Multi-player Equilibria Verification for Concurrent Stochastic Games

Kwiatkowska, Marta; Norman, Gethin; Parker, David; Santos, Gabriel

doi:10.1007/978-3-030-59854-9_7

Cited by 15 publications

(28 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A comprehensive survey of main results in this area can be found in (Chatterjee and Henzinger 2012). Of the many studies on the analysis and verification of probabilistic systems, the work in (Kwiatkowska et al 2020a;Kwiatkowska et al 2019) is the closest to that presented here. In common with (Kwiatkowska et al 2020a;Kwiatkowska et al 2019), we use CSGs as the underlying model and focus on properties satisfied in equilibrium.…”

Section: Discussion and Related Workmentioning

confidence: 85%

Rational Verification for Probabilistic Systems

Gutiérrez

Hammond

Lin

et al. 2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

View full text Add to dashboard Cite

Rational verification is the problem of determining which temporal logic properties will hold in a multi-agent system, under the assumption that agents in the system act rationally, by choosing strategies that collectively form a game-theoretic equilibrium. Previous work in this area has largely focussed on deterministic systems. In this paper, we develop the theory and algorithms for rational verification in probabilistic systems. We focus on concurrent stochastic games (CSGs), which can be used to model uncertainty and randomness in complex multi-agent environments. We study the rational verification problem for both non-cooperative games and cooperative games in the qualitative probabilistic setting. In the former case, we consider LTL properties satisfied by the Nash equilibria of the game and in the latter case LTL properties satisfied by the core. In both cases, we show that the problem is 2EXPTIME-complete, thus not harder than the much simpler verification problem of model checking LTL properties of systems modelled as Markov decision processes (MDPs).

show abstract

Section: Discussion and Related Workmentioning

confidence: 85%

Rational Verification for Probabilistic Systems

Gutiérrez

Hammond

Lin

et al. 2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

View full text Add to dashboard Cite

show abstract

“…We are also working on extending the implementation to consider alternative solution methods (e.g., policy iteration and using CPLEX [40] to solve matrix games) and a symbolic (binary decision diagram based) implementation and other techniques for Nash equilibria synthesis such as an MILP-based solution using regret minimisation. Lastly, we are considering extending the approach to partially observable strategies, multi-coalitional games, building on [47], and mechanism design. state s 1 does not reach either the target of the formula or an absorbing state with probability 1 under all strategy profiles, while the reward for the state-action pair (s 1 , (a 1 , a 2 )) is negative.…”

Section: Discussionmentioning

confidence: 99%

“…Technically, therefore, we could remove the second coalition C from the syntax. However, we retain it for clarity about which coalition corresponds to each of the two objectives, and to allow a later extension to more than two coalitions [47]. Both types of formula, zero-sum and nonzero-sum, are composed of path (ψ) and reward (ρ) formulae, used in probabilistic and reward objectives included within P and R operators, respectively.…”

Section: Definition 12 (Extended Rpatl Syntax)mentioning

confidence: 99%

Automatic verification of concurrent stochastic systems

Kwiatkowska

Norman

Parker

et al. 2021

Form Methods Syst Des

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…[12,15,16]. Other types of SGs include concurrent games [10,31], limited information games [2,13], and bidding games [3]. Stochastic systems with multiple objectives have been extensively studied for more than a decade.…”

Section: Contributions and Overview In Summary This Paper Makes The Following Contributionsmentioning

confidence: 99%

Stochastic Games with Disjunctions of Multiple Objectives

Winkler

Weininger

2021

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural in situations where several-possibly conflictingperformance criteria like time and energy consumption are relevant. Such conjunctive combinations are the most studied multi-objective setting in the literature. In this paper, we consider the dual disjunctive problem. More concretely, we study turn-based stochastic two-player games on graphs where the winning condition is to guarantee at least one reachability or safety objective from a given set of alternatives. We present a fine-grained overview of strategy and computational complexity of such disjunctive queries (DQs) and provide new lower and upper bounds for several variants of the problem, significantly extending previous works. We also propose a novel value iteration-style algorithm for approximating the set of Pareto optimal thresholds for a given DQ.

show abstract

Multi-player Equilibria Verification for Concurrent Stochastic Games

Cited by 15 publications

References 38 publications

Rational Verification for Probabilistic Systems

Rational Verification for Probabilistic Systems

Automatic verification of concurrent stochastic systems

Stochastic Games with Disjunctions of Multiple Objectives

Contact Info

Product

Resources

About