We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of -player equilibria converges to it as . However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that me…
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48 results for “equilibria”
Study shows randomized strategies can't be Nash equilibria in markets with transient price impact.
problem Existence of pure Nash equilibria in markets with transient price impact.
method Considered randomized strategies and showed that they cannot be Nash equilibria.
result Nash equilibria cannot contain randomized strategies.
The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.
problem Characterizing and comparing different types of equilibria for time-inconsistent stopping problems.
method Analyzes log sub-additive discount functions and one-dimensional diffusion processes to derive necessary and sufficient conditions for weak equilibria and other types of equilibria.
result Conditions for weak equilibria and their implications for other types of equilibria are provided.
We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
Paper develops efficient algorithms for learning rationalizable equilibria in multiplayer games.
problem Learning rationalizable behavior in multiplayer games under bandit feedback.
method New algorithms for finding rationalizable Coarse Correlated Equilibria and Correlated Equilibria with polynomial sample complexity.
result Achieved polynomial sample complexity for learning rationalizable equilibria, improving over existing exponential complexity.
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak …
Study global geometry of dynamical systems with entire vector fields.
problem Understanding the global structure of equilibria and their basins.
method Step-by-step analysis of basins of centers, nodes, and foci; introduction of global elliptic sectors.
result Characterization of heteroclinic regions connecting equilibria.
New results on financial equilibria in markets with general semimartingales.
problem Existence and uniqueness of mean-variance equilibria in semimartingale markets.
method Analysis of dynamic mean-variance hedging and fixed-point problems.
result First results allowing for general semimartingales and both discrete and continuous time.
We prove a criterion for stability of relative equilibria in symmetric Hamiltonian systems at singular points of the momentum map. This generalizes a theorem of G.W. Patrick. The method of the proof is also useful in studying the bifurcation of relative equilibria.
Equilibria analysis of a networked bivirus epidemic model using Poincaré--Hopf and Manifold Theorymath.DS
This paper analyzes complex equilibria in a networked bivirus epidemic model.
problem Identify conditions for coexistence equilibria in a networked bivirus model.
method Employ Poincaré-Hopf Theorem with modifications and Morse inequalities.
result Establish properties on the local stability/instability of coexistence equilibria.
New findings show pure strategy equilibria are more robust in a war of attrition game.
problem Analyzing a game of war of attrition under complete information.
method Examined the stability of equilibria in pure and mixed strategies under varying payoffs.
result Pure strategy equilibria are more robust to perturbations of the canonical model.
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertaintyq-fin.MF
Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the equilibrium allocation are m…
In this paper the possibility of computing equilibrium in pure exchange and production economies by a homotopy method is investigated. The performance of the algorithm is tested on examples with known equilibria taken from the literature on general equilibrium models and numerical results are presented. In computing eq…
The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.
problem Existence and uniqueness of Nash equilibria in multiplicative performance criteria games.
method General characterization of Nash equilibria for a large class of utility functions.
result Existence and uniqueness of Nash equilibria for arbitrary initial wealth vectors.
Study of MHD equilibria with orientation-reversing symmetry, showing all orbits are periodic.
problem Understanding MHD equilibria with non-reflection symmetry.
method Topological techniques to analyze invariant 2-tori and their orbits.
result All orbits on tori are periodic under certain conditions.
Study on symmetries and equilibria in Poisson manifolds, with applications to rigid body dynamics.
problem Characterizing conformal relative equilibria on Poisson manifolds.
method Introducing conformally Poisson actions and momentum maps, establishing algebraic criteria.
result Classification of nontrivial conformal relative equilibria in Lie algebras, with applications to rigid body dynamics.
New method finds all Nash equilibria via vector optimization.
problem Finding all Nash equilibria in games.
method Formulate vector optimization problem to find Pareto optimal solutions.
result Characterize set of all Nash equilibria as Pareto optimal solutions.
We obtain a formula for the number of horizontal equilibria of a planar convex body with respect to a center of mass in terms of the winding number of the evolute of with respect to . The formula extends to the case where lies on the evolute of and a suitably modified version ho…
We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of vector fields on differentiable stacks. Here we argue in favor of the usefulness of …
Study optimal stopping times for multi-dimensional processes with non-exponential discounting.
problem Optimal stopping in multi-dimensional processes with non-exponential discounting.
method Probabilistic potential theory to establish existence of optimal equilibria.
result Existence of optimal equilibria for multi-dimensional stopping problems.
We undertake a fundamental study of network equilibria modeled as solutions of fixed point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk in networks of financial institutions interconnected by mutual obligations and is…
New approach tackles non-stationary multi-agent games with black-box methods.
problem Challenges in learning equilibria in non-stationary multi-agent systems.
method Versatile black-box approach applicable to various games, including general-sum, potential, and Markov games.
result Achieves optimal regret bounds for non-stationary games, with or without knowledge of total variation.
We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist.
Large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum gamesstat.ML
This work finds mixed equilibria in zero-sum games using interacting particle dynamics.
problem Finding mixed equilibrium points in continuous minmax games.
method A method based on entropic regularisation of two-layer zero-sum games with interacting particle dynamics.
result The sequence of empirical measures of the particle system satisfies a large deviation principle as the number of particles grows to infinity, implying convergence of the empirical measure and the Nikaidô-Isoda error.
