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An Updated Survey of Bidding Games on Graphs (Invited Talk)

Authors Guy Avni, Thomas A. Henzinger



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Guy Avni
  • University of Haifa, Israel
Thomas A. Henzinger
  • IST Austria, Austria

Acknowledgements

We would like to thank all our collaborators Milad Aghajohari, Ventsislav Chonev, Rasmus Ibsen-Jensen, Ismäel Jecker, Petr Novotný, Josef Tkadlec, and Đorđe Žikelić; we hope the collaboration was as fun and meaningful for you as it was for us.

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Guy Avni and Thomas A. Henzinger. An Updated Survey of Bidding Games on Graphs (Invited Talk). In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 3:1-3:6, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.MFCS.2022.3

Abstract

A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token. In this survey, we consider several bidding mechanisms and their effect on the properties of the game. Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly. We summarize how minor changes in the bidding mechanism lead to unexpected differences in the equivalence with random-turn games.

Subject Classification

ACM Subject Classification
  • Theory of computation → Solution concepts in game theory
  • Theory of computation → Formal languages and automata theory
Keywords
  • Bidding games
  • Richman bidding
  • poorman bidding
  • mean-payoff
  • parity

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