4 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
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
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
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