Infinite-duration bidding games

Guy Avni, Thomas A. Henzinger, Ventsislav Chonev

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

Abstract

Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common modes to determine how the players move the token through the graph; e.g., in turn-based games the players alternate turns in moving the token. We study the bidding mode of moving the token, which, to the best of our knowledge, has never been studied in infinite-duration games. Both players have separate budgets, which sum up to 1. In each turn, a bidding takes place. Both players submit bids simultaneously, and a bid is legal if it does not exceed the available budget. The winner of the bidding pays his bid to the other player and moves the token. For reachability objectives, repeated bidding games have been studied and are called Richman games [36, 35]. There, a central question is the existence and computation of threshold budgets; namely, a value t ∼ [0, 1] such that if Player 1's budget exceeds t, he can win the game, and if Player 2's budget exceeds 1-t, he can win the game. We focus on parity games and mean-payoff games. We show the existence of threshold budgets in these games, and reduce the problem of finding them to Richman games. We also determine the strategy-complexity of an optimal strategy. Our most interesting result shows that memoryless strategies suffice for mean-payoff bidding games.

Original languageEnglish
Title of host publication28th International Conference on Concurrency Theory, CONCUR 2017
EditorsRoland Meyer, Uwe Nestmann
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770484
DOIs
StatePublished - 1 Aug 2017
Externally publishedYes
Event28th International Conference on Concurrency Theory, CONCUR 2017 - Berlin, Germany
Duration: 5 Sep 20178 Sep 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume85
ISSN (Print)1868-8969

Conference

Conference28th International Conference on Concurrency Theory, CONCUR 2017
Country/TerritoryGermany
CityBerlin
Period5/09/178/09/17

Bibliographical note

Publisher Copyright:
© Guy Avni, Thomas A. Henzinger, and Ventsislav Chonev.

Keywords

  • Bidding games
  • Mean-payoff games
  • Parity games
  • Richman games

ASJC Scopus subject areas

  • Software

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