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In general, finite concurrent two-player reachability games are only determined in a weak sense: the supremum probability to win can be approached via stochastic strategies, but cannot be realized. We introduce a class of concurrent games…
We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is…
The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the cost incurred between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games…
Infinite-state games are a commonly used model for the synthesis of reactive systems with unbounded data domains. Symbolic methods for solving such games need to be able to construct intricate arguments to establish the existence of winning…
Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…
This paper studies two-player zero-sum games played on graphs and makes contributions toward the following question: given an objective, how much memory is required to play optimally for that objective? We study regular objectives, where…
Graph games provide the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic reactive processes, the traditional model is perfect-information stochastic games, where some transitions of the game graph…
We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the…
We study infinite two-player win/lose games $(A,B,W)$ where $A,B$ are finite and $W \subseteq (A \times B)^\omega$. At each round Player 1 and Player 2 concurrently choose one action in $A$ and $B$, respectively. Player 1 wins iff the…
Two-player games on graphs provide the mathematical foundation for the study of reactive systems. In the quantitative framework, an objective assigns a value to every play, and the goal of player 1 is to minimize the value of the objective.…
We investigate concurrent two-player win/lose stochastic games on finite graphs with prefix-independent objectives. We characterize subgame optimal strategies and use this characterization to show various memory transfer results: 1) For a…
Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…
Quantitative extensions of parity games have recently attracted significant interest. These extensions include parity games with energy and payoff conditions as well as finitary parity games and their generalization to parity games with…
In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always…
We propose a method to construct finite-state reactive controllers for systems whose interactions with their adversarial environment are modeled by infinite-duration two-player games over (possibly) infinite graphs. The proposed method…
What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question by presenting a very general framework that allows to remove delay: finite-state strategies exist for all winning conditions where the…
In a single-state repeated game, zero-determinant strategies can unilaterally force functions of the payoffs to take values in particular closed intervals. When the explicit use of a determinant is absent from the analysis, they are instead…
We address a central (and classical) issue in the theory of infinite games: the reduction of the memory size that is needed to implement winning strategies in regular infinite games (i.e., controllers that ensure correct behavior against…
Adversarial Patrolling games form a subclass of Security games where a Defender moves between locations, guarding vulnerable targets. The main algorithmic problem is constructing a strategy for the Defender that minimizes the worst damage…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…