Timezone: »
Nash equilibrium strategies have the known weakness that they do not prescribe rational play in situations that are reached with zero probability according to the strategies themselves, for example, if players have made mistakes. Trembling-hand refinements---such as extensive-form perfect equilibria and quasi-perfect equilibria---remedy this problem in sound ways. Despite their appeal, they have not received attention in practice since no known algorithm for computing them scales beyond toy instances. In this paper, we design an exact polynomial-time algorithm for finding trembling-hand equilibria in zero-sum extensive-form games. It is several orders of magnitude faster than the best prior ones, numerically stable, and quickly solves game instances with tens of thousands of nodes in the game tree. It enables, for the first time, the use of trembling-hand refinements in practice.
Author Information
Gabriele Farina (Carnegie Mellon University)
Nicola Gatti (Politecnico di Milano)
Tuomas Sandholm (Carnegie Mellon University)
More from the Same Authors
-
2021 Spotlight: Subgame solving without common knowledge »
Brian Zhang · Tuomas Sandholm -
2021 Spotlight: Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond »
Maria-Florina Balcan · Siddharth Prasad · Tuomas Sandholm · Ellen Vitercik -
2021 : The Evolutionary Dynamics of Soft-Max PolicyGradient in Multi-Agent Settings »
Martino Bernasconi · Federico Cacciamani · Simone Fioravanti · Nicola Gatti · Francesco Trovò -
2021 : Public Information Representation for Adversarial Team Games »
Luca Carminati · Federico Cacciamani · Marco Ciccone · Nicola Gatti -
2022 : Clairvoyant Regret Minimization: Equivalence with Nemirovski’s Conceptual Prox Method and Extension to General Convex Games »
Gabriele Farina · Christian Kroer · Chung-Wei Lee · Haipeng Luo -
2022 : Multi-Armed Bandit Problem with Temporally-Partitioned Rewards »
Giulia Romano · Andrea Agostini · Francesco Trovò · Nicola Gatti · Marcello Restelli -
2022 : Mastering the Game of No-Press Diplomacy via Human-Regularized Reinforcement Learning and Planning »
Anton Bakhtin · David Wu · Adam Lerer · Jonathan Gray · Athul Jacob · Gabriele Farina · Alexander Miller · Noam Brown -
2022 : A General Framework for Safe Decision Making: A Convex Duality Approach »
Martino Bernasconi · Federico Cacciamani · Nicola Gatti · Francesco Trovò -
2022 : A Unifying Framework for Online Safe Optimization »
Matteo Castiglioni · Andrea Celli · Alberto Marchesi · Giulia Romano · Nicola Gatti -
2022 : ESCHER: ESCHEWING IMPORTANCE SAMPLING IN GAMES BY COMPUTING A HISTORY VALUE FUNCTION TO ESTIMATE REGRET »
Stephen McAleer · Gabriele Farina · Marc Lanctot · Tuomas Sandholm -
2022 : Poster Session 2 »
Jinwuk Seok · Bo Liu · Ryotaro Mitsuboshi · David Martinez-Rubio · Weiqiang Zheng · Ilgee Hong · Chen Fan · Kazusato Oko · Bo Tang · Miao Cheng · Aaron Defazio · Tim G. J. Rudner · Gabriele Farina · Vishwak Srinivasan · Ruichen Jiang · Peng Wang · Jane Lee · Nathan Wycoff · Nikhil Ghosh · Yinbin Han · David Mueller · Liu Yang · Amrutha Varshini Ramesh · Siqi Zhang · Kaifeng Lyu · David Yunis · Kumar Kshitij Patel · Fangshuo Liao · Dmitrii Avdiukhin · Xiang Li · Sattar Vakili · Jiaxin Shi -
2022 Poster: Sequential Information Design: Learning to Persuade in the Dark »
Martino Bernasconi · Matteo Castiglioni · Alberto Marchesi · Nicola Gatti · Francesco Trovò -
2022 Poster: Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts »
Maria-Florina Balcan · Siddharth Prasad · Tuomas Sandholm · Ellen Vitercik -
2022 Poster: Uncoupled Learning Dynamics with $O(\log T)$ Swap Regret in Multiplayer Games »
Ioannis Anagnostides · Gabriele Farina · Christian Kroer · Chung-Wei Lee · Haipeng Luo · Tuomas Sandholm -
2022 Poster: Maximizing Revenue under Market Shrinkage and Market Uncertainty »
Maria-Florina Balcan · Siddharth Prasad · Tuomas Sandholm -
2022 Poster: Polynomial-Time Optimal Equilibria with a Mediator in Extensive-Form Games »
Brian Zhang · Tuomas Sandholm -
2022 Poster: A Unifying Framework for Online Optimization with Long-Term Constraints »
Matteo Castiglioni · Andrea Celli · Alberto Marchesi · Giulia Romano · Nicola Gatti -
2022 Poster: Optimistic Mirror Descent Either Converges to Nash or to Strong Coarse Correlated Equilibria in Bimatrix Games »
Ioannis Anagnostides · Gabriele Farina · Ioannis Panageas · Tuomas Sandholm -
2022 Poster: Subgame Solving in Adversarial Team Games »
