ON THE GLOBAL CONVERGENCE OF STOCHASTIC FICTITIOUS PLAY

By Josef Hofbauer, William H. Sandholm. 2002

488 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/55bcd4614d0024d5b304b170e6a6fb9fed51da39

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In Management Science and Operations Research

Citations in the corpus

Autonomous Vehicle-Target Assignment: A Game-Theoretical Formulation (2007, background): “We should also mention numerous stochastic versions of FP with similar convergence properties (cid:1) 20 (cid:2) .”
A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning (2017, background): “Computing approximate responses is more computationally feasible, and fictitious play can handle approximations [42, 61].”
Deep Fictitious Play for Games with Continuous Action Spaces (2019, methodology): “This hypothesis is partly supported by a variant of FP called Stochastic Fictitious Play (SFP) [10] which adds an entropy-maximizing objective to FP and has been shown to converge under more diverse settings: discrete time [10], continuous time [20] and with continuous action sets [19] under reasona”
Monotone Dynamical Systems (2013, unknown): “For applications of competitive and cooperative systems, see for example Benäım [15], Benäım and Hirsch [16, 17], Hirsch [68, 73] Hofbauer and Sandholm [80], Hsu and Waltman [83], Smith [193, 194], Smith and Waltman [203].”
From Poincaré Recurrence to Convergence in Imperfect Information Games: Finding Equilibrium via Regularization (2020, background): “The best response sequences of Fictitious Play (Brown, 1951) and smoother variants (Hofbauer & Sandholm, 2002) converge in time-average.”
Prediction, learning, and games (2006, background): “See the references within [163] for various related results.”
Re-evaluating evaluation (2018, background): “Perturbed best response converges to a more stable approximation to Nash [65,66] that unfortunately is not invariant.”
4. Monotone Dynamical Systems (2005, background): “For applications of competitive and cooperative systems, see for example Benäım [15], Benäım and Hirsch [16, 17], Hirsch [68, 73] Hofbauer and Sandholm [80], Hsu and Waltman [83], Smith [193, 194], Smith and Waltman [203].”
Stochastic Approximations and Differential Inclusions (2005, methodology): “It is partially motivated by Smale’s approach to the prisoner’s dilemma [27] (see also Benäım and Hirsch [4, 5]), Blackwell’s approachability theory ([8]; see also Sorin [28]), as well as fictitious play (Brown [10], Robinson [26]) and stochastic fictitious play (Benäım and Hirsch [6], Fudenberg and”
Learning in games with continuous action sets and unknown payoff functions (2016, background): “In the same game-theoretic context, the composite map Qi ◦vi is often called a smooth, perturbed, or regularized best response; for a detailed discussion, see Hofbauer and Sandholm [16] and Mertikopoulos and Sandholm [26].”
Generalised weakened fictitious play (2006, background): “The assumption is either that players choose to play this mixed strategy, or alternatively that they receive payoff perturbations that induce such a mixed strategy (Hofbauer and Sandholm, 2002).”
Wasserstein Distributional Robustness and Regularization in Statistical Learning (2017, methodology): “The regularization problem (5) is equivalent to the formulation of representative agent choice model (Anderson et al. 1988, Hofbauer and Sandholm 2002), which states that the choice probability vector is given by the solution of the regularization problem (5).”