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Thomas Brihaye

Publications and source records attributed to Thomas Brihaye.

At least 19 recordsLinked to original sources
arXiv2026

A Decision-Making Framework for New Member Integration in Renewable Energy Communities under Prospect Theory

This paper introduces an original approach to an underexplored issue: the integration of a new member into an existing renewable energy community. The problem involves actions with both long-term consequences, such as investment and local pricing, and short-term operational ones, such as daily energy and financial flow management. Long-term decision-making is modeled using finite extensive-form game theory, while short-term day-ahead scheduling decisions are formulated as a generalized Nash equilibrium problem. This framework explicitly accounts for heterogeneous stakeholder preferences and bounded rationality, modeled through prospect theory. The proposed approach is flexible and general, making it applicable to various objectives and decision-making contexts in the evolving landscape of renewable energy communities. It is applied to two communities with five members, eleven candidate users, multiple preference configurations and a comparison with heuristic metrics from the literature is also addressed. The model also exhibits that equilibrium outcomes and stakeholder behavior are influenced by the order of decisions, their preference criteria, and prospect theory parameters particularly the reference point selection.

cs.GT↗
arXiv2025

Stackelberg-Pareto Synthesis with Quantitative Reachability Objectives

In this paper, we deepen the study of two-player Stackelberg games played on graphs in which Player $0$ announces a strategy and Player $1$, having several objectives, responds rationally by following plays providing him Pareto-optimal payoffs given the strategy of Player $0$. The Stackelberg-Pareto synthesis problem, asking whether Player $0$ can announce a strategy which satisfies his objective, whatever the rational response of Player $1$, has been recently investigated for $ω$-regular objectives. We solve this problem for weighted graph games and quantitative reachability objectives such that Player $0$ wants to reach his target set with a total cost less than some given upper bound. We show that it is NEXPTIME-complete, as for Boolean reachability objectives.

cs.GT↗
arXiv2025

Multi-weighted Reachability Games and Their Application to Permissiveness

We study two-player multi-weighted reachability games played on a finite directed graph, where an agent, called P1, has several quantitative reachability objectives that he wants to optimize against an antagonistic environment, called P2. In this setting, we ask what cost profiles P1 can ensure regardless of the opponent's behavior. Cost profiles are compared thanks to: (i) a lexicographic order that ensures the unicity of an upper value and (ii) a componentwise order for which we consider the Pareto frontier. We synthesize (i) lexico-optimal strategies and (ii) Pareto-optimal strategies. The strategies are obtained thanks to a fixpoint algorithm which also computes the upper value in polynomial time and the Pareto frontier in exponential time. The constrained existence problem is proved in P for the lexicographic order and PSPACE-complete for the componentwise order. Finally, we show how complexity results about permissiveness of multi-strategies in two-player quantitative reachability games can be derived from the results we obtained in the two-player multi-weighted reachability games setting.

cs.GT↗
arXiv2025

Risk-aware Markov Decision Processes Using Cumulative Prospect Theory

Cumulative prospect theory (CPT) is the first theory for decision-making under uncertainty that combines full theoretical soundness and empirically realistic features [P.P. Wakker - Prospect theory: For risk and ambiguity, Page 2]. While CPT was originally considered in one-shot settings for risk-aware decision-making, we consider CPT in sequential decision-making. The most fundamental and well-studied models for sequential decision-making are Markov chains (MCs), and their generalization Markov decision processes (MDPs). The complexity theoretic study of MCs and MDPs with CPT is a fundamental problem that has not been addressed in the literature. Our contributions are as follows: First, we present an alternative viewpoint for the CPT-value of MCs and MDPs. This allows us to establish a connection with multi-objective reachability analysis and conclude the strategy complexity result that memoryless randomized strategies are necessary and sufficient for optimality. Second, based on this connection, we provide an algorithm for computing the CPT-value in MDPs with infinite-horizon objectives. We show that the problem is in EXPTIME and fixed-parameter tractable. Moreover, we provide a polynomial-time algorithm for the special case of MCs.

