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Reachability in two-clock timed automata is PSPACE-complete
TLDR
It is shown that reachability in bounded one-counter automata is PSPACE-complete, and the previous result was shown to be log-space equivalent to reachable in boundedOne-Counter automata. Expand
Exponential Lower Bounds for Policy Iteration
TLDR
This work extends lower bounds to Markov decision processes with the total reward and average-reward optimality criteria to show policy iteration style algorithms have exponential lower bounds in a two player game setting. Expand
Non-oblivious Strategy Improvement
TLDR
A structural property of these games is described, and it is shown that these structures can affect the behaviour of strategy improvement and can be used to accelerate strategy improvement algorithms. Expand
An ordered approach to solving parity games in quasi-polynomial time and quasi-linear space
TLDR
This work provides a first implementation for a quasi-polynomial algorithm, test it on small examples, and provides a number of side results, including minor algorithmic improvements, and a complexity index associated to the approach, which is compared to the recently proposed register index. Expand
The Complexity of the Simplex Method
TLDR
This paper uses the known connection between Markov decision processes (MDPs) and linear programming, and an equivalence between Dantzig's pivot rule and a natural variant of policy iteration for average-reward MDPs to prove that it is PSPACE-complete to find the solution that is computed by the simplex method using Dantzes' pivot rule. Expand
Computing Approximate Nash Equilibria in Polymatrix Games
TLDR
Inspired by the algorithm of Tsaknakis and Spirakis [28], the algorithm uses gradient descent style approach on the maximum regret of the players and can be applied to efficiently find a 0.5+δ)-Nash equilibrium in a two-player Bayesian game. Expand
Time and Parallelizability Results for Parity Games with Bounded Treewidth
TLDR
This paper shows that, if a tree decomposition is provided, then parity games with bounded treewidth can be solved in O(k3k+2 ·n2 ·(d+1)3k) time, where n, k, and d are the size,treewidth, and number of priorities in the parity game. Expand
An ordered approach to solving parity games in quasi polynomial time and quasi linear space
TLDR
A first implementation for a quasi-polynomial algorithm is provided, and a number of side results are provided, including minor algorithmic improvements, a quasi bi-linear complexity in the number of states and edges for a fixed number of colours, and matching lower bounds for the algorithm of Calude et al. Expand
Finding Approximate Nash Equilibria of Bimatrix Games via Payoff Queries
TLDR
It is shown that randomized algorithms require Ω(k2) payoff queries in order to find an ϵ-Nash equilibrium with ϵ < 1/4k, even in zero-one constant-sum games, which rules out query-efficient randomized algorithms for finding exact Nash equilibria. Expand
Distributed Methods for Computing Approximate Equilibria
TLDR
A new, distributed method to compute approximate Nash equilibria in bimatrix games that first solves two independent LPs, each of which is derived from one of the two payoff matrices, and then computes an approximate Nash equilibrium using only limited communication between the players. Expand
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