# Bounded rationality in concurrent parity games

K. Chatterjee, ArXiv (2011) 1–51.

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Abstract

We consider 2-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves inde- pendently and simultaneously; the current state and the two moves determine the successor state. We study concurrent games with 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, respec- tively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). 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 power- ful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(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. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms, that are obtained by characterization of the winning sets as μ-calculus formulas, are considerably more involved than those for turn-based games.

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Date Published

2011-07-11

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arXiv

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1 - 51

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### Cite this

Chatterjee K. Bounded rationality in concurrent parity games.

*arXiv*. 2011:1-51.Chatterjee, K. (2011). Bounded rationality in concurrent parity games.

*arXiv*. ArXiv.Chatterjee, Krishnendu. “Bounded Rationality in Concurrent Parity Games.”

*ArXiv*. ArXiv, 2011.K. Chatterjee, “Bounded rationality in concurrent parity games,”

*arXiv*. ArXiv, pp. 1–51, 2011.Chatterjee K. 2011. Bounded rationality in concurrent parity games. arXiv, 1–51, .

Chatterjee, Krishnendu. “Bounded Rationality in Concurrent Parity Games.”

*ArXiv*, ArXiv, 2011, pp. 1–51.**All files available under the following license(s):**

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arXiv 1107.2146