相关论文: Sink equilibria and the attractors of learning in …

In this paper we examine the relationship between the flow of the replicator dynamic, the continuum limit of Multiplicative Weights Update, and a game's response graph. We settle an open problem establishing that under the replicator, sink…

In this paper we characterise the long-run behaviour of the replicator dynamic in zero-sum games (symmetric or non-symmetric). Specifically, we prove that every zero-sum game possesses a unique global replicator attractor, which we then…

Many well-studied learning dynamics, such as fictitious play and the replicator, are known to not converge in general $N$-player games. The simplest mode of non-convergence is cyclical or periodic behavior. Such cycles are fundamental…

This work introduces a unified framework for analyzing games in greater depth. In the existing literature, players' strategies are typically assigned scalar values, and equilibrium concepts are used to identify compatible choices. However,…

Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in…

Except for special classes of games, there is no systematic framework for analyzing the dynamical properties of multi-agent strategic interactions. Potential games are one such special but restrictive class of games that allow for tractable…

We analyze the problem of distributed power allocation for orthogonal multiple access channels by considering a continuous non-cooperative game whose strategy space represents the users' distribution of transmission power over the network's…

This paper investigates the convergence of learning dynamics in Stackelberg games. In the class of games we consider, there is a hierarchical game being played between a leader and a follower with continuous action spaces. We establish a…

What does it mean to fully understand the behavior of a network of adaptive agents? The golden standard typically is the behavior of learning dynamics in potential games, where many evolutionary dynamics, e.g., replicator, are known to…

During 2023, two interesting results were proven about the limit behavior of game dynamics: First, it was shown that there is a game for which no dynamics converges to the Nash equilibria. Second, it was shown that the sink equilibria of a…

Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players' behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile…

Studying Nash dynamics is an important approach for analyzing the outcome of games with repeated selfish behavior of self-interested agents. Sink equilibria has been introduced by Goemans, Mirrokni, and Vetta for studying social cost on…

Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and…

Imitating successful behavior is a natural and frequently applied approach to trust in when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic…

Do boundedly rational players learn to choose equilibrium strategies as they play a game repeatedly? A large literature in behavioral game theory has proposed and experimentally tested various learning algorithms, but a comparative analysis…

Examining the behavior of multi-agent systems is vitally important to many emerging distributed applications - game theory has emerged as a powerful tool set in which to do so. The main approach of game-theoretic techniques is to model…

A seminal result in game theory is von Neumann's minmax theorem, which states that zero-sum games admit an essentially unique equilibrium solution. Classical learning results build on this theorem to show that online no-regret dynamics…

Games are natural models for multi-agent machine learning settings, such as generative adversarial networks (GANs). The desirable outcomes from algorithmic interactions in these games are encoded as game theoretic equilibrium concepts, e.g.…

Evolutionary game theory studies populations that change in response to an underlying game. Often, the functional form relating outcome to player attributes or strategy is complex, preventing mathematical progress. In this work, we…

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For…