相关论文: On the Decomposition of Differential Game
We search for non-constant normalized solutions to the semilinear elliptic system \[ \begin{cases} - \nu \Delta v_i + g_i(v_j^2) v_i = \lambda_i v_i,\quad v_i>0 & \text{in $\Omega$} \\ \partial_n v_i = 0 & \text{on $\partial \Omega$}\\…
We give a global geometric decomposition of continuously differentiable vector fields on $\mathbb{R}^n$. More precisely, given a vector field of class $\mathcal{C}^{1}$ on $\mathbb{R}^{n}$, and a geometric structure on $\mathbb{R}^n$, we…
We investigate the value of parallel repetition of one-round games with any number of players $k\ge 2$. It has been an open question whether an analogue of Raz's Parallel Repetition Theorem holds for games with more than two players, i.e.,…
We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust…
In cosmological perturbation theory it is convenient to use the scalar, vector, tensor (SVT) basis as defined according to how these components transform under 3-dimensional rotations. In attempting to solve the fluctuation equations that…
We study Nash equilibrium learning in partially observable Markov games (POMGs), a multi-agent reinforcement learning framework in which agents cannot fully observe the underlying state. Prior work in this setting relies on centralization…
Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…
This paper presents new families of algorithms for the repeated play of two-agent (near) zero-sum games and two-agent zero-sum stochastic games. For example, the family includes fictitious play and its variants as members. Commonly, the…
Mirror play (MP) is a well-accepted primal-dual multi-agent learning algorithm where all agents simultaneously implement mirror descent in a distributed fashion. The advantage of MP over vanilla gradient play lies in its usage of mirror…
The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study…
In this paper, we review the construction of periodic fundamental solutions and periodic layer potentials for various differential operators. Specifically, we focus on the Laplace equation, the Helmholtz equation, the Lam\'e system, and the…
Hybrid games are models which combine discrete, continuous, and adversarial dynamics. Game logic enables proving (classical) existence of winning strategies. We introduce constructive differential game logic (CdGL) for hybrid games, where…
Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…
A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…
We introduce a new methodology that enables detection of the onset of convergence towards Nash equilibria in simple repeated games with infinitely large strategy spaces, thereby revealing the heuristics used in decision-making. The method…
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…
A game-theoretic model for the study of dynamic networks is analyzed. The model is motivated by communication networks that are subject to failure of nodes and where the restoration needs resources. The corresponding two-player game is…
The Kelly or proportional allocation mechanism is a simple and efficient auction-based scheme that distributes an infinitely divisible resource proportionally to the agents bids. When agents are aware of the allocation rule, their…
Tree projections provide a mathematical framework that encompasses all the various (purely) structural decomposition methods that have been proposed in the literature to single out classes of nearly-acyclic (hyper)graphs, such as the tree…