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

Computer aided synthesis: a game theoretic approach

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

Decidability Results for Multi-objective Stochastic Games

We study stochastic two-player turn-based games in which the objective of one player is to ensure several infinite-horizon total reward objectives, while the other player attempts to spoil at least one of the objectives. The games have previously been shown not to be determined, and an approximation algorithm for computing a Pareto curve has been given. The major drawback of the existing algorithm is that it needs to compute Pareto curves for finite horizon objectives (for increasing length of the horizon), and the size of these Pareto curves can grow unboundedly, even when the infinite-horizon Pareto curve is small. By adapting existing results, we first give an algorithm that computes the Pareto curve for determined games. Then, as the main result of the paper, we show that for the natural class of stopping games and when there are two reward objectives, the problem of deciding whether a player can ensure satisfaction of the objectives with given thresholds is decidable. The result relies on intricate and novel proof which shows that the Pareto curves contain only finitely many points. As a consequence, we get that the two-objective discounted-reward problem for unrestricted class of stochastic games is decidable.Comment: 35 page

On Relevant Equilibria in Reachability Games

We study multiplayer reachability games played on a finite directed graph equipped with target sets, one for each player. In those reachability games, it is known that there always exists a Nash equilibrium (NE) and a subgame perfect equilibrium (SPE). But sometimes several equilibria may coexist such that in one equilibrium no player reaches his target set whereas in another one several players reach it. It is thus very natural to identify "relevant" equilibria. In this paper, we consider different notions of relevant equilibria including Pareto optimal equilibria and equilibria with high social welfare. We provide complexity results for various related decision problems

Passive monitoring of anisotropy change associated with the Parkfield 2004 earthquake

International audienceWe investigate temporal variations in the polarization of surface waves determined using ambient seismic noise cross-correlations between station pairs at the time of the Mw 6.0 Parkfield earthquake of September 28, 2004. We use data recorded by the High Resolution Seismic Network's 3-component seismometers located along the San Andreas Fault. Our results show strong variations in azimuthal surface wave polarizations, Psi, for the paths containing station VARB, one of the closest stations to the San Andreas Fault, synchronous with the Parkfield earthquake. Concerning the other station pair, only smooth temporal variations of Y are observed. Two principal contributions to these changes in Y are identified and separated. They are: (1) slow and weak variations due to seasonal changes in the incident direction of seismic noise; and (2) strong and rapid rotations synchronous with the Parkfield earthquake for paths containing station VARB. Strong shifts in Y are interpreted in terms of changes in crack-induced anisotropy due to the co-seismic rotation of the stress field. Because these changes are only observed on paths containing station VARB, the anisotropic layer responsible for the changes is most likely localized around VARB in the shallow crust. These results suggest that the polarization of surface waves may be very sensitive to changes in the orientations of distributed cracks and that implementation of our technique on a routine basis may prove useful for monitoring stress changes deep within seismogenic zones. Citation: Durand, S., J. P. Montagner, P. Roux, F. Brenguier, R. M. Nadeau, and Y. Ricard (2011), Passive monitoring of anisotropy change associated with the Parkfield 2004 earthquake, Geophys. Res. Lett., 38, L13303, doi: 10.1029/2011GL047875

Structural Synthesis for GXW Specifications

We define the GXW fragment of linear temporal logic (LTL) as the basis for synthesizing embedded control software for safety-critical applications. Since GXW includes the use of a weak-until operator we are able to specify a number of diverse programmable logic control (PLC) problems, which we have compiled from industrial training sets. For GXW controller specifications, we develop a novel approach for synthesizing a set of synchronously communicating actor-based controllers. This synthesis algorithm proceeds by means of recursing over the structure of GXW specifications, and generates a set of dedicated and synchronously communicating sub-controllers according to the formula structure. In a subsequent step, 2QBF constraint solving identifies and tries to resolve potential conflicts between individual GXW specifications. This structural approach to GXW synthesis supports traceability between requirements and the generated control code as mandated by certification regimes for safety-critical software. Synthesis for GXW specifications is in PSPACE compared to 2EXPTIME-completeness of full-fledged LTL synthesis. Indeed our experimental results suggest that GXW synthesis scales well to industrial-sized control synthesis problems with 20 input and output ports and beyond.Comment: The long (including appendix) version being reviewed by CAV'16 program committee. Compared to the submitted version, one author (out of her wish) is moved to the Acknowledgement. (v2) Corrected typos. (v3) Add an additional remark over environment assumption and easy corner case

The Impatient May Use Limited Optimism to Minimize Regret

Discounted-sum games provide a formal model for the study of reinforcement learning, where the agent is enticed to get rewards early since later rewards are discounted. When the agent interacts with the environment, she may regret her actions, realizing that a previous choice was suboptimal given the behavior of the environment. The main contribution of this paper is a PSPACE algorithm for computing the minimum possible regret of a given game. To this end, several results of independent interest are shown. (1) We identify a class of regret-minimizing and admissible strategies that first assume that the environment is collaborating, then assume it is adversarial---the precise timing of the switch is key here. (2) Disregarding the computational cost of numerical analysis, we provide an NP algorithm that checks that the regret entailed by a given time-switching strategy exceeds a given value. (3) We show that determining whether a strategy minimizes regret is decidable in PSPACE

Toward Forecasting Volcanic Eruptions using Seismic Noise

During inter-eruption periods, magma pressurization yields subtle changes of the elastic properties of volcanic edifices. We use the reproducibility properties of the ambient seismic noise recorded on the Piton de la Fournaise volcano to measure relative seismic velocity variations of less than 0.1 % with a temporal resolution of one day. Our results show that five studied volcanic eruptions were preceded by clearly detectable seismic velocity decreases within the zone of magma injection. These precursors reflect the edifice dilatation induced by magma pressurization and can be useful indicators to improve the forecasting of volcanic eruptions.Comment: Supplementary information: http://www-lgit.obs.ujf-grenoble.fr/~fbrengui/brenguier_SI.pdf Supplementary video: http://www-lgit.obs.ujf-grenoble.fr/~fbrengui/brenguierMovieVolcano.av

Decrease in Seismic Velocity Observed Prior to the 2018 Eruption of Kīlauea Volcano With Ambient Seismic Noise Interferometry

The 2018 Kīlauea eruption was a complex event that included deformation and eruption at the summit and along the East Rift Zone. We use ambient seismic noise interferometry to measure time‐lapse changes in seismic velocity of the volcanic edifice prior to the lower East Rift Zone eruption. Our results show that seismic velocities increase in relation to gradual inflation of the edifice between 1 March and 20 April. In the 10 days prior to the 3rd of May eruption onset, a rapid seismic velocity decrease occurs even though the summit is still inflating. We confirm that intereruptive velocity change is correlated with surface deformation, while the velocity decrease prior to eruption is likely due to accumulating damage induced by the pressure exerted by the magma reservoir on the edifice. The accumulating damage and subsequent decrease in bulk edifice strength may have facilitated increased transport of magma from the summit reservoir to the Middle East Rift Zone

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