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.
CONCUR: International Conference on Concurrency Theory
2019-08-27 – 2019-08-30
Aghajohari M, Avni G, Henzinger TA. Determinacy in discrete-bidding infinite-duration games. In: Vol 140. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:20. doi:10.4230/LIPICS.CONCUR.2019.20
Aghajohari, M., Avni, G., & Henzinger, T. A. (2019). Determinacy in discrete-bidding infinite-duration games (Vol. 140, p. 20). Presented at the CONCUR: International Conference on Concurrency Theory, Amsterdam, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.CONCUR.2019.20
Aghajohari, Milad, Guy Avni, and Thomas A Henzinger. “Determinacy in Discrete-Bidding Infinite-Duration Games,” 140:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.CONCUR.2019.20.
M. Aghajohari, G. Avni, and T. A. Henzinger, “Determinacy in discrete-bidding infinite-duration games,” presented at the CONCUR: International Conference on Concurrency Theory, Amsterdam, Netherlands, 2019, vol. 140, p. 20.
Aghajohari M, Avni G, Henzinger TA. 2019. Determinacy in discrete-bidding infinite-duration games. CONCUR: International Conference on Concurrency Theory, LIPIcs, vol. 140. 20.
Aghajohari, Milad, et al. Determinacy in Discrete-Bidding Infinite-Duration Games. Vol. 140, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 20, doi:10.4230/LIPICS.CONCUR.2019.20.
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