conference paper
Qualitative concurrent parity games: Bounded rationality
LNCS
published
yes
Krishnendu
Chatterjee
author 2E5DCA20-F248-11E8-B48F-1D18A9856A870000-0002-4561-241X
PaoloBaldan
editor
DanieleGorla
editor
KrCh
department
CONCUR: Concurrency Theory
Modern Graph Algorithmic Techniques in Formal Verification
project
Game Theory
project
Quantitative Graph Games: Theory and Applications
project
Microsoft Research Faculty Fellowship
project
We study two-player concurrent games on finite-state graphs played for an infinite number of rounds, where in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. The objectives are ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). While the qualitative analysis problem for concurrent parity games with infinite-memory, infinite-precision randomized strategies was studied before, we study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision, or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory, or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in (n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. Our symbolic algorithms are based on a characterization of the winning sets as μ-calculus formulas, however, our μ-calculus formulas are crucially different from the ones for concurrent parity games (without bounded rationality); and our memoryless witness strategy constructions are significantly different from the infinite-memory witness strategy constructions for concurrent parity games.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik2014Rome, Italy
eng
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)10.1007/978-3-662-44584-6_37
8704544 - 559
https://research-explorer.app.ist.ac.at/record/3354
Chatterjee K. Qualitative concurrent parity games: Bounded rationality. In: Baldan P, Gorla D, eds. <i>Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)</i>. Vol 8704. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2014:544-559. doi:<a href="https://doi.org/10.1007/978-3-662-44584-6_37">10.1007/978-3-662-44584-6_37</a>
Chatterjee, K. (2014). Qualitative concurrent parity games: Bounded rationality. In P. Baldan & D. Gorla (Eds.), <i>Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)</i> (Vol. 8704, pp. 544–559). Rome, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.1007/978-3-662-44584-6_37">https://doi.org/10.1007/978-3-662-44584-6_37</a>
Chatterjee, Krishnendu. “Qualitative Concurrent Parity Games: Bounded Rationality.” In <i>Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)</i>, edited by Paolo Baldan and Daniele Gorla, 8704:544–59. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014. <a href="https://doi.org/10.1007/978-3-662-44584-6_37">https://doi.org/10.1007/978-3-662-44584-6_37</a>.
Chatterjee, Krishnendu. “Qualitative Concurrent Parity Games: Bounded Rationality.” <i>Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)</i>, edited by Paolo Baldan and Daniele Gorla, vol. 8704, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014, pp. 544–59, doi:<a href="https://doi.org/10.1007/978-3-662-44584-6_37">10.1007/978-3-662-44584-6_37</a>.
K. Chatterjee, “Qualitative concurrent parity games: Bounded rationality,” in <i>Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)</i>, Rome, Italy, 2014, vol. 8704, pp. 544–559.
K. Chatterjee, in:, P. Baldan, D. Gorla (Eds.), Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014, pp. 544–559.
Chatterjee K. 2014. Qualitative concurrent parity games: Bounded rationality. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). CONCUR: Concurrency Theory, LNCS, vol. 8704. 544–559.
20542018-12-11T11:55:27Z2019-08-02T12:38:11Z