Infinite-duration poorman-bidding games

Avni, G, Henzinger, TA and Ibsen-Jensen, R ORCID: 0000-0003-4783-0389 (2018) Infinite-duration poorman-bidding games Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 11316 . pp. 21-36. ISSN 0302-9743, 1611-3349

Text arxiv.pdf - Submitted version Download (331kB)

Abstract

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner or payoff of the game. Such games are central in formal verification since they model the interaction between a non-terminating system and its environment. We study bidding games in which the players bid for the right to move the token. Two bidding rules have been defined. In Richman bidding, in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Poorman bidding is similar except that the winner of the bidding pays the “bank” rather than the other player. While poorman reachability games have been studied before, we present, for the first time, results on infinite-duration poorman games. A central quantity in these games is the ratio between the two players’ initial budgets. The questions we study concern a necessary and sufficient ratio with which a player can achieve a goal. For reachability objectives, such threshold ratios are known to exist for both bidding rules. We show that the properties of poorman reachability games extend to complex qualitative objectives such as parity, similarly to the Richman case. Our most interesting results concern quantitative poorman games, namely poorman mean-payoff games, where we construct optimal strategies depending on the initial ratio, by showing a connection with random-turn based games. The connection in itself is interesting, because it does not hold for reachability poorman games. We also solve the complexity problems that arise in poorman bidding games.

Item Type:	Article
Uncontrolled Keywords:	46 Information and Computing Sciences
Depositing User:	Symplectic Admin
Date Deposited:	06 Dec 2018 09:40
Last Modified:	01 Mar 2026 12:06
DOI:	10.1007/978-3-030-04612-5_2
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3029560
Disclaimer:	The University of Liverpool is not responsible for content contained on other websites from links within repository metadata. Please contact us if you notice anything that appears incorrect or inappropriate.