Related papers: Doubly Fair Parity Games
We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…
We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this work we focus on the case of Breaker playing randomly and Maker being "clever". The…
We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number…
We study the fair division of indivisible goods with conflicts between pairs of goods, represented by a graph $G = (V, E)$. We consider ``soft'' conflicts: assigning two adjacent goods to the same agent is allowed, but we seek allocations…
An edge-weighted, vertex-capacitated graph G is called stable if the value of a maximum-weight capacity-matching equals the value of a maximum-weight fractional capacity-matching. Stable graphs play a key role in characterizing the…
The domination game is played on a graph $G$ by two players, named Dominator and Staller. They alternatively select vertices of $G$ such that each chosen vertex enlarges the set of vertices dominated before the move on it. Dominator's goal…
We construct several definitions of imbalance and playability, both of which are related to the existence of dominated strategies. Specifically, a maximally balanced game and a playable game cannot have dominated strategies for any player.…
The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…
A vertex $u$ in a graph $G$ totally dominates a vertex $v$ if $u$ is adjacent to $v$ in $G$. A total dominating set of $G$ is a set $S$ of vertices of $G$ such that every vertex of $G$ is totally dominated by a vertex in $S$. The indicated…
In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some…
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…
Repeated interactions are ubiquitous and known to promote social behaviour. While research often focuses on cooperation in the Prisoner's Dilemma, experimental evidence suggests repeated interactions also foster fairness. This study…
In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states.…
We continue the investigation of finite-duration variants of infinite-duration games by extending known results for games played on finite graphs to those played on infinite ones. In particular, we establish an equivalence between pushdown…
Solving parity games, which are equivalent to modal $\mu$-calculus model checking, is a central algorithmic problem in formal methods. Besides the standard computation model with the explicit representation of games, another important…
Two-player games on graphs is central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can…
Feature-based SPL analysis and family-based model checking have seen rapid development. Many model checking problems can be reduced to two-player games on finite graphs. A prominent example is mu-calculus model checking, which is generally…
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…
We propose a class of two person perfect information games based on weighted graphs. One of these games can be described in terms of a round pizza which is cut radially into pieces of varying size. The two players alternately take pieces…
Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…