cs.LO↗
arXiv2025

Decisiveness for countable MDPs and insights for NPLCSs and POMDPs

Markov chains and Markov decision processes (MDPs) are well-established probabilistic models. While finite Markov models are well-understood, analysing their infinite counterparts remains a significant challenge. Decisiveness has proven to be an elegant property for countable Markov chains: it is general enough to be satisfied by several natural classes of countable Markov chains, and it is a sufficient condition for simple qualitative and approximate quantitative model-checking algorithms to exist. In contrast, existing works on the formal analysis of countable MDPs usually rely on ad hoc techniques tailored to specific classes. We provide here a general framework to analyse countable MDPs by extending the notion of decisiveness. Compared to Markov chains, MDPs exhibit extra non-determinism that can be resolved in an adversarial or cooperative way, leading to multiple natural notions of decisiveness. We show that these notions enable the approximation of reachability and safety probabilities in countable MDPs using simple model-checking procedures. We then instantiate our generic approach to two concrete classes of models inducing countable MDPs: non-deterministic probabilistic lossy channel systems and partially observable MDPs. This leads to an algorithm to approximately compute safety probabilities in each of these classes.

cs.LO↗
arXiv2023

Semantics of Attack-Defense Trees for Dynamic Countermeasures and a New Hierarchy of Star-free Languages

We present a mathematical setting for attack-defense trees, a classic graphical model to specify attacks and countermeasures. We equip attack-defense trees with (trace) language semantics allowing to have an original dynamic interpretation of countermeasures. Interestingly, the expressiveness of attack-defense trees coincides with star-free languages, and the nested countermeasures impact the expressiveness of attack-defense trees. With an adequate notion of countermeasure-depth, we exhibit a strict hierarchy of the star-free languages that does not coincides with the classic one. Additionally, driven by the use of attack-defense trees in practice, we address the decision problems of trace membership and of non-emptiness, and study their computational complexities parameterized by the countermeasure-depth.

cs.FL↗
arXiv2023

Valuing the Electricity Produced Locally in Renewable Energy Communities through Noncooperative Resources Scheduling Games

We propose two market designs for the optimal day-ahead scheduling of energy exchanges within renewable energy communities. The first one implements a cooperative demand side management scheme inside a community where members objectives are coupled through grid tariffs, whereas the second allows in addition the valuation of excess generation in the community and on the retail market. Both designs are formulated as centralized optimization problems first, and as non cooperative games then. In the latter case, the existence and efficiency of the corresponding (Generalized) Nash Equilibria are rigorously studied and proven, and distributed implementations of iterative solution algorithms for finding these equilibria are proposed, with proofs of convergence. The models are tested on a use-case made by 55 members with PV generation, storage and flexible appliances, and compared with a benchmark situation where members act individually (situation without community). We compute the global REC costs and individual bills, inefficiencies of the decentralized models compared to the centralized optima, as well as technical indices such as self-consumption ratio, self-sufficiency ratio, and peak-to-average ratio.

cs.GT↗
arXiv2022

Adversarial Formal Semantics of Attack Trees and Related Problems

Security is a subject of increasing attention in our actual society in order to protect critical resources from information disclosure, theft or damage. The informal model of attack trees introduced by Schneier, and widespread in the industry, is advocated in the 2008 NATO report to govern the evaluation of the threat in risk analysis. Attack-defense trees have since been the subject of many theoretical works addressing different formal approaches. In 2017, M. Audinot et al. introduced a path semantics over a transition system for attack trees. Inspired by the later, we propose a two-player interpretation of the attack-tree formalism. To do so, we replace transition systems by concurrent game arenas and our associated semantics consist of strategies. We then show that the emptiness problem, known to be NP-complete for the path semantics, is now PSPACE-complete. Additionally, we show that the membership problem is coNP-complete for our two-player interpretation while it collapses to P in the path semantics.

