Related papers: Attack--Defense Trees and Two-Player Binary Zero-S…

We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…

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…

Attack trees are a popular way to represent and evaluate potential security threats on systems or infrastructures. The goal of this work is to provide a framework allowing to express and check whether an attack tree is consistent with the…

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…

This paper considers a class of two-player zero-sum games on directed graphs whose vertices are equipped with random payoffs of bounded support known by both players. Starting from a fixed vertex, players take turns to move a token along…

Attack-defense trees are a novel methodology for graphical security modeling and assessment. The methodology includes visual, intuitive tree models whose analysis is supported by a rigorous mathematical formalism. Both, the intuitive and…

We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…

We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are "strategically equivalent" if, for every…

We propose an alternative to the tree representation of extensive form games. Games in product form represent information with $\sigma$-fields over a product set, and do not require an explicit description of the play temporality, as…

Attack-Defence Trees (ADTs) are well-suited to assess possible attacks to systems and the efficiency of counter-measures. In this paper, we first enrich the available constructs with reactive patterns that cover further security scenarios,…

We study strategic similarity of game positions in two-player extensive games of perfect information, by looking at the structure of their local game trees, with the aim of improving the performance of game playing agents in detecting…

Attack trees and attack graphs are both common graphical threat models used by organizations to better understand possible cybersecurity threats. These models have been primarily seen as separate entities, to be used and researched in…

Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…

We present two zero-sum games modeling situations where one player attacks (or hides in) a finite dimensional nonempty compact set, and the other tries to prevent the attack (or find him). The first game, called patrolling game, corresponds…

Effective risk management in cybersecurity requires a thorough understanding of the interplay between attacker capabilities and defense strategies. Attack-Defense Trees (ADTs) are a commonly used methodology for representing this interplay;…

Security games are an example of a successful real-world application of game theory. The paper defines blameworthiness of the defender and the attacker in security games using the principle of alternative possibilities and provides a sound…

Attempts at predatory capture may provoke a defensive response that reduces the very value of the predated resource. We provide a game-theoretic analysis of simultaneous-move, two-player Attacker-Defender games that model such interactions.…

This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections…

We study the problem of learning classifiers robust to universal adversarial perturbations. While prior work approaches this problem via robust optimization, adversarial training, or input transformation, we instead phrase it as a…

We present solutions to a continuous patrolling game played on network. In this zero-sum game, an Attacker chooses a time and place to attack a network for a fixed amount of time. A Patroller patrols the network with the aim of intercepting…