Games on Graphs

This volume introduces the fundamental results and the state of the art in infinite duration games on graphs. These versatile game models first appeared in the study of automata and logic, but later became important for program verification and synthesis. They have many more applications. In particular, this book covers models from the fields of optimisation, reinforcement learning, model theory, and set theory. The material is presented at a level accessible to beginning graduate students, requiring only a basic understanding of discrete algorithms and graphs. The book's primary objective is constructing efficient algorithms for analysing different types of games. Rather than describe their implementation in full detail, it investigates their theoretical foundations and proves their properties and winning strategies. This tutorial reference from experts across the field is ideal for students, researchers, and professionals in logic and automata, verification and synthesis, and related fields.

Table of Contents:
List of contributors; Preface; 1. Introduction Nathanaël Fijalkow; I. Classic: 2. Parity games John Fearnley and Nathanaël Fijalkow; 3. Regular games Nathanael Fijalkow and Florian Horn; 4. Positionality and memory Antonio Casares, Pierre Ohlmann and Pierre Vandenhov; 5. Games with payoffs Nathanaël Fijalkow and Benjamin Monmege; II. Stochastic: 6. Markov decision processes Petr Novotný; 7. Stochastic games Nathalie Betrand, Patricia Bouyer and Nathanaël Fijalkow; III. Information: 8. Concurrent games Rasmus Ibsen-Jensen; 9. Games with signals Hugo Gimbert; 10. Synchronous distributed games C. Aiswarya, Paul Gastin and Nathalie Sznajder; IV. Infinite: 11. Timed games Nicolas Markey and Ocan Sankur; 12. Pushdown games Arnaud Carayol and Olivier Serre; 13. Games with counters Sylvain Schmitz; V. Multi: 14. Games with multiple objectives Mickael Randour; 15. Multiplayer games Romain Brenguier and Ocan Sankue; 16. Bidding games Guy Avni and Thomas A. Henzinger; Bibliography.

About the Author :
Nathanaël Fijalkow is Director of Research at CNRS, LaBRI, University of Bordeaux. He has been on games on graphs for over a decade and contributed to some of the field's most important recent results. He has taught games on graphs at several universities (Paris, Warsaw, Bordeaux) and been heavily involved in organising scientific events on the topic.

Review :
'Games on Graphs: From Logic and Automata to Algorithms, coordinated by Nathanaël Fijalkow, is a must-read book that I highly recommend. Written with rigor and clarity, it presents the state of the art on games on graphs and their algorithms, a selection of exciting open problems and a wealth of new research directions. A book destined to become the essential reference work in its field!' Jean-Éric Pin, Paris 'Games on graphs have witnessed an explosive growth of research over the past decade. This Handbook of 16 articles written by leading experts offers an integrated and nevertheless detailed presentation of this fascinating landscape, covering 'classical' results as well as stochastic, distributed, infinite-duration, and multiplayer games. Editor and authors are to be congratulated for this brilliant work.' Wolfgang Thomas, RWTH Aachen University 'Games on graphs is a mathematical paradigm, both rigorous and intuitive, integrating hot issues in theoretical computer science-nondeterminism, decision making, interaction, randomness, complexity. In this passionate book, experts in the field guide the reader from basic concepts and ideas to a wealth of research directions at the cutting edge. Mathematics is challenging, but games make it fun.' Damian Niwiński, University of Warsaw