License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2019.20
URN: urn:nbn:de:0030-drops-109226
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10922/
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Aghajohari, Milad ; Avni, Guy ; Henzinger, Thomas A.

Determinacy in Discrete-Bidding Infinite-Duration Games

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LIPIcs-CONCUR-2019-20.pdf (0.7 MB)

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.

BibTeX - Entry

@InProceedings{aghajohari_et_al:LIPIcs:2019:10922,
  author =	{Milad Aghajohari and Guy Avni and Thomas A. Henzinger},
  title =	{{Determinacy in Discrete-Bidding Infinite-Duration Games}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Wan Fokkink and Rob van Glabbeek},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10922},
  URN =		{urn:nbn:de:0030-drops-109226},
  doi =		{10.4230/LIPIcs.CONCUR.2019.20},
  annote =	{Keywords: Bidding games, Richman games, determinacy, concurrent games, discrete bidding}
}

Keywords: Bidding games, Richman games, determinacy, concurrent games, discrete bidding
Collection: 30th International Conference on Concurrency Theory (CONCUR 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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