Large-Scale Optimization for Games and Markets

ion methods for dimensionality-reduction Abstractions methods are used to complement iterative algorithms for computing equilibria. Abstractions are usually created algorithmically, by utilizing domain-dependent structure to set up a manageable optimization problem that produces a smaller game which retains as much of the original game structure as possible. No reasonable bounds on solution quality for solving an abstracted game rather than the full game existed before my work (strong previous results were known only for lossless abstraction). The only previous results of mildly comparable, though significantly lower, generality had a linear dependence on the number of information sets in the game, leading to very loose bounds. In contrast to this, I developed results with no dependence on the number of information sets, but rather a constant dependence on payoff error for perfect-recall abstraction [7] and linear dependence on game height (which is logarithmic in the number of information sets) for imperfect-recall abstraction [11]. In addition to this linearto-constant or linear-to-logarithmic improvement, my results were also the first to allow any error in the modeling of stochastic outcomes. I verified experimentally that the theoretical bounds were within an order of magnitude of the actual error introduced by abstracting. I also introduced the first complexity-theoretic results for understanding the computationally hard problems embedded in constructing a good abstraction. I later extended these results to