4,655 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
Intelligent escalation and the principle of relativity
Escalation is the fact that in a game (for instance in an auction), the
agents play forever. The -game is an extremely simple infinite game with
intelligent agents in which escalation arises. It shows at the light of
research on cognitive psychology the difference between intelligence
(algorithmic mind) and rationality (algorithmic and reflective mind) in
decision processes. It also shows that depending on the point of view (inside
or outside) the rationality of the agent may change which is proposed to be
called the principle of relativity.Comment: arXiv admin note: substantial text overlap with arXiv:1306.228
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
Reasoning about Knowledge and Strategies under Hierarchical Information
Two distinct semantics have been considered for knowledge in the context of
strategic reasoning, depending on whether players know each other's strategy or
not. The problem of distributed synthesis for epistemic temporal specifications
is known to be undecidable for the latter semantics, already on systems with
hierarchical information. However, for the other, uninformed semantics, the
problem is decidable on such systems. In this work we generalise this result by
introducing an epistemic extension of Strategy Logic with imperfect
information. The semantics of knowledge operators is uninformed, and captures
agents that can change observation power when they change strategies. We solve
the model-checking problem on a class of "hierarchical instances", which
provides a solution to a vast class of strategic problems with epistemic
temporal specifications on hierarchical systems, such as distributed synthesis
or rational synthesis
Non-Zero Sum Games for Reactive Synthesis
In this invited contribution, we summarize new solution concepts useful for
the synthesis of reactive systems that we have introduced in several recent
publications. These solution concepts are developed in the context of non-zero
sum games played on graphs. They are part of the contributions obtained in the
inVEST project funded by the European Research Council.Comment: LATA'16 invited pape
Automated Temporal Equilibrium Analysis: Verification and Synthesis of Multi-Player Games
In the context of multi-agent systems, the rational verification problem is
concerned with checking which temporal logic properties will hold in a system
when its constituent agents are assumed to behave rationally and strategically
in pursuit of individual objectives. Typically, those objectives are expressed
as temporal logic formulae which the relevant agent desires to see satisfied.
Unfortunately, rational verification is computationally complex, and requires
specialised techniques in order to obtain practically useable implementations.
In this paper, we present such a technique. This technique relies on a
reduction of the rational verification problem to the solution of a collection
of parity games. Our approach has been implemented in the Equilibrium
Verification Environment (EVE) system. The EVE system takes as input a model of
a concurrent/multi-agent system represented using the Simple Reactive Modules
Language (SRML), where agent goals are represented as Linear Temporal Logic
(LTL) formulae, together with a claim about the equilibrium behaviour of the
system, also expressed as an LTL formula. EVE can then check whether the LTL
claim holds on some (or every) computation of the system that could arise
through agents choosing Nash equilibrium strategies; it can also check whether
a system has a Nash equilibrium, and synthesise individual strategies for
players in the multi-player game. After presenting our basic framework, we
describe our new technique and prove its correctness. We then describe our
implementation in the EVE system, and present experimental results which show
that EVE performs favourably in comparison to other existing tools that support
rational verification
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