Given a multifunction from to the fold symmetric product , we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixe…
Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal constraints.We deal with random endowment density streams which admit jumps and g…
In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We p…
Study explores optimal strategies in games with multiple players and mean-field interactions.
problem Optimal strategies in games with multiple players and mean-field interactions.
method Exploration of three different notions of optimality, including mean-field control solution, mean-field coarse correlated equilibria, and mean-field Nash equilibria.
result Approximation of cooperative and competitive equilibria in large -player games by mean-field control and mean-field equilibria.
The paper solves portfolio optimization problems with risk constraints.
problem Maximizing utility while ensuring a certain wealth threshold with risk constraints.
method Derives Nash equilibria for two agents and characterizes them for more than two agents.
result Characterizes Nash equilibria for different cases of competition probabilities.
Optimal fees for CFMMs prevent liquidity pools from competing to the bottom.
problem Maximizing liquidity provider returns in CFMMs with multiple pools.
method Theoretical and numerical analysis of Nash equilibria for optimal fees.
result Pure Nash equilibria of optimal fees exist for CFMMs using Uniswap's trade function.
Method identifies mixed Nash equilibria in high dimensions for training mixtures of GANs.
problem Finding Nash equilibria in two-player zero-sum continuous games, especially in high dimensions.
method Parametrizing mixed strategies as mixtures of particles, updating their positions and weights using gradient descent-ascent.
result Global convergence to an approximate equilibrium for the related Langevin gradient-ascent dynamic.
Method locates equilibria on unknown Riemannian manifolds using iterative sampling and parallel transport.
problem Locating equilibria on unknown Riemannian manifolds defined by point-clouds.
method Iterative sampling, parallel transport, and generalized isoclines.
result Algorithm reliably locates equilibria of dynamical systems on unknown manifolds.
A new game-theoretic approach balances downside risk with expected reward.
problem Traditional game theory views risk only from the upside perspective, ignoring downside risk.
method Introduces downside risk aware equilibria (DRAE) based on lower partial moments.
result Successfully finds equilibria that balance downside risk with expected reward.
Study on MHD equilibria on curved spaces without symmetries.
problem Analyzing MHD equilibria on curved spaces without symmetries.
method Examined MHD equilibria on Riemannian 3-manifolds with various adapted metrics.
result Found that for an open and dense set of adapted metrics, MHD equilibria on compact 3-manifolds without boundary admit no continuous Killing symmetries.
The paper explores the geometry of holomorphic flows and orbits.
problem Understanding the local geometry of holomorphic flows and their equilibria.
method Analyzing the local geometry of first-order equilibria and higher-order equilibria under holomorphic conditions.
result Holomorphic Poincaré-Bendixson theorem: bounded non-periodic orbits are homoclinic or heteroclinic.
New methods learn correlated equilibria in large games without structural assumptions.
problem Learning correlated equilibria in large, anonymous games with exponential player count.
method Developed Mean-Field correlated and coarse-correlated equilibria, and used classical algorithms to learn them efficiently.
result Efficiently learned correlated equilibria in all games without structural assumptions.
This work finds mixed equilibria in machine learning problems using measures and simultaneous gradient ascent-descent.
problem Finding pure equilibria in machine learning problems is computationally hard.
method Entropic regularization, simultaneous gradient ascent-descent, and particle discretization in the Wasserstein metric.
result Global convergence towards the global equilibrium in mixed equilibria problems.
Area-Constrained Planar Elasticacond-mat.soft
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties: not on…
Two firms compete in a financial market, choosing dividend strategies to avoid default and maximize profits.
problem Strategic interaction between two financially constrained firms in a market with default risk.
method Construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control.
result Explicit identification of optimal strategies and equilibrium payoffs for different initial conditions.
The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independe…
We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become functions of the common noise that all agents are exposed to, whereas idiosyncratic r…
Classifies solitons for surface diffusion flow of graphs.
problem Classifying solitons for surface diffusion flow of graphs.
method Classifies solitons including equilibria, self-similar solutions, and travelling waves.
result Classified solitons for surface diffusion flow of entire graphs.
We reconsider the training objective of Generative Adversarial Networks (GANs) from the mixed Nash Equilibria (NE) perspective. Inspired by the classical prox methods, we develop a novel algorithmic framework for GANs via an infinite-dimensional two-player game and prove rigorous convergence rates to the mixed NE, reso…
Algorithm converges to Nash equilibria in competitive games.
problem Finding Nash equilibria in decentralized, competitive Markov games.
method Decentralized Optimistic Gradient Descent/Ascent with a critic.
result Converges to the set of Nash equilibria under self-play.
Study on asset price dynamics in OLG economies with and without a bubbly asset.
problem Analyzing asset price dynamics and optimality in OLG economies with an asset that yields dividends.
method Deriving conditions for three scenarios of equilibrium existence, providing a complete characterization of the equilibrium set, and investigating the relationship between asset price behaviors and optimality.
result A bubbly equilibrium exists if and only if the interest rate is lower than the population growth rate and the sum of per capita dividends is finite.
Study on mean field games with singular controls and their applications.
problem Optimal productivity expansion in dynamic oligopolies.
method Existence and uniqueness of mean field equilibria through nonlinear equations, Abelian limit for discounted and ergodic games.
result Valid connection between discounted and ergodic games, approximation of Nash equilibria.