Related papers: The Attractor of the Replicator Dynamic in Zero-Su…

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…

We introduce and study a two-player zero-sum game between a probabilist and Nature defined by a convex function $f$, a finite collection $\mathcal{B}$ of Markov generators (or its convex hull), and a target distribution $\pi$. The…

The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. In a weakly acyclic game, from any starting state, there is a sequence of better-response moves…

Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the possibility to use conditional strategies that depend on the outcome of…

Subgame perfect equilibria are specific Nash equilibria in perfect information games in extensive form. They are important because they relate to the rationality of the players. They always exist in infinite games with continuous…

For the classical backward induction algorithm, the input is an arbitrary $n$-person positional game with perfect information modeled by a finite acyclic directed graph (digraph) and the output is a profile $(x_1, \ldots, x_n)$ of pure…

We study strategic games on weighted directed graphs, where the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy augmented by a fixed non-negative bonus for picking a given…

We study the convergence time of the best response dynamics in player-specific singleton congestion games. It is well known that this dynamics can cycle, although from every state a short sequence of best responses to a Nash equilibrium…

This paper investigates the impact of perturbations on the best-response-based algorithms approximating Nash equilibria in zero-sum games, namely Double Oracle and Fictitious Play. More precisely, we assume that the oracle computing the…

Zero-sum games arise in a wide variety of problems, including robust optimization and adversarial learning. However, algorithms deployed for finding a local Nash equilibrium in these games often converge to non-Nash stationary points. This…

Multi-agent games are becoming an increasing prevalent formalism for the study of electronic commerce and auctions. The speed at which transactions can take place and the growing complexity of electronic marketplaces makes the study of…

In this paper we establish a new connection between a class of 2-player nonzero-sum games of optimal stopping and certain $2$-player nonzero-sum games of singular control. We show that whenever a Nash equilibrium in the game of stopping is…

Projection games constitute an important class of nonlocal games where, for any answer from the first player, there is a unique correct answer for the second player. This class of games captures nonlocal games arising from constraint…

Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to…

In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph $\mathcal{H}$ by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the…

Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions…

Adversarial training is a standard technique for training adversarially robust models. In this paper, we study adversarial training as an alternating best-response strategy in a 2-player zero-sum game. We prove that even in a simple…

Strategic interactions can be represented more concisely, and analyzed and solved more efficiently, if we are aware of the symmetries within the multiagent system. Symmetries also have conceptual implications, for example for equilibrium…

We consider a stochastic differential equation that is controlled by means of an additive finite-variation process. A singular stochastic controller, who is a minimizer, determines this finite-variation process, while a discretionary…

We prove that differential Nash equilibria are generic amongst local Nash equilibria in continuous zero-sum games. That is, there exists an open-dense subset of zero-sum games for which local Nash equilibria are non-degenerate differential…