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Learning Probably Approximately Correct Maximin Strategies in Simulation-Based Games with Infinite Strategy Spaces
We tackle the problem of learning equilibria in simulation-based games. ...
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Quantal Response Equilibria in Binary Choice Games on Graphs
Static and dynamic equilibria in noisy binary choice games on graphs are...
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Augmented Probability Simulation Methods for Non-cooperative Games
We present a comprehensive robust decision support framework with novel ...
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Modeling and Analysis of Leaky Deception using Signaling Games with Evidence
Deception plays critical roles in economics and technology, especially i...
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Approximating Nash Equilibria for Black-Box Games: A Bayesian Optimization Approach
Game theory has emerged as a powerful framework for modeling a large ran...
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Approximating the Existential Theory of the Reals
The existential theory of the reals (ETR) consists of existentially quan...
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Finding and Certifying (Near-)Optimal Strategies in Black-Box Extensive-Form Games
Often – for example in war games, strategy video games, and financial si...
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Learning Equilibria of Simulation-Based Games
We tackle a fundamental problem in empirical game-theoretic analysis (EGTA), that of learning equilibria of simulation-based games. Such games cannot be described in analytical form; instead, a black-box simulator can be queried to obtain noisy samples of utilities. Our approach to EGTA is in the spirit of probably approximately correct learning. We design algorithms that learn so-called empirical games, which uniformly approximate the utilities of simulation-based games with finite-sample guarantees. These algorithms can be instantiated with various concentration inequalities. Building on earlier work, we first apply Hoeffding's bound, but as the size of the game grows, this bound eventually becomes statistically intractable; hence, we also use the Rademacher complexity. Our main results state: with high probability, all equilibria of the simulation-based game are approximate equilibria in the empirical game (perfect recall); and conversely, all approximate equilibria in the empirical game are approximate equilibria in the simulation-based game (approximately perfect precision). We evaluate our algorithms on several synthetic games, showing that they make frugal use of data, produce accurate estimates more often than the theory predicts, and are robust to different forms of noise.
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