scholarly journals Probabilistic Strategy Logic

2019 ◽  
Author(s):  
Benjamin Aminof ◽  
Marta Kwiatkowska ◽  
Bastien Maubert ◽  
Aniello Murano ◽  
Sasha Rubin
Keyword(s):  
Model Checking ◽  
Nash Equilibria ◽  
Stochastic Systems ◽  
Solution Concepts ◽  
Imperfect Recall ◽  
Double Exponential ◽  
Temporal Operator ◽  
Standard Solution ◽  
Strategy Logic ◽  
Exponential Space

We introduce Probabilistic Strategy Logic, an extension of Strategy Logic for stochastic systems. The logic has probabilistic terms that allow it to express many standard solution concepts, such as Nash equilibria in randomised strategies, as well as constraints on probabilities, such as independence. We study the model-checking problem for agents with perfect- and imperfect-recall. The former is undecidable, while the latter is decidable in space exponential in the system and triple-exponential in the formula. We identify a natural fragment of the logic, in which every temporal operator is immediately preceded by a probabilistic operator, and show that it is decidable in space exponential in the system and the formula, and double-exponential in the nesting depth of the probabilistic terms. Taking a fixed nesting depth, this gives a fragment that still captures many standard solution concepts, and is decidable in exponential space.

Nondeterministic Strategies and their Refinement in Strategy Logic

2020 ◽  
Author(s):  
Giuseppe De Giacomo ◽  
Bastien Maubert ◽  
Aniello Murano
Keyword(s):  
Model Checking ◽  
Nash Equilibria ◽  
Computational Cost ◽  
Strategy Logic ◽  
State Of Affairs

Nondeterministic strategies are strategies (or protocols, or plans) that, given a history in a game, assign a set of possible actions, all of which are winning. An important problem is that of refining such strategies. For instance, given a nondeterministic strategy that allows only safe executions, refine it to, additionally, eventually reach a desired state of affairs. We show that strategic problems involving strategy refinement can be solved elegantly in the framework of Strategy Logic (SL), a very expressive logic to reason about strategic abilities. Specifically, we introduce an extension of SL with nondeterministic strategies and an operator expressing strategy refinement. We show that model checking this logic can be done at no additional computational cost with respect to standard SL, and can be used to solve a variety of problems such as synthesis of maximally permissive strategies or refinement of Nash equilibria.

scholarly journals Reasoning About Agents That May Know Other Agents’ Strategies

2021 ◽  
Author(s):  
Francesco Belardinelli ◽  
Sophia Knight ◽  
Alessio Lomuscio ◽  
Bastien Maubert ◽  
Aniello Murano ◽  
...  
Keyword(s):  
Model Checking ◽  
Strategic Reasoning ◽  
Strategy Logic ◽  
Strategic Ability

We study the semantics of knowledge in strategic reasoning. Most existing works either implicitly assume that agents do not know one another’s strategies, or that all strategies are known to all; and some works present inconsistent mixes of both features. We put forward a novel semantics for Strategy Logic with Knowledge that cleanly models whose strategies each agent knows. We study how adopting this semantics impacts agents’ knowledge and strategic ability, as well as the complexity of the model-checking problem.

ORDINAL GAMES

2008 ◽  
Vol 10 (02) ◽  
pp. 177-194 ◽  
Author(s):  
JACQUES DURIEU ◽  
HANS HALLER ◽  
NICOLAS QUEROU ◽  
PHILIPPE SOLAL
Keyword(s):  
Complete Lattice ◽  
Nash Equilibria ◽  
Potential Game ◽  
Game Form ◽  
Strategic Games ◽  
Solution Concepts ◽  
Ordinal Games ◽  
Characterization Result ◽  
Supermodular Game ◽  
Best Response

We study strategic games where players' preferences are weak orders which need not admit utility representations. First of all, we extend Voorneveld's concept of best-response potential from cardinal to ordinal games and derive the analogue of his characterization result: An ordinal game is a best-response potential game if and only if it does not have a best-response cycle. Further, Milgrom and Shannon's concept of quasi-supermodularity is extended from cardinal games to ordinal games. We find that under certain topological assumptions, the ordinal Nash equilibria of a quasi-supermodular game form a nonempty complete lattice. Finally, we extend several set-valued solution concepts from cardinal to ordinal games in our sense.

scholarly journals Model Checking Coalition Nash Equilibria in MAD Distributed Systems

2009 ◽  
pp. 531-546 ◽  
Author(s):  
Federico Mari ◽  
Igor Melatti ◽  
Ivano Salvo ◽  
Enrico Tronci ◽  
Lorenzo Alvisi ◽  
...  
Keyword(s):  
Distributed Systems ◽  
Model Checking ◽  
Nash Equilibria

scholarly journals Complexity Results for Model Checking

1995 ◽  
Vol 2 (18) ◽  
Author(s):  
Allan Cheng
Keyword(s):  
Model Checking ◽  
Linear Time ◽  
Kripke Model ◽  
Upper Bounds ◽  
Polynomial Space ◽  
Turing Machines ◽  
Temporal Logics ◽  
Kripke Structures ◽  
Np Complete ◽  
Exponential Space

The complexity of model checking branching and linear time<br />temporal logics over Kripke structures has been addressed in e.g. [SC85,<br />CES86]. In terms of the size of the Kripke model and the length of the<br />formula, they show that the model checking problem is solvable in <br />polynomial time for CTL and NP-complete for L(F). The model checking<br />problem can be generalised by allowing more succinct descriptions of<br />systems than Kripke structures. We investigate the complexity of the<br />model checking problem when the instances of the problem consist of<br />a formula and a description of a system whose state space is at most<br />exponentially larger than the description. Based on Turing machines,<br />we define compact systems as a general formalisation of such system<br />descriptions. Examples of such compact systems are K-bounded Petri<br />nets and synchronised automata, and in these cases the well-known <br />algorithms presented in [SC85, CES86] would require exponential space in<br />term of the sizes of the system descriptions and the formulas; we present<br />polynomial space upper bounds for the model checking problem over<br />compact systems and the logics CTL and L(X,U,S). As an example of<br />an application of our general results we show that the model checking<br />problems of both the branching time temporal logic CTL and the linear<br />time temporal logics L(F) and L(X,U, S) over K-bounded Petri nets are<br />PSPACE-complete.

scholarly journals Verification of Broadcasting Multi-Agent Systems against an Epistemic Strategy Logic

2017 ◽  
Author(s):  
Francesco Belardinelli ◽  
Alessio Lomuscio ◽  
Aniello Murano ◽  
Sasha Rubin
Keyword(s):  
Model Checking ◽  
Secret Sharing ◽  
Imperfect Information ◽  
Multi Agent Systems ◽  
Perfect Recall ◽  
Agent Systems ◽  
Multi Agent ◽  
Strategy Logic

We study a class of synchronous, perfect-recall multi-agent systemswith imperfect information and broadcasting (i.e., fully observableactions). We define an epistemic extension of strategy logic withincomplete information and the assumption of uniform and coherentstrategies. In this setting, we prove that the model checking problem,and thus rational synthesis, is decidable with non-elementarycomplexity. We exemplify the applicability of the framework on arational secret-sharing scenario.

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