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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Asymptotically Truthful Equilibrium Selection in Large Co...
Ryan Rogers, Aaron Roth · 2013-11-12 · via cs.DS updates on arXiv.org

Studying games in the complete information model makes them analytically tractable. However, large $n$ player interactions are more realistically modeled as games of incomplete information, where players may know little to nothing about the types of other players. Unfortunately, games in incomplete information settings lose many of the nice properties of complete information games: the quality of equilibria can become worse, the equilibria lose their ex-post properties, and coordinating on an equilibrium becomes even more difficult. Because of these problems, we would like to study games of incomplete information, but still implement equilibria of the complete information game induced by the (unknown) realized player types. This problem was recently studied by Kearns et al. and solved in large games by means of introducing a weak mediator: their mediator took as input reported types of players, and output suggested actions which formed a correlated equilibrium of the underlying game. Players had the option to play independently of the mediator, or ignore its suggestions, but crucially, if they decided to opt-in to the mediator, they did not have the power to lie about their type. In this paper, we rectify this deficiency in the setting of large congestion games. We give, in a sense, the weakest possible mediator: it cannot enforce participation, verify types, or enforce its suggestions. Moreover, our mediator implements a Nash equilibrium of the complete information game. We show that it is an (asymptotic) ex-post equilibrium of the incomplete information game for all players to use the mediator honestly, and that when they do so, they end up playing an approximate Nash equilibrium of the induced complete information game. In particular, truthful use of the mediator is a Bayes-Nash equilibrium in any Bayesian game for any prior.