an adversarial attack,
as well as immunization against attack. An agent's benefit is the expected size
of her connected component post-attack, and agents may also choose to immunize
themselves from attack at some additional cost. Our framework is a stylized
model of settings where reachability rather than centrality is the primary
concern and vertices vulnerable to attacks may reduce risk via costly measures.
In the reachability benefit model without attack or immunization, the set of
equilibria is the empty graph and any tree. The introduction of attack and
immunization changes the game dramatically; new equilibrium topologies emerge,
some more sparse and some more dense than trees. We show that, under a mild
assumption on the adversary, every equilibrium network with agents contains
at most edges for . So despite permitting topologies denser
than trees, the amount of overbuilding is limited. We also show that attack and
immunization don't significantly erode social welfare: every non-trivial
equilibrium with respect to several adversaries has welfare at least as that of
any equilibrium in the attack-free model.
We complement our theory with simulations demonstrating fast convergence of a
new bounded rationality dynamic which generalizes linkstable best response but
is considerably more powerful in our game. The simulations further elucidate
the wide variety of asymmetric equilibria and demonstrate topological
consequences of the dynamics e.g. heavy-tailed degree distributions. Finally,
we report on a behavioral experiment on our game with over 100 participants,
where despite the complexity of the game, the resulting network was
surprisingly close to equilibrium.Comment: The short version of this paper appears in the proceedings of WINE-1
Multi-objective Robust Strategy Synthesis for Interval Markov Decision Processes
Interval Markov decision processes (IMDPs) generalise classical MDPs by
having interval-valued transition probabilities. They provide a powerful
modelling tool for probabilistic systems with an additional variation or
uncertainty that prevents the knowledge of the exact transition probabilities.
In this paper, we consider the problem of multi-objective robust strategy
synthesis for interval MDPs, where the aim is to find a robust strategy that
guarantees the satisfaction of multiple properties at the same time in face of
the transition probability uncertainty. We first show that this problem is
PSPACE-hard. Then, we provide a value iteration-based decision algorithm to
approximate the Pareto set of achievable points. We finally demonstrate the
practical effectiveness of our proposed approaches by applying them on several
case studies using a prototypical tool.Comment: This article is a full version of a paper accepted to the Conference
on Quantitative Evaluation of SysTems (QEST) 201
- …