Infinite-duration bidding games Conference Paper

Author(s): Avni, Guy; Henzinger, Thomas A; Chonev, Ventsislav
Title: Infinite-duration bidding games
Title Series: LIPIcs
Affiliation IST Austria
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. There, a central question is the existence and computation of threshold budgets; namely, a value t\in [0,1] such that if\PO's budget exceeds $t$, he can win the game, and if\PT'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.
Keywords: Bidding games, Richman games, parity games, mean-payoff games
Conference Title: CONCUR: Concurrency Theory
Volume: 85
Conference Dates: September 4-9, 2017
Conference Location: Berlin, Germany
ISBN: 978-3-95977-017-0
Publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik  
Start Page: Article number: 17
Copyright Statement: CC BY
Sponsor: This research was supported in part by the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award).
DOI: 10.4230/LIPIcs.CONCUR.2017.21
Notes: We thank Petr Novotný for helpful discussions and pointer
Open access: yes (OA journal)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
  2. Guy Avni
    9 Avni
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