1,940 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
Computer-aided verification in mechanism design
In mechanism design, the gold standard solution concepts are dominant
strategy incentive compatibility and Bayesian incentive compatibility. These
solution concepts relieve the (possibly unsophisticated) bidders from the need
to engage in complicated strategizing. While incentive properties are simple to
state, their proofs are specific to the mechanism and can be quite complex.
This raises two concerns. From a practical perspective, checking a complex
proof can be a tedious process, often requiring experts knowledgeable in
mechanism design. Furthermore, from a modeling perspective, if unsophisticated
agents are unconvinced of incentive properties, they may strategize in
unpredictable ways.
To address both concerns, we explore techniques from computer-aided
verification to construct formal proofs of incentive properties. Because formal
proofs can be automatically checked, agents do not need to manually check the
properties, or even understand the proof. To demonstrate, we present the
verification of a sophisticated mechanism: the generic reduction from Bayesian
incentive compatible mechanism design to algorithm design given by Hartline,
Kleinberg, and Malekian. This mechanism presents new challenges for formal
verification, including essential use of randomness from both the execution of
the mechanism and from the prior type distributions. As an immediate
consequence, our work also formalizes Bayesian incentive compatibility for the
entire family of mechanisms derived via this reduction. Finally, as an
intermediate step in our formalization, we provide the first formal
verification of incentive compatibility for the celebrated
Vickrey-Clarke-Groves mechanism
A Probabilistic Approach to Mean Field Games with Major and Minor Players
We propose a new approach to mean field games with major and minor players.
Our formulation involves a two player game where the optimization of the
representative minor player is standard while the major player faces an
optimization over conditional McKean-Vlasov stochastic differential equations.
The definition of this limiting game is justified by proving that its solution
provides approximate Nash equilibriums for large finite player games. This
proof depends upon the generalization of standard results on the propagation of
chaos to conditional dynamics. Because it is on independent interest, we prove
this generalization in full detail. Using a conditional form of the Pontryagin
stochastic maximum principle (proven in the appendix), we reduce the solution
of the mean field game to a forward-backward system of stochastic differential
equations of the conditional McKean-Vlasov type, which we solve in the Linear
Quadratic setting. We use this class of models to show that Nash equilibriums
in our formulation can be different from those of the formulations contemplated
so far in the literature
Automatic Verification of Concurrent Stochastic Systems
Automated verification techniques for stochastic games allow formal reasoning
about systems that feature competitive or collaborative behaviour among
rational agents in uncertain or probabilistic settings. Existing tools and
techniques focus on turn-based games, where each state of the game is
controlled by a single player, and on zero-sum properties, where two players or
coalitions have directly opposing objectives. In this paper, we present
automated verification techniques for concurrent stochastic games (CSGs), which
provide a more natural model of concurrent decision making and interaction. We
also consider (social welfare) Nash equilibria, to formally identify scenarios
where two players or coalitions with distinct goals can collaborate to optimise
their joint performance. We propose an extension of the temporal logic rPATL
for specifying quantitative properties in this setting and present
corresponding algorithms for verification and strategy synthesis for a variant
of stopping games. For finite-horizon properties the computation is exact,
while for infinite-horizon it is approximate using value iteration. For
zero-sum properties it requires solving matrix games via linear programming,
and for equilibria-based properties we find social welfare or social cost Nash
equilibria of bimatrix games via the method of labelled polytopes through an
SMT encoding. We implement this approach in PRISM-games, which required
extending the tool's modelling language for CSGs, and apply it to case studies
from domains including robotics, computer security and computer networks,
explicitly demonstrating the benefits of both CSGs and equilibria-based
properties
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
Automated verification of concurrent stochastic games
We present automatic verifcation techniques for concurrent
stochastic multi-player games (CSGs) with rewards. To express properties
of such models, we adapt the temporal logic rPATL (probabilistic
alternating-time temporal logic with rewards), originally introduced for
the simpler model of turn-based games, which enables quantitative reasoning
about the ability of coalitions of players to achieve goals related to
the probability of an event or reward measures. We propose and implement
a modelling approach and model checking algorithms for property
verifcation and strategy synthesis of CSGs, as an extension of PRISMgames.
We evaluate the performance, scalability and applicability of our
techniques on case studies from domains such as security, networks and
finance, showing that we can analyse systems with probabilistic, cooperative
and competitive behaviour between concurrent components, including
many scenarios that cannot be analysed with turn-based models
Collusion in Peer-to-Peer Systems
Peer-to-peer systems have reached a widespread use, ranging from academic and industrial applications to home entertainment. The key advantage of this paradigm lies in its scalability and flexibility, consequences of the participants sharing their resources for the common welfare. Security in such systems is a desirable goal. For example, when mission-critical operations or bank transactions are involved, their effectiveness strongly depends on the perception that users have about the system dependability and trustworthiness. A major threat to the security of these systems is the phenomenon of collusion. Peers can be selfish colluders, when they try to fool the system to gain unfair advantages over other peers, or malicious, when their purpose is to subvert the system or disturb other users. The problem, however, has received so far only a marginal attention by the research community. While several solutions exist to counter attacks in peer-to-peer systems, very few of them are meant to directly counter colluders and their attacks. Reputation, micro-payments, and concepts of game theory are currently used as the main means to obtain fairness in the usage of the resources. Our goal is to provide an overview of the topic by examining the key issues involved. We measure the relevance of the problem in the current literature and the effectiveness of existing philosophies against it, to suggest fruitful directions in the further development of the field
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