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Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
Computing approximate Nash equilibria in multi-player general-sum Markov games is a computationally intractable task. However, multi-player Markov games with certain cooperative or competitive structures might circumvent this…
We present an algorithm for computing evolutionarily stable strategies (ESSs) in symmetric perfect-recall extensive-form games of imperfect information. Our main algorithm is for two-player games, and we describe how it can be extended to…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…
Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…
Adversarial team games model multiplayer strategic interactions in which a team of identically-interested players is competing against an adversarial player in a zero-sum game. Such games capture many well-studied settings in game theory,…
Two-player games on graphs provide the theoretical frame- work for many important problems such as reactive synthesis. While the traditional study of two-player zero-sum games has been extended to multi-player games with several notions of…
Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…
Computational game theory has many applications in the modern world in both adversarial situations and the optimization of social good. While there exist many algorithms for computing solutions in two-player interactions, finding optimal…
We consider the problem of computing Nash equilibria in potential games where each player's strategy set is subject to private uncoupled constraints. This scenario is frequently encountered in real-world applications like road network…
The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics,…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
Considering linear-quadratic discrete-time games with unknown input/output/state (i/o/s) dynamics and state, we provide necessary and sufficient conditions for the existence and uniqueness of feedback Nash equilibria (FNE) in the…
A fundamental question in reinforcement learning theory is: suppose the optimal value functions are linear in given features, can we learn them efficiently? This problem's counterpart in supervised learning, linear regression, can be solved…
This paper studies the last-iterate convergence properties of the exponential weights algorithm with constant learning rates. We consider a repeated interaction in discrete time, where each player uses an exponential weights algorithm…
We give a direct polynomial-time reduction from parity games played over the configuration graphs of collapsible pushdown systems to safety games played over the same class of graphs. That a polynomial-time reduction would exist was known…
We examine the problem of efficiently learning coarse correlated equilibria (CCE) in polyhedral games, that is, normal-form games with an exponentially large number of actions per player and an underlying combinatorial structure. Prominent…
Motivated by applications to data networks where fast convergence is essential, we analyze the problem of learning in generic N-person games that admit a Nash equilibrium in pure strategies. Specifically, we consider a scenario where…
The convergence of online learning algorithms in games under self-play is a fundamental question in game theory and machine learning. Among various notions of convergence, last-iterate convergence is particularly desirable, as it reflects…
This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a…