Brian Zhang · Luca Carminati · Federico Cacciamani · Gabriele Farina · Pierriccardo Olivieri · Nicola Gatti · Tuomas Sandholm -
2022 Poster: Near-Optimal No-Regret Learning Dynamics for General Convex Games »
Gabriele Farina · Ioannis Anagnostides · Haipeng Luo · Chung-Wei Lee · Christian Kroer · Tuomas Sandholm -
2022 Expo Demonstration: Human Modeling and Strategic Reasoning in the Game of Diplomacy »
Noam Brown · Alexander Miller · Gabriele Farina -
2021 : Spotlight Talk: Public Information Representation for Adversarial Team Games »
Luca Carminati · Federico Cacciamani · Marco Ciccone · Nicola Gatti -
2021 Poster: Subgame solving without common knowledge »
Brian Zhang · Tuomas Sandholm -
2021 Poster: Equilibrium Refinement for the Age of Machines: The One-Sided Quasi-Perfect Equilibrium »
Gabriele Farina · Tuomas Sandholm -
2021 Poster: Exploiting Opponents Under Utility Constraints in Sequential Games »
Martino Bernasconi · Federico Cacciamani · Simone Fioravanti · Nicola Gatti · Alberto Marchesi · Francesco Trovò -
2021 Poster: Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond »
Maria-Florina Balcan · Siddharth Prasad · Tuomas Sandholm · Ellen Vitercik -
2020 Poster: Small Nash Equilibrium Certificates in Very Large Games »
Brian Zhang · Tuomas Sandholm -
2020 Poster: Polynomial-Time Computation of Optimal Correlated Equilibria in Two-Player Extensive-Form Games with Public Chance Moves and Beyond »
Gabriele Farina · Tuomas Sandholm -
2020 Poster: Online Bayesian Persuasion »
Matteo Castiglioni · Andrea Celli · Alberto Marchesi · Nicola Gatti -
2020 Poster: No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium »
Andrea Celli · Alberto Marchesi · Gabriele Farina · Nicola Gatti -
2020 Spotlight: Online Bayesian Persuasion »
Matteo Castiglioni · Andrea Celli · Alberto Marchesi · Nicola Gatti -
2020 Oral: No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium »
Andrea Celli · Alberto Marchesi · Gabriele Farina · Nicola Gatti -
2020 Poster: Improving Policy-Constrained Kidney Exchange via Pre-Screening »
Duncan McElfresh · Michael Curry · Tuomas Sandholm · John Dickerson -
2019 Poster: Correlation in Extensive-Form Games: Saddle-Point Formulation and Benchmarks »
Gabriele Farina · Chun Kai Ling · Fei Fang · Tuomas Sandholm -
2019 Poster: Learning to Correlate in Multi-Player General-Sum Sequential Games »
Andrea Celli · Alberto Marchesi · Tommaso Bianchi · Nicola Gatti -
2019 Poster: Efficient Regret Minimization Algorithm for Extensive-Form Correlated Equilibrium »
Gabriele Farina · Chun Kai Ling · Fei Fang · Tuomas Sandholm -
2019 Spotlight: Efficient Regret Minimization Algorithm for Extensive-Form Correlated Equilibrium »
Gabriele Farina · Chun Kai Ling · Fei Fang · Tuomas Sandholm -
2019 Poster: Optimistic Regret Minimization for Extensive-Form Games via Dilated Distance-Generating Functions »
Gabriele Farina · Christian Kroer · Tuomas Sandholm -
2018 : Regret Decomposition in Sequential Games with Convex Action Spaces and Losses »
Gabriele Farina -
2018 Poster: A Unified Framework for Extensive-Form Game Abstraction with Bounds »
Christian Kroer · Tuomas Sandholm -
2018 Poster: Depth-Limited Solving for Imperfect-Information Games »
Noam Brown · Tuomas Sandholm · Brandon Amos -
2018 Poster: Solving Large Sequential Games with the Excessive Gap Technique »
Christian Kroer · Gabriele Farina · Tuomas Sandholm -
2018 Spotlight: Solving Large Sequential Games with the Excessive Gap Technique »
Christian Kroer · Gabriele Farina · Tuomas Sandholm -
2018 Poster: Ex ante coordination and collusion in zero-sum multi-player extensive-form games »
Gabriele Farina · Andrea Celli · Nicola Gatti · Tuomas Sandholm -
2017 Demonstration: Libratus: Beating Top Humans in No-Limit Poker »
Noam Brown · Tuomas Sandholm -
2017 Poster: Safe and Nested Subgame Solving for Imperfect-Information Games »
Noam Brown · Tuomas Sandholm -
2017 Oral: Safe and Nested Subgame Solving for Imperfect-Information Games »
Noam Brown · Tuomas Sandholm -
2016 Poster: Sample Complexity of Automated Mechanism Design »
Maria-Florina Balcan · Tuomas Sandholm · Ellen Vitercik -
2015 Poster: Regret-Based Pruning in Extensive-Form Games »
Noam Brown · Tuomas Sandholm -
2015 Demonstration: Claudico: The World's Strongest No-Limit Texas Hold'em Poker AI »
Noam Brown · Tuomas Sandholm -
2014 Poster: Diverse Randomized Agents Vote to Win »
Albert Jiang · Leandro Soriano Marcolino · Ariel Procaccia · Tuomas Sandholm · Nisarg Shah · Milind Tambe