Related papers: Winning Cores in Parity Games

Parity games are an expressive framework to consider realizability questions for omega-regular languages. However, it is open whether they can be solved in polynomial time, making them unamenable for practical usage. To overcome this…

Game-theoretical approach to the analysis of parallel algorithms is proposed. The approach is based on presentation of the parallel computing as a congestion game. In the game processes compete for resources such as core of a central…

The classic paper of Shapley and Shubik \cite{Shapley1971assignment} characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game…

An energy community is modeled as a cooperative game, where a veto player is needed beyond the prosumers to manage the community, and the worth of a coalition is its benefit compared to the selfish behaviour of the prosumers. Properties of…

We consider two-player games played in real time on game structures with clocks and parity objectives. The games are concurrent in that at each turn, both players independently propose a time delay and an action, and the action with the…

Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application…

Parity games play a central role in model checking and satisfiability checking. Solving parity games is computationally expensive, among others due to the size of the games, which, for model checking problems, can easily contain $10^9$…

In a two-player zero-sum graph game, the players move a token throughout a graph to produce an infinite play, which determines the winner of the game. Bidding games are graph games in which in each turn, an auction (bidding) determines…

It is known that the model checking problem for the modal mu-calculus reduces to the problem of solving a parity game and vice-versa. The latter is realised by the Walukiewicz formulas which are satisfied by a node in a parity game iff…

We study Markov decision processes and turn-based stochastic games with parity conditions. There are three qualitative winning criteria, namely, sure winning, which requires all paths must satisfy the condition, almost-sure winning, which…

We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions. We show that the integration of…

An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…

Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different…

We consider the problem of solving random parity games. We prove that parity games exibit a phase transition threshold above $d_P$, so that when the degree of the graph that defines the game has a degree $d > d_P$ then there exists a…

Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…

Sortition is based on the idea of choosing randomly selected representatives for decision making. The main properties that make sortition particularly appealing are fairness -- all the citizens can be selected with the same probability --…

Coreness represents solution concepts related to core in cooperative games, which captures the stability of players. Motivated by the scale effect in social networks, economics and other scenario, we study the coreness of cooperative game…

We present a general framework to model strategic aspects and stable and fair resource allocations in networks via variants and generalizations of path coalitional games. In these games, a coalition of edges or vertices is successful if it…

This paper revisits timed games by building upon the semantics introduced in "The Element of Surprise in Timed Games". We introduce some modifications to this semantics for two primary reasons: firstly, we recognize instances where the…

Cooperative 2-matching games are a generalization of cooperative matching games, where the value function is given by maximum-weight b-matchings, for a vertex capacity vector $b \leq 2$. We show how to separate over the core of 2-matching…