Related papers: A Super-Polynomial Lower Bound for the Parity Game…
We study strategy improvement algorithms for mean-payoff and parity games. We describe a structural property of these games, and we show that these structures can affect the behaviour of strategy improvement. We show how awareness of these…
This paper investigates a class of games with large strategy spaces, motivated by challenges in AI alignment and language games. We introduce the hidden game problem, where for each player, an unknown subset of strategies consistently…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multi-dimensional mean-payoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but…
The notion of separating automata was introduced by Bojanczyk and Czerwinski for understanding the first quasipolynomial time algorithm for parity games. In this paper we show that separating automata is a powerful tool for constructing…
Additively separable hedonic games and fractional hedonic games have received considerable attention. They are coalition forming games of selfish agents based on their mutual preferences. Most of the work in the literature characterizes the…
We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
Parity games are positionally determined. This is a fundamental and classical result. In 2010, Calude et al. showed a breakthrough result for finite parity games: the winning regions and their positional winning strategies can be computed…
Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to…
We consider games played on graphs with the winning conditions for the players specified as weak-parity conditions. In weak-parity conditions the winner of a play is decided by looking into the set of states appearing in the play, rather…
We present a deterministic algorithm, solving discounted games with $n$ nodes in $n^{O(1)}\cdot (2 + \sqrt{2})^n$-time. For bipartite discounted games our algorithm runs in $n^{O(1)}\cdot 2^n$-time. Prior to our work no deterministic…
We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose…
This paper studies a variant of the multi-player reach-avoid game played between intruders and defenders with applications to perimeter defense. The intruder team tries to score by sending as many intruders as possible to the target area,…
We study policy iteration for infinite-horizon Markov decision processes. It has recently been shown policy iteration style algorithms have exponential lower bounds in a two player game setting. We extend these lower bounds to Markov…
We consider two-player partial-observation stochastic games on finite-state graphs where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are \omega-regular conditions specified as parity…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
Attractors in parity games are a technical device for solving "alternating" reachability of given node sets. A well known solver of parity games - Zielonka's algorithm - uses such attractor computations recursively. We here propose new…
The exact complexity of solving parity games is a major open problem. Several authors have searched for efficient algorithms over specific classes of graphs. In particular, Obdr\v{z}\'{a}lek showed that for graphs of bounded tree-width or…
We develop an algorithm that combines the advantages of priority promotion - one of the leading approaches to solving large parity games in practice - with the quasi-polynomial time guarantees offered by Parys' algorithm. Hybridising these…