Related papers: On the Equivalence of Zero-Sum Games and Conic Pro…
We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the…
For a primal-dual pair of conic linear problems that are described by convex cones $S\subset X$, $T\subset Y$, bilinear symmetric objective functions $\langle\cdot,\cdot\rangle_X$, $\langle\cdot,\cdot\rangle_Y$ and a linear operator…
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em bilinear games}, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
In this paper we consider the problem of computing an $\epsilon$-approximate Nash Equilibrium of a zero-sum game in a payoff matrix $A \in \mathbb{R}^{m \times n}$ with $O(1)$-bounded entries given access to a matrix-vector product oracle…
This paper provides sufficient conditions for the existence of solutions for two-person zero-sum games with inf/sup-compact payoff functions and with possibly noncompact decision sets for both players. Payoff functions may be unbounded, and…
We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction…
This paper extends Berge's maximum theorem for possibly noncompact action sets and unbounded cost functions to minimax problems and studies applications of these extensions to two-player zero-sum games with possibly noncompact action sets…
Pursuing a new approach to the study of infinite games in combinatorics, we introduce the categories $\mathbf{Game}_{A}$ and $\mathbf{Game}_{B}$ and improve some classical results concerning topological games related to the duality between…
We develop a rigorous mathematical framework for quantum game theory applied to static 2x2 games, extending classical concepts to the quantum setting where players may employ arbitrary unitary operations (pure strategies) or probability…
We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave…
Differential games, in particular two-player sequential zero-sum games (a.k.a. minimax optimization), have been an important modeling tool in applied science and received renewed interest in machine learning due to many recent applications,…
The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…
We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…
In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function. This problem arises for example in game-theory-inspired…
Much of recent success in multiagent reinforcement learning has been in two-player zero-sum games. In these games, algorithms such as fictitious self-play and minimax tree search can converge to an approximate Nash equilibrium. While…