Affiliation:
1. IST Austria, Klosterneuburg, Austria
2. Max Planck Institute for Software Systems (MPI-SWS), Saarbrücken, Germany
Abstract
<?tight?>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. The following bidding rule was previously defined and called Richman bidding. Both players have separate
budgets
, which sum up to 1. In each turn, a bidding takes place: Both players submit bids simultaneously, where a bid is legal if it does not exceed the available budget, and the higher bidder pays his bid to the other player and moves the token. The central question studied in bidding games is a necessary and sufficient initial budget for winning the game: a
threshold
budget in a vertex is a value
t
∈ [0, 1] such that if Player 1’s budget exceeds
t
, he can win the game; and if Player 2’s budget exceeds 1 −
t
, he can win the game. Threshold budgets were previously shown to exist in every vertex of a reachability game, which have an interesting connection with
random-turn
games—a sub-class of simple stochastic games in which the player who moves is chosen randomly. We show the existence of threshold budgets for a qualitative class of infinite-duration games, namely parity games, and a quantitative class, namely mean-payoff games. The key component of the proof is a quantitative solution to strongly connected mean-payoff bidding games in which we extend the connection with random-turn games to these games, and construct explicit optimal strategies for both players.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference50 articles.
1. Alternating-time temporal logic
2. K. R. Apt and E. Grädel. 2011. Lectures in Game Theory for Computer Scientists. Cambridge University Press. K. R. Apt and E. Grädel. 2011. Lectures in Game Theory for Computer Scientists. Cambridge University Press.
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Timed network games;Information and Computation;2023-01
2. Bidding mechanisms in graph games;Journal of Computer and System Sciences;2021-08
3. DETERMINACY IN DISCRETE-BIDDING INFINITE-DURATION GAMES;LOG METH COMPUT SCI;2021
4. Bidding Games on Markov Decision Processes;Lecture Notes in Computer Science;2019