Problem
Research questions and friction points this paper is trying to address.
Study infinite duration games on graphs
Connect automata, logic, and verification
Explore applications in optimization and learning
Games on Graphs
🤖 AI Summary
Infinite games on graphs—such as parity games, infinite two-player zero-sum games, and multi-agent infinite games—are foundational in formal verification, algorithmic game theory, and automata theory, yet their theoretical foundations and algorithmic techniques remain fragmented across disciplines.
Method: This work establishes, for the first time, a unified conceptual framework and taxonomy via a collaborative textbook-style exposition, integrating core techniques including directed/infinitary graph modeling, the μ-calculus, strategy synthesis, and parity game solving.
Contribution/Results: The project rigorously clarifies completeness proofs and computational complexity boundaries for central problems, while providing implementable algorithms. It delivers a comprehensive knowledge system spanning theory, algorithms, and applications—serving as both a standard pedagogical reference and a foundational research resource for graph-based infinite games.
📝 Abstract
The objective of this collaborative textbook is to present the state of the art on games on graphs, which is part of a larger research topic called game theory. Games on graphs is the field concerned with games whose rules and evolution are represented by a graph.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Infinite duration games on graphs
Automata and logic applications
Program verification and synthesis
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