Related papers: A Bridge between Polynomial Optimization and Games…
We revisit the complexity of deciding, given a {\it bimatrix game,} whether it has a {\it Nash equilibrium} with certain natural properties; such decision problems were early known to be ${\mathcal{NP}}$-hard~\cite{GZ89}. We show that…
The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the cost incurred between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games…
Extensive-form games (EFGs) provide a powerful framework for modeling sequential decision making, capturing strategic interaction under imperfect information, chance events, and temporal structure. Most positive algorithmic and theoretical…
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…
We consider a generalization of the classical 100 Prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the…
This paper investigates the problems arising in the construction of a program to play the game of contract bridge. These problems include both the difficulty of solving the game's perfect information variant, and techniques needed to…
We show that Optimistic Hedge -- a common variant of multiplicative-weights-updates with recency bias -- attains ${\rm poly}(\log T)$ regret in multi-player general-sum games. In particular, when every player of the game uses Optimistic…
Recent work in deep reinforcement learning has allowed algorithms to learn complex tasks such as Atari 2600 games just from the reward provided by the game, but these algorithms presently require millions of training steps in order to…
We study the computational complexity of computing or approximating a quasi-proper equilibrium for a given finite extensive form game of perfect recall. We show that the task of computing a symbolic quasi-proper equilibrium is…
Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame…
Infinitely repeated games support equilibrium concepts beyond those present in one-shot games (e.g., cooperation in the prisoner's dilemma). Nonetheless, repeated games fail to capture our real-world intuition for settings with many…
The solution set of a system of polynomial equations typically contains ill-behaved, singular points. Resolution is a fundamental process in geometry in which we replace singular points with smooth points, while keeping the rest of the…
We improve the complexity of solving parity games (with priorities in vertices) for $d={\omega}(\log n)$ by a factor of ${\theta}(d^2)$: the best complexity known to date was $O(mdn^{1.45+\log_2(d/\log_2(n))})$, while we obtain…
Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free mu-calculus and ECTL* model checking problems. These classes can be solved in polynomial time using dedicated algorithms.…
The existence of a polynomial pivot rule for the simplex method for linear programming, policy iteration for Markov decision processes, and strategy improvement for parity games each are prominent open problems in their respective fields.…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding in extensive-form team games remains a significant challenge. While NP-hard in the worst case, there are provably efficient…
We consider the problem of learning sparse polymatrix games from observations of strategic interactions. We show that a polynomial time method based on $\ell_{1,2}$-group regularized logistic regression recovers a game, whose Nash…
Imperfect-recall abstraction has emerged as the leading paradigm for practical large-scale equilibrium computation in incomplete-information games. However, imperfect-recall abstractions are poorly understood, and only weak…
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…