Related papers: Parity Game Reductions

Parity games are games that are played on directed graphs whose vertices are labeled by natural numbers, called priorities. The players push a token along the edges of the digraph. The winner is determined by the parity of the greatest…

Parity games are combinatorial representations of closed Boolean mu-terms. By adding to them draw positions, they have been organized by Arnold and one of the authors into a mu-calculus. As done by Berwanger et al. for the propositional…

A naive way to solve the model-checking problem of the mu-calculus uses fixpoint iteration. Traditionally however mu-calculus model-checking is solved by a reduction in linear time to a parity game, which is then solved using one of the…

We study the underlying mathematical properties of various partial order models of concurrency based on transition systems, Petri nets, and event structures, and show that the concurrent behaviour of these systems can be captured in a…

Strategic interactions can be represented more concisely, and analyzed and solved more efficiently, if we are aware of the symmetries within the multiagent system. Symmetries also have conceptual implications, for example for equilibrium…

Solving parity games is a major building block for numerous applications in reactive program verification and synthesis. While they can be solved efficiently in practice, no known approach has a polynomial worst-case runtime complexity. We…

We investigate quantitative extensions of modal logic and the modal mu-calculus, and study the question whether the tight connection between logic and games can be lifted from the qualitative logics to their quantitative counterparts. It…

In recent work, Watanabe, Eberhart, Asada, and Hasuo have shown that parity games can be seen as string diagrams, that is, as the morphisms of a symmetric monoidal category, an algebraic structure with two different operations of…

Utilitarian games such as dictator games to measure fairness have been studied in the social sciences for decades. These games have given us insight into not only how humans view fairness but also in what conditions the frequency of…

As part of an effort to apply the rigorous guarantees of formal verification to multi-agent systems, the field of equilibrium analysis, also called rational verification, studies equilibria in multiplayer games to reason about system-level…

Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an…

We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal…

We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the…

Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone…

A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…

Parity games are a much researched class of games in NP intersect CoNP that are not known to be in P. Consequently, researchers have considered specialised algorithms for the case where certain graph parameters are small. In this paper, we…

We provide several tests to determine whether a game is a potential game or whether it is a zero-sum equivalent game---a game which is strategically equivalent to a zero-sum game in the same way that a potential game is strategically…

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…

The performance of two pivoting algorithms, due to Lemke and Cottle and Dantzig, is studied on linear complementarity problems (LCPs) that arise from infinite games, such as parity, average-reward, and discounted games. The algorithms have…

The problem of solving a parity game is at the core of many problems in model checking, satisfiability checking and program synthesis. Some of the best algorithms for solving parity game are strategy improvement algorithms. These are global…