Determinacy in discrete-bidding infinite-duration games

Aghajohari M, Avni G, Henzinger TA. 2021. Determinacy in discrete-bidding infinite-duration games. Logical Methods in Computer Science. 17(1), 10:1-10:23.

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Journal Article | Published | English

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Author
Aghajohari, Milad; Avni, GuyISTA ; Henzinger, Thomas AISTA
Department
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.
Publishing Year
Date Published
2021-02-03
Journal Title
Logical Methods in Computer Science
Acknowledgement
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).
Volume
17
Issue
1
Page
10:1-10:23
eISSN
IST-REx-ID

Cite this

Aghajohari M, Avni G, Henzinger TA. Determinacy in discrete-bidding infinite-duration games. Logical Methods in Computer Science. 2021;17(1):10:1-10:23. doi:10.23638/LMCS-17(1:10)2021
Aghajohari, M., Avni, G., & Henzinger, T. A. (2021). Determinacy in discrete-bidding infinite-duration games. Logical Methods in Computer Science. International Federation for Computational Logic. https://doi.org/10.23638/LMCS-17(1:10)2021
Aghajohari, Milad, Guy Avni, and Thomas A Henzinger. “Determinacy in Discrete-Bidding Infinite-Duration Games.” Logical Methods in Computer Science. International Federation for Computational Logic, 2021. https://doi.org/10.23638/LMCS-17(1:10)2021.
M. Aghajohari, G. Avni, and T. A. Henzinger, “Determinacy in discrete-bidding infinite-duration games,” Logical Methods in Computer Science, vol. 17, no. 1. International Federation for Computational Logic, p. 10:1-10:23, 2021.
Aghajohari M, Avni G, Henzinger TA. 2021. Determinacy in discrete-bidding infinite-duration games. Logical Methods in Computer Science. 17(1), 10:1-10:23.
Aghajohari, Milad, et al. “Determinacy in Discrete-Bidding Infinite-Duration Games.” Logical Methods in Computer Science, vol. 17, no. 1, International Federation for Computational Logic, 2021, p. 10:1-10:23, doi:10.23638/LMCS-17(1:10)2021.
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