Reachability Poorman Discrete-Bidding Games

Guy Avni, Tobias Meggendorfer, Suman Sadhukhan, Josef Tkadlec, Dorde Žikelić

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


We consider bidding games, a class of two-player zero-sum graph games. The game proceeds as follows. Both players have bounded budgets. A token is placed on a vertex of a graph, in each turn the players simultaneously submit bids, and the higher bidder moves the token, where we break bidding ties in favor of Player 1. Player 1 wins the game iff the token visits a designated target vertex. We consider, for the first time, poorman discrete-bidding in which the granularity of the bids is restricted and the higher bid is paid to the bank. Previous work either did not impose granularity restrictions or considered Richman bidding (bids are paid to the opponent). While the latter mechanisms are technically more accessible, the former is more appealing from a practical standpoint. Our study focuses on threshold budgets, which is the necessary and sufficient initial budget required for Player 1 to ensure winning against a given Player 2 budget. We first show existence of thresholds. In DAGs, we show that threshold budgets can be approximated with error bounds by thresholds under continuous-bidding and that they exhibit a periodic behavior. We identify closed-form solutions in special cases. We implement and experiment with an algorithm to find threshold budgets.

Original languageEnglish
Title of host publicationECAI 2023 - 26th European Conference on Artificial Intelligence, including 12th Conference on Prestigious Applications of Intelligent Systems, PAIS 2023 - Proceedings
EditorsKobi Gal, Kobi Gal, Ann Nowe, Grzegorz J. Nalepa, Roy Fairstein, Roxana Radulescu
PublisherIOS Press BV
Number of pages8
ISBN (Electronic)9781643684369
StatePublished - 28 Sep 2023
Event26th European Conference on Artificial Intelligence, ECAI 2023 - Krakow, Poland
Duration: 30 Sep 20234 Oct 2023

Publication series

NameFrontiers in Artificial Intelligence and Applications
ISSN (Print)0922-6389
ISSN (Electronic)1879-8314


Conference26th European Conference on Artificial Intelligence, ECAI 2023

Bibliographical note

Publisher Copyright:
© 2023 The Authors.

ASJC Scopus subject areas

  • Artificial Intelligence


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