Related papers: Computational Complexity of Computing a Quasi-Prop…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
The recent breakthrough paper by Calude et al. has given the first algorithm for solving parity games in quasi-polynomial time, where previously the best algorithms were mildly subexponential. We devise an alternative quasi-polynomial time…
Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…
Correlated equilibria are a fundamental solution concept in game theory. However, despite decades of research, the complexity beyond games of polynomial type -- such as extensive-form games, congestion or routing games, and more broadly…
We investigate the complexity of computing approximate Nash equilibria in anonymous games. Our main algorithmic result is the following: For any $n$-player anonymous game with a bounded number of strategies and any constant $\delta>0$, an…
We prove that there exists a constant $\epsilon>0$ such that, assuming the Exponential Time Hypothesis for PPAD, computing an $\epsilon$-approximate Nash equilibrium in a two-player (nXn) game requires quasi-polynomial time,…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
We compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with pre-fixed structure. Using this representation, we show conditions under which a game has the maximum possible number of this…
Policy-based methods with function approximation are widely used for solving two-player zero-sum games with large state and/or action spaces. However, it remains elusive how to obtain optimization and statistical guarantees for such…
We show that the problem of finding an {\epsilon}-approximate Nash equilibrium in an anonymous game with seven pure strategies is complete in PPAD, when the approximation parameter {\epsilon} is exponentially small in the number of players.
We provide a complete characterization for the computational complexity of finding approximate equilibria in two-action graphical games. We consider the two most well-studied approximation notions: $\varepsilon$-Nash equilibria…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was…
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…
We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated,…
We suggest a novel stochastic-approximation algorithm to compute a symmetric Nash-equilibrium strategy in a general queueing game with a finite action space. The algorithm involves a single simulation of the queueing process with dynamic…
Two-player zero-sum games are a well-established model for synthesising controllers that optimise some performance criterion. In such games one player represents the controller, while the other describes the (adversarial) environment, and…
We present a unifying representation of computation as a two-player game between an \emph{Algorithm} and \emph{Nature}, grounded in domain theory and game theory. The Algorithm produces progressively refined approximations within a Scott…