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The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games

Thomas Brihaye ; Véronique Bruyère ; Aline Goeminne ; Jean-François Raskin ; Marie van den Bogaard.

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&nbsp;[&hellip;]

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

Thomas Brihaye ; Florent Delgrange ; Youssouf Oualhadj ; Mickael Randour.

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&nbsp;[&hellip;]

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One-Clock Priced Timed Games with Negative Weights

Thomas Brihaye ; Gilles Geeraerts ; Axel Haddad ; Engel Lefaucheux ; Benjamin Monmege.

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&nbsp;[&hellip;]

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On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games

Thomas Brihaye ; Véronique Bruyère ; Julie De Pril ; Hugo Gimbert.

We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. secure equilibria) are&nbsp;[&hellip;]

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Stochastic Timed Automata

Nathalie Bertrand ; Patricia Bouyer ; Thomas Brihaye ; Quentin Menet ; Christel Baier ; Marcus Groesser ; Marcin Jurdzinski.

A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a stochastic timed automaton A and a property $\Phi$, we want to&nbsp;[&hellip;]

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O-Minimal Hybrid Reachability Games

Patricia Bouyer ; Thomas Brihaye ; Fabrice Chevalier.

In this paper, we consider reachability games over general hybrid systems, and distinguish between two possible observation frameworks for those games: either the precise dynamics of the system is seen by the players (this is the perfect observation framework), or only the starting point and the&nbsp;[&hellip;]

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