Empirical Game-Theoretic Methods for Strategy Design and Analysis in Complex Games.

Complex multi-agent systems often are not amenable to standard game-theoretic analysis. I study methods for strategic reasoning that scale to more complex interactions, drawing on computational and empirical techniques. Several recent studies have applied simulation to estimate game models, using a methodology known as empirical game-theoretic analysis. I report a successful application of this methodology to the Trading Agent Competition Supply Chain Management game. Game theory has previously played little—if any—role in analyzing this scenario, or others like it. In the rest of the thesis, I perform broader evaluations of empirical game analysis methods using a novel experimental framework. I introduce meta-games to model situations where players make strategy choices based on estimated game models. Each player chooses a meta-strategy, which is a general method for strategy selection that can be applied to a class of games. These meta-strategies can be used to select strategies based on empirical models, such as an estimated payoff matrix. I investigate candidate meta-strategies experimentally, testing them across different classes of games and observation models to identify general performance patterns. For example, I show that the strategy choices made using a naive equilibrium model quickly degrade in quality as observation noise is introduced. I analyze three families of meta-strategies that predict distributions of play, each interpolating between uninformed and naive equilibrium predictions using a single parameter. These strategy spaces improve on the naive method, capturing (to some degree) the effects of observation uncertainty. Of these candidates, I identify logit equilibrium as the champion, supported by considerable evidence that its predictions generalize across many contexts. I also evaluate exploration policies for directing game simulations on two tasks: equilibrium confirmation and strategy selection. Policies based on computing best responses are able to exploit a variety of structural properties to confirm equilibria with limited payoff evidence. A novel policy I propose—subgame best-response dynamics—improves previous methods for this task by confirming mixed equilibria in addition to pure equilibria. I apply meta-strategy analysis to show that these exploration policies can improve the strategy selections of logit equilibrium.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/61590/1/ckiekint_1.pd

A Game-theoretic Machine Learning Approach for Revenue Maximization in Sponsored Search

Sponsored search is an important monetization channel for search engines, in which an auction mechanism is used to select the ads shown to users and determine the prices charged from advertisers. There have been several pieces of work in the literature that investigate how to design an auction mechanism in order to optimize the revenue of the search engine. However, due to some unrealistic assumptions used, the practical values of these studies are not very clear. In this paper, we propose a novel \emph{game-theoretic machine learning} approach, which naturally combines machine learning and game theory, and learns the auction mechanism using a bilevel optimization framework. In particular, we first learn a Markov model from historical data to describe how advertisers change their bids in response to an auction mechanism, and then for any given auction mechanism, we use the learnt model to predict its corresponding future bid sequences. Next we learn the auction mechanism through empirical revenue maximization on the predicted bid sequences. We show that the empirical revenue will converge when the prediction period approaches infinity, and a Genetic Programming algorithm can effectively optimize this empirical revenue. Our experiments indicate that the proposed approach is able to produce a much more effective auction mechanism than several baselines.Comment: Twenty-third International Conference on Artificial Intelligence (IJCAI 2013

Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data

We consider learning, from strictly behavioral data, the structure and parameters of linear influence games (LIGs), a class of parametric graphical games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic inference (CSI): Making inferences from causal interventions on stable behavior in strategic settings. Applications include the identification of the most influential individuals in large (social) networks. Such tasks can also support policy-making analysis. Motivated by the computational work on LIGs, we cast the learning problem as maximum-likelihood estimation (MLE) of a generative model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation uncovers the fundamental interplay between goodness-of-fit and model complexity: good models capture equilibrium behavior within the data while controlling the true number of equilibria, including those unobserved. We provide a generalization bound establishing the sample complexity for MLE in our framework. We propose several algorithms including convex loss minimization (CLM) and sigmoidal approximations. We prove that the number of exact PSNE in LIGs is small, with high probability; thus, CLM is sound. We illustrate our approach on synthetic data and real-world U.S. congressional voting records. We briefly discuss our learning framework's generality and potential applicability to general graphical games.Comment: Journal of Machine Learning Research. (accepted, pending publication.) Last conference version: submitted March 30, 2012 to UAI 2012. First conference version: entitled, Learning Influence Games, initially submitted on June 1, 2010 to NIPS 201