cs.GT↗
arXiv2022

One-Clock Priced Timed Games with Negative Weights

Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modelling the cost of spending time in a state and executing an action, respectively). The goals of the players are to minimise and maximise the cost to reach a target location, respectively. We consider priced timed games with one clock and arbitrary integer weights and show that, for an important subclass of them (the so-called simple priced timed games), one can compute, in pseudo-polynomial time, the optimal values that the players can achieve, with their associated optimal strategies. As side results, we also show that one-clock priced timed games are determined and that we can use our result on simple priced timed games to solve the more general class of so-called negative-reset-acyclic priced timed games (with arbitrary integer weights and one clock). The decidability status of the full class of priced timed games with one-clock and arbitrary integer weights still remains open.

cs.GT↗
arXiv2022

Decisiveness of Stochastic Systems and its Application to Hybrid Models (Full Version)

In [ABM07], Abdulla et al. introduced the concept of decisiveness, an interesting tool for lifting good properties of finite Markov chains to denumerable ones. Later, this concept was extended to more general stochastic transition systems (STSs), allowing the design of various verification algorithms for large classes of (infinite) STSs. We further improve the understanding and utility of decisiveness in two ways. First, we provide a general criterion for proving decisiveness of general STSs. This criterion, which is very natural but whose proof is rather technical, (strictly) generalizes all known criteria from the literature. Second, we focus on stochastic hybrid systems (SHSs), a stochastic extension of hybrid systems. We establish the decisiveness of a large class of SHSs and, under a few classical hypotheses from mathematical logic, we show how to decide reachability problems in this class, even though they are undecidable for general SHSs. This provides a decidable stochastic extension of o-minimal hybrid systems. [ABM07] Parosh A. Abdulla, Noomene Ben Henda, and Richard Mayr. 2007. Decisive Markov Chains. Log. Methods Comput. Sci. 3, 4 (2007).

cs.LO↗
arXiv2020

Life is Random, Time is Not: Markov Decision Processes with Window Objectives

The window mechanism was introduced by Chatterjee et al. to strengthen classical game objectives with time bounds. It permits to synthesize system controllers that exhibit acceptable behaviors within a configurable time frame, all along their infinite execution, in contrast to the traditional objectives that only require correctness of behaviors in the limit. The window concept has proved its interest in a variety of two-player zero-sum games because it enables reasoning about such time bounds in system specifications, but also thanks to the increased tractability that it usually yields. In this work, we extend the window framework to stochastic environments by considering Markov decision processes. A fundamental problem in this context is the threshold probability problem: given an objective it aims to synthesize strategies that guarantee satisfying runs with a given probability. We solve it for the usual variants of window objectives, where either the time frame is set as a parameter, or we ask if such a time frame exists. We develop a generic approach for window-based objectives and instantiate it for the classical mean-payoff and parity objectives, already considered in games. Our work paves the way to a wide use of the window mechanism in stochastic models.

cs.LO↗
arXiv2020

The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games

We study multiplayer quantitative reachability games played on a finite directed graph, where the objective of each player is to reach his target set of vertices as quickly as possible. Instead of the well-known notion of Nash equilibrium (NE), we focus on the notion of subgame perfect equilibrium (SPE), a refinement of NE well-suited in the framework of games played on graphs. It is known that there always exists an SPE in quantitative reachability games and that the constrained existence problem is decidable. We here prove that this problem is PSPACE-complete. To obtain this result, we propose a new algorithm that iteratively builds a set of constraints characterizing the set of SPE outcomes in quantitative reachability games. This set of constraints is obtained by iterating an operator that reinforces the constraints up to obtaining a fixpoint. With this fixpoint, the set of SPE outcomes can be represented by a finite graph of size at most exponential. A careful inspection of the computation allows us to establish PSPACE membership.

