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

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

Practical Strategic Reasoning with Applications in Market Games.

Strategic reasoning is part of our everyday lives: we negotiate prices, bid in auctions, write contracts, and play games. We choose actions in these scenarios based on our preferences, and our beliefs about preferences of the other participants. Game theory provides a rich mathematical framework through which we can reason about the influence of these preferences. Clever abstractions allow us to predict the outcome of complex agent interactions, however, as the scenarios we model increase in complexity, the abstractions we use to enable classical game-theoretic analysis lose fidelity. In empirical game-theoretic analysis, we construct game models using empirical sources of knowledge—such as high-fidelity simulation. However, utilizing empirical knowledge introduces a host of different computational and statistical problems. I investigate five main research problems that focus on efficient selection, estimation, and analysis of empirical game models. I introduce a flexible modeling approach, where we may construct multiple game-theoretic models from the same set of observations. I propose a principled methodology for comparing empirical game models and a family of algorithms that select a model from a set of candidates. I develop algorithms for normal-form games that efficiently identify formations—sets of strategies that are closed under a (correlated) best-response correspondence. This aids in problems, such as finding Nash equilibria, that are key to analysis but hard to solve. I investigate policies for sequentially determining profiles to simulate, when constrained by a budget for simulation. Efficient policies allow modelers to analyze complex scenarios by evaluating a subset of the profiles. The policies I introduce outperform the existing policies in experiments. I establish a principled methodology for evaluating strategies given an empirical game model. I employ this methodology in two case studies of market scenarios: first, a case study in supply chain management from the perspective of a strategy designer; then, a case study in Internet ad auctions from the perspective of a mechanism designer. As part of the latter analysis, I develop an ad-auctions scenario that captures several key strategic issues in this domain for the first time.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75848/1/prjordan_1.pd

A Study of Problems Modelled as Network Equilibrium Flows

This thesis presents an investigation into selfish routing games from three main perspectives. These three areas are tied together by a common thread that runs through the main text of this thesis, namely selfish routing games and network equilibrium flows. First, it investigates methods and models for nonatomic selfish routing and then develops algorithms for solving atomic selfish routing games. A number of algorithms are introduced for the atomic selfish routing problem, including dynamic programming for a parallel network and a metaheuristic tabu search. A piece-wise mixed-integer linear programming problem is also presented which allows standard solvers to solve the atomic selfish routing problem. The connection between the atomic selfish routing problem, mixed-integer linear programming and the multicommodity flow problem is explored when constrained by unsplittable flows or flows that are restricted to a number of paths. Additionally, some novel probabilistic online learning algorithms are presented and compared with the equilibrium solution given by the potential function of the nonatomic selfish routing game. Second, it considers multi-criteria extensions of selfish routing and the inefficiency of the equilibrium solutions when compared with social cost. Models are presented that allow exploration of the Pareto set of solutions for a weighted sum model (akin to the social cost) and the equilibrium solution. A means by which these solutions can be measured based on the Price of Anarchy for selfish routing games is also presented. Third, it considers the importance and criticality of components of the network (edges, vertices or a collection of both) within a selfish routing game and the impact of their removal. Existing network science measures and demand-based measures are analysed to assess the change in total travel time and issues highlighted. A new measure which solves these issues is presented and the need for such a measure is evaluated. Most of the new findings have been disseminated through conference talks and journal articles, while others represent the subject of papers currently in preparation

Protocolos de intercambio racional

An exchange protocol describes a sequence of steps by which several entities are capable of exchanging certain pieces of information in a particular context. Rational{exchange protocols serve that core purpose with several important advantages over the existing exchange paradigms, those referred to as fair{exchange solutions. Traditional fair{exchange protocols impose strong restrictions on the protocol exe- cution context. They ensure fairness to participants but at the expense of entities such as TTPs (trusted third parties) having to be involved in the exchange. By con- trast, rational schemes, although not ensuring fairness, assure that rational entities would have no reason to deviate from the steps described in the protocol and, have the enormous advantage of not needing the services of a TTP. Rational{exchange protocols therefore represent the only viable option in many modern ad{hoc and unstructured environments. The main goal of this thesis is to apply