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This paper investigates the convergence of learning dynamics in Stackelberg games.
An estimate for the perturbations of the solutions of ordinary differential equations
V. M. Alekseev · 1961
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Existence and uniqueness of equilibrium points for concave n-person games
J. B. Rosen · 1965
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The theory of max-min, with applications
John M. Danskin · 1966
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The Theory of Max-Min and its Application to Weapons Allocation Problems
John M. Danskin · 1967
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Closed-loop stackelberg strategies with applications in the optimal control of multilevel systems
Tamer Basar and Hasan Selbuz · 1979
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Nonclassical control problems and stackelberg games
G Papavassilopoulos and J Cruz · 1979
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Sufficient conditions for stackelberg and nash strategies with memory
George P Papavassilopoulos and JB Cruz · 1980
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Duopoly models with consistent conjectures
Timothy F Bresnahan · 1981
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Linear Systems Theory
F. Callier and C. Desoer · 1991
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Stackelberg versus cournot oligopoly equilibrium
Simon P Anderson and Maxim Engers · 1992
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Markov games as a framework for multi-agent reinforcement learning
Michael L Littman · 1994
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Dynamic Noncooperative Game Theory
Tamer Basar and Geert Jan Olsder · 1998
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The theory of learning in games , volume 2
Drew Fudenberg, Fudenberg Drew, David K Levine, and David K Levine · 1998
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Dynamics of stochastic approximation algorithms
Michel Benaïm · 1999
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Mixed equilibria and dynamical systems arising from fictitious play in perturbed games
Michel Benaım and Morris W Hirsch · 1999
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Nonlinear Systems Theory
S. S. Sastry · 1999
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Honeycombs and sums of hermitian matrices
Allen Knutson and Terence Tao · 2001
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Convergent multiple-timescales reinforcement learning algorithms in normal form games
E. J. Collins and D. S. Leslie · 2003
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Correlated q-learning
Amy Greenwald, Keith Hall, and Roberto Serrano · 2003
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Nash q-learning for general-sum stochastic games
Junling Hu and Michael P Wellman · 2003
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Stochastic approximation and recursive algorithms and applications , volume 35
Harold J. Kushner and G. George Yin · 2003
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If multi-agent learning is the answer, what is the question?
Yoav Shoham, Rob Powers, and Trond Grenager · 2007
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Stochastic Approximation: A Dynamical Systems Viewpoint
Vivek S. Borkar · 2008
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Spectral Theory of Block Operator Matrices and Applications
C. Tretter · 2008
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Multi-agent learning with policy prediction
Chongjie Zhang and Victor Lesser · 2010
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Topics in Matrix Analysis
Roger Horn and Charles Johnson · 2011
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Game-theoretic modeling of human adaptation in human-robot collaboration
Stefanos Nikolaidis, Swaprava Nath, Ariel D Procaccia, and Siddhartha Srinivasa · 2017
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The mechanics of n-player differentiable games
David Balduzzi, Sebastien Racaniere, James Martens, Jakob Foerster, Karl Tuyls, and Thore Graepel · 2018
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On a Class of Non-Hermitian Matrices with Positive Definite Schur Complements
T Berger, J Giribet, F M Pería, and C Trunk · 2018
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Concentration bounds for two time scale stochastic approximation
Vivek S Borkar and Sarath Pattathil · 2018
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The limit points of (optimistic) gradient descent in min-max optimization
Constantinos Daskalakis and Ioannis Panageas · 2018
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Min-max and min-min stackelberg strategies with closed-loop information structure
Marc Jungers, Emmanuel Trélat, and Hisham Abou-Kandil · 2011
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Stochastic recursive algorithms for optimization: simultaneous perturbation methods , volume 434
Shalabh Bhatnagar, HL Prasad, and LA Prashanth · 2012
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Introduction to smooth manifolds
John Lee · 2012
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Necessary optimality conditions for bilevel minimization problems
Alexander J Zaslavski · 2012
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Alec Radford, Luke Metz, and Soumith Chintala · 2015
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Jaime F Fisac, Eli Bronstein, Elis Stefansson, Dorsa Sadigh, S Shankar Sastry, and Anca D Dragan · 2018
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Learning with opponent-learning awareness
Jakob Foerster, Richard Y Chen, Maruan Al-Shedivat, Shimon Whiteson, Pieter Abbeel, and Igor Mordatch · 2018
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On the convergence of gradient-based learning in continuous games
Eric Mazumdar and Lillian J Ratliff · 2018
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Optimistic mirror descent in saddle-point problems: Going the extra (-gradient) mile
Panayotis Mertikopoulos, Bruno Lecouat, Houssam Zenati, Chuan-Sheng Foo, Vijay Chandrasekhar, and Georgios Piliouras · 2018
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Which training methods for gans do actually converge?
Lars Mescheder, Andreas Geiger, and Sebastian Nowozin · 2018
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Lillian J Ratliff and Tanner Fiez · 2018
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A perspective on incentive design: Challenges and opportunities
Lillian J Ratliff, Roy Dong, Shreyas Sekar, and Tanner Fiez · 2018
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A closer look at the optimization landscapes of generative adversarial networks
H Berard, G Gidel, A Almahairi, P Vincent, and S Lacoste-Julien · 2019
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Minmax optimization: Stable limit points of gradient descent ascent are locally optimal
Chi Jin, Praneeth Netrapalli, and Michael I Jordan · 2019
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Stable opponent shaping in differentiable games
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On gradient descent ascent for nonconvex-concave minimax problems
Tianyi Lin, Chi Jin, and Michael I Jordan · 2019
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On finding local nash equilibria (and only local nash equilibria) in zero-sum games
E. Mazumdar, M. Jordan, and S. S. Sastry · 2019
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Towards a better understanding and regularization of gan training dynamics
Weili Nie and Ankit B. Patel · 2019
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Solving a class of non-convex min-max games using iterative first order methods
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A concentration bound for stochastic approximation via alekseev’s formula
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