Strategy complexity of concurrent safety games

Chatterjee, K, Hansen, KA and Ibsen-Jensen, R
(2017) Strategy complexity of concurrent safety games. .

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We consider two player, zero-sum, finite-state concurrent reachability games, played for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. Player 1 wins iff a designated goal state is eventually visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed. Our main results are as follows: We show that: (i) the optimal bound on the patience of optimal and -optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary.

Item Type: Conference or Workshop Item (Unspecified)
Depositing User: Symplectic Admin
Date Deposited: 06 Dec 2018 09:22
Last Modified: 12 Apr 2022 08:11
DOI: 10.4230/LIPIcs.MFCS.2017.55