### Abstract

We present a formalization of parity games (a two-player game on directed graphs) and a proof of their positional determinacy in Isabelle/HOL. This proof works for both finite and infinite games.

### License

BSD License

### Topics

- Mathematics/Games and economics
- Mathematics/Graph theory

### Session Parity_Game

- MoreCoinductiveList
- ParityGame
- Strategy
- AttractingStrategy
- Attractor
- WinningStrategy
- WellOrderedStrategy
- WinningRegion
- UniformStrategy
- AttractorStrategy
- PositionalDeterminacy
- AttractorInductive
- Graph_TheoryCompatibility

### Depends on

- Coinductive
- Graph Theory

### Used by

- Gale-Stewart Games

## Cite

×

Parity_Game-AFP

    @article{Parity_Game-AFP,
      author  = {Christoph Dittmann},
      title   = {Positional Determinacy of Parity Games},
      journal = {Archive of Formal Proofs},
      month   = {November},
      year    = {2015},
      note    = {\url{https://isa-afp.org/entries/Parity_Game.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
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- Apr 20, 2020 : Isabelle2020
- Jun 11, 2019 : Isabelle2019
- Aug 16, 2018 : Isabelle2018
- Oct 10, 2017 : Isabelle2017
- Dec 17, 2016 : Isabelle2016-1
- Feb 22, 2016 : Isabelle2016
- Nov 2, 2015 : Isabelle2015