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.
|Title of host publication||Web and Internet Economics - 14th International Conference, WINE 2018, Proceedings|
|Editors||Tobias Harks, George Christodoulou|
|Number of pages||16|
|State||Published - 2018|
|Event||14th International Conference on Web and Internet Economics, WINE 2018 - Oxford, United Kingdom|
Duration: 15 Dec 2018 → 17 Dec 2018
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||14th International Conference on Web and Internet Economics, WINE 2018|
|Period||15/12/18 → 17/12/18|
Bibliographical noteFunding Information:
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).
© Springer Nature Switzerland AG 2018.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)