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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…

A celebrated result in the interface of online learning and game theory guarantees that the repeated interaction of no-regret players leads to a coarse correlated equilibrium (CCE) -- a natural game-theoretic solution concept. Despite the…

This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed…

We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward…

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…

For many nonlinear physical systems, approximate solutions are pursued by conventional perturbation theory in powers of the non-linear terms. Unfortunately, this often produces divergent asymptotic series, collectively dismissed by Abel as…

We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…

The parameter convergence relies on a stringent persistent excitation (PE) condition in adaptive control. Several works have proposed a memory term in the last decade to translate the PE condition to a feasible finite excitation (FE)…

We define solution concepts appropriate for computationally bounded players playing a fixed finite game. To do so, we need to define what it means for a \emph{computational game}, which is a sequence of games that get larger in some…

We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst…

We extend anytime constraints to the Markov game setting and the corresponding solution concept of an anytime-constrained equilibrium (ACE). Then, we present a comprehensive theory of anytime-constrained equilibria that includes (1) a…

Counterfactual Regret Minimization (CFR) and its variants developed based upon Regret Matching (RM) have been considered to be the best method to solve incomplete information extensive form games. In addition to RM and CFR, Fictitious Play…

We study the problem of stochastic combinatorial pure exploration (CPE), where an agent sequentially pulls a set of single arms (a.k.a. a super arm) and tries to find the best super arm. Among a variety of problem settings of the CPE, we…

The sequential equilibrium is a standard solution concept for extensive-form games with imperfect information that includes an explicit representation of the players' beliefs. An assessment consisting of a strategy and a belief is a…

Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or…

Infinite-duration games with disturbances extend the classical framework of infinite-duration games, which captures the reactive synthesis problem, with a discrete measure of resilience against non-antagonistic external influence. This…

Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…

We study multi-player turn-based games played on (potentially infinite) directed graphs. An outcome is assigned to every play of the game. Each player has a preference relation on the set of outcomes which allows him to compare plays. We…

We consider a dynamical approach to sequential games. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction…

We study the long-term behavior of the fictitious play process in repeated extensive-form games of imperfect information with perfect recall. Each player maintains incorrect beliefs that the moves at all information sets, except the one at…