cs.GT↗
arXiv2020

Decisiveness of Stochastic Systems and its Application to Hybrid Models

In [ABM07], Abdulla et al. introduced the concept of decisiveness, an interesting tool for lifting good properties of finite Markov chains to denumerable ones. Later, this concept was extended to more general stochastic transition systems (STSs), allowing the design of various verification algorithms for large classes of (infinite) STSs. We further improve the understanding and utility of decisiveness in two ways. First, we provide a general criterion for proving decisiveness of general STSs. This criterion, which is very natural but whose proof is rather technical, (strictly) generalizes all known criteria from the literature. Second, we focus on stochastic hybrid systems (SHSs), a stochastic extension of hybrid systems. We establish the decisiveness of a large class of SHSs and, under a few classical hypotheses from mathematical logic, we show how to decide reachability problems in this class, even though they are undecidable for general SHSs. This provides a decidable stochastic extension of o-minimal hybrid systems. [ABM07] Parosh A. Abdulla, Noomene Ben Henda, and Richard Mayr. 2007. Decisive Markov Chains. Log. Methods Comput. Sci. 3, 4 (2007).

cs.LO↗
arXiv2020

Adding Negative Prices to Priced Timed Games

Priced timed games (PTGs) are two-player zero-sum games played on the infinite graph of configurations of priced timed automata where two players take turns to choose transitions in order to optimize cost to reach target states. Bouyer et al. and Alur, Bernadsky, and Madhusudan independently proposed algorithms to solve PTGs with nonnegative prices under certain divergence restriction over prices. Brihaye, Bruyere, and Raskin later provided a justification for such a restriction by showing the undecidability of the optimal strategy synthesis problem in the absence of this divergence restriction. This problem for PTGs with one clock has long been conjectured to be in polynomial time, however the current best known algorithm, by Hansen, Ibsen-Jensen, and Miltersen, is exponential. We extend this picture by studying PTGs with both negative and positive prices. We refine the undecidability results for optimal strategy synthesis problem, and show undecidability for several variants of optimal reachability cost objectives including reachability cost, time-bounded reachability cost, and repeated reachability cost objectives. We also identify a subclass with bi-valued price-rates and give a pseudo-polynomial algorithm to partially answer the conjecture on the complexity of one-clock PTGs.

cs.GT↗
arXiv2019

Dynamics on Games: Simulation-Based Techniques and Applications to Routing

We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly update their respective strategies (for instance, to improve the outcome w.r.t. the current strategy profile). This generates a dynamics in the game which may eventually stabilise to an equilibrium. The objective of the present paper is twofold. First, we aim at drawing a general framework to reason about the termination of such dynamics. In particular, we identify preorders on games (inspired from the classical notion of simulation between transitions systems, and from the notion of graph minor) which preserve termination of dynamics. Second, we show the applicability of the previously developed framework to interdomain routing problems.

cs.GT↗
arXiv2019

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.

cs.GT↗
arXiv2018

Constrained Existence Problem for Weak Subgame Perfect Equilibria with $ω$-Regular Boolean Objectives

We study multiplayer turn-based games played on a finite directed graph such that each player aims at satisfying an omega-regular Boolean objective. Instead of the well-known notions of Nash equilibrium (NE) and subgame perfect equilibrium (SPE), we focus on the recent notion of weak subgame perfect equilibrium (weak SPE), a refinement of SPE. In this setting, players who deviate can only use the subclass of strategies that differ from the original one on a finite number of histories. We are interested in the constrained existence problem for weak SPEs. We provide a complete characterization of the computational complexity of this problem: it is P-complete for Explicit Muller objectives, NP-complete for Co-Büchi, Parity, Muller, Rabin, and Streett objectives, and PSPACE-complete for Reachability and Safety objectives (we only prove NP-membership for Büchi objectives). We also show that the constrained existence problem is fixed parameter tractable and is polynomial when the number of players is fixed. All these results are based on a fine analysis of a fixpoint algorithm that computes the set of possible payoff profiles underlying weak SPEs.

cs.GT↗