# Generalized Parity Games

@inproceedings{Chatterjee2007GeneralizedPG, title={Generalized Parity Games}, author={Krishnendu Chatterjee and Thomas A. Henzinger and Nir Piterman}, booktitle={Foundations of Software Science and Computation Structure}, year={2007} }

We consider games where the winning conditions are disjunctions (or dually, conjunctions) of parity conditions; we call them generalized parity games. These winning conditions, while ω-regular, arise naturally when considering fair simulation between parity automata, secure equilibria for parity conditions, and determinization of Rabin automata. We show that these games retain the computational complexity of Rabin and Streett conditions; i.e., they are NP-complete and co-NP-complete…

## 65 Citations

### Stochastic o-regular games

- Computer Science
- 2007

It is shown how the notion of secure equilibrium extends the assume-guarantee style of reasoning in the game theoretic framework, and the existence of unique maximal secure equilibrium payoff profiles in turn-based deterministic games is proved.

### Combinations of Qualitative Winning for Stochastic Parity Games

- MathematicsCONCUR
- 2019

A complete picture for the study of combinations of qualitative winning criteria for parity conditions in MDPs and turn-based stochastic games is presented.

### Two-Player Boundedness Counter Games

- Computer Science
- 2022

This work considers two-player zero-sum games with winning objectives beyond regular languages, expressed as a parity condition in conjunction with a Boolean combination of boundedness conditions on a finite set of counters, and proves that they are in solvable in NP ∩ CoNP and in PTime if the parity condition is fixed.

### Window Parity Games: An Alternative Approach Toward Parity Games with Time Bounds (Full Version)

- EconomicsGandALF
- 2016

This work considers two approaches toward inclusion of time bounds in parity games, based on the notion of finitary parity games and parity games with costs and extends both approaches to the multi-dimension setting.

### Deciding parity games in quasipolynomial time

- Computer Science, MathematicsSTOC
- 2017

It is shown that the parity game can be solved in quasipolynomial time and it is proven that coloured Muller games with n nodes and m colours can be decided in time O((mm · n)5); it is also shown that this bound cannot be improved to O((2m · n), for any c, unless FPT = W[1].

### On the Complexity of SPEs in Parity Games

- Computer ScienceCSL
- 2022

The techniques are based on a recent characterization of SPEs in prefix-independent games that is grounded on the notions of requirements and negotiation, and according to which the plays supported by SPEs are exactly the plays consistent with the requirement that is the least fixed point of the negotiation function.

### Doomsday Equilibria for Omega-Regular Games

- Economics, Computer ScienceVMCAI
- 2014

A new notion of equilibria is proposed, called doomsdayEquilibria, which is a strategy profile such that all players satisfy their own objective, and if any coalition of players deviates and violates even one of the players objective, then the objective of every player is violated.

### Constrained existence problem for weak subgame perfect equilibria with omega-regular Boolean objectives

- EconomicsGandALF
- 2018

This work focuses on the recent notion of weak subgame perfect equilibrium (weak SPE), a refinement of SPE, and shows that the constrained existence problem for weak SPEs is fixed parameter tractable and is polynomial when the number of players is fixed.

### Languages and strategies: a study of regular infinite games

- Computer Science
- 2013

The fundamental Büchi-Landweber Theorem is extended and refine to subclasses of the class of regular languages, in particular the authors consider hierarchies below the starfree languages and distinguish between weak games and strong games.

### Measuring Permissiveness in Parity Games: Mean-Payoff Parity Games Revisited

- Computer Science, EconomicsATVA
- 2011

It is proved that deciding (the permissiveness of) a most permissive winning strategy is in NP ∩ coNP, which provides a new study of mean-payoff parity games and gives a new algorithm for solving these games, which beats all previously known algorithms for this problem.

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