Determinacy in discrete-bidding infinite-duration games

Milad Aghajohari, Guy Avni, Thomas A. Henzinger

Research output: Contribution to journalArticlepeer-review


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
Pages (from-to)10:1-10:23
JournalLogical Methods in Computer Science
Issue number1
StatePublished - 2021
Externally publishedYes

Bibliographical note

Funding Information:
Key words and phrases: Graph games, discrete bidding games, Richman games, parity games, determinacy. ∗ A preliminary version of this paper appeared in the proceedings of the 30th CONCUR, LIPIcs 140, pages 20:1–20:17, Schloss Dagstuhl, 2019. 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:
© M. Aghajohari, G. Avni, and T.A. Henzinger.


  • Determinacy
  • Discrete bidding games
  • Graph games
  • Parity games
  • Richman games

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


Dive into the research topics of 'Determinacy in discrete-bidding infinite-duration games'. Together they form a unique fingerprint.

Cite this