Determinacy in discrete-bidding infinite-duration games

Milad Aghajohari, Guy Avni, Thomas A. Henzinger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a non-terminating system and its environment. In bidding games the players bid for the right to move the token: in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Bidding games are known to have a clean and elegant mathematical structure that relies on the ability of the players to submit arbitrarily small bids. Many applications, however, require a fixed granularity for the bids, which can represent, for example, the monetary value expressed in cents. We study, for the first time, the combination of discrete-bidding and infinite-duration games. Our most important result proves that these games form a large determined subclass of concurrent games, where determinacy is the strong property that there always exists exactly one player who can guarantee winning the game. In particular, we show that, in contrast to non-discrete bidding games, the mechanism with which tied bids are resolved plays an important role in discrete-bidding games. We study several natural tie-breaking mechanisms and show that, while some do not admit determinacy, most natural mechanisms imply determinacy for every pair of initial budgets.

Original languageEnglish
Title of host publication30th International Conference on Concurrency Theory, CONCUR 2019
EditorsWan Fokkink, Rob van Glabbeek
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771214
DOIs
StatePublished - Aug 2019
Externally publishedYes
Event30th International Conference on Concurrency Theory, CONCUR 2019 - Amsterdam, Netherlands
Duration: 27 Aug 201930 Aug 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume140
ISSN (Print)1868-8969

Conference

Conference30th International Conference on Concurrency Theory, CONCUR 2019
Country/TerritoryNetherlands
CityAmsterdam
Period27/08/1930/08/19

Bibliographical note

Funding Information:
Funding This research was supported in part by the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE/SHiNE), Z211-N23 (Wittgenstein Award), and M 2369-N33 (Meitner fellowship).

Publisher Copyright:
© Milad Aghajohari, Guy Avni, and Thomas A. Henzinger.

Keywords

  • Bidding games
  • Concurrent games
  • Determinacy
  • Discrete bidding
  • Richman games

ASJC Scopus subject areas

  • Software

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