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Learning Equilibria of Simulation-Based Games: Applications to Empirical Mechanism Design


In this thesis, we first contribute to the empirical-game theoretic analysis (EGTA) literature both from a theoretical and a computational perspective. Theoretically, we present a mathematical framework to precisely describe simulation-based games and analyze their properties. In a simulation-based game, one only gets to observe samples of utility functions but never a complete analytical description. We provide results that complement and strengthen previous results on guarantees of the approximate Nash equilibria learned from samples. Computationally, we find and thoroughly evaluate Probably Approximate Correct (PAC) learning algorithms, which we show make frugal use of data to provably solve simulation-based games, up to a user's given error tolerance. Next, we turn our attention to mechanism design. When mechanism design depends on EGTA, it is called empirical mechanism design (EMD). Equipped with our EGTA framework, we further present contributions to EMD, in particular to parametric EMD. In parametric EMD, there is an overall (parameterized) mechanism (e.g., a second price auction with reserve prices as parameters). The choice of parameters then determines a mechanism (e.g., the reserve price being $10 instead of $100). Our EMD contributions are again two-fold. From a theoretical point of view, we formulate the problem of finding the optimal parameters of a mechanism as a black-box optimization problem. For the special case where the parameter space is finite, we present an algorithm that, with high probability, provably finds an approximate global optimal. For more general cases, we present a Bayesian optimization algorithm and empirically show its effectiveness. EMD is only as effective as the set of heuristic strategies used to optimize a mechanism's parameters. To demonstrate our methodology's effectiveness, we developed rich bidding heuristics in one specific domain: electronic advertisement auctions. These auctions are an instance of combinatorial auctions, a vastly important auction format used in practice to allocate many goods of interest (e.g., electromagnetic spectra). Our work on designing heuristics for electronic advertisement led us to contribute heuristics for the computation of approximate competitive (or Walrasian) equilibrium, work of interest in its own right.
Thesis (Ph. D.)--Brown University, 2021


Areyan Viqueira, Enrique Alejandro, "Learning Equilibria of Simulation-Based Games: Applications to Empirical Mechanism Design" (2021). Computer Science Theses and Dissertations. Brown Digital Repository. Brown University Library.