Related papers: Solving Large Imperfect Information Games Using CF…
Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…
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…
Monte-Carlo counterfactual regret minimization (MCCFR) is the state-of-the-art algorithm for solving sequential games that are too large for full tree traversals. It works by using gradient estimates that can be computed via sampling.…
This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…
In recent years, empirical game-theoretic analysis (EGTA) has emerged as a powerful tool for analyzing games in which an exact specification of the utilities is unavailable. Instead, EGTA assumes access to an oracle, i.e., a simulator,…
Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash…
Imperfect information games, such as Bridge and Skat, present challenges due to state-space explosion and hidden information, posing formidable obstacles for search algorithms. Determinization-based algorithms offer a resolution by sampling…
We study the complexity of computing or approximating refinements of Nash equilibrium for a given finite n-player extensive form game of perfect recall (EFGPR), where n >= 3. Our results apply to a number of well-studied refinements,…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method…
Fictitious play is a popular learning algorithm in which players that utilize the history of actions played by the players and the knowledge of their own payoff matrix can converge to the Nash equilibrium under certain conditions on the…
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…
Regret Matching+ (RM+) and its variants are important algorithms for solving large-scale games. However, a theoretical understanding of their success in practice is still a mystery. Moreover, recent advances on fast convergence in games are…
Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such…
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…
This work considers a stochastic Nash game in which each player solves a parameterized stochastic optimization problem. In deterministic regimes, best-response schemes have been shown to be convergent under a suitable spectral property…
We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is \emph{query…
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…
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…
In imperfect-information games, the optimal strategy in a subgame may depend on the strategy in other, unreached subgames. Thus a subgame cannot be solved in isolation and must instead consider the strategy for the entire game as a whole,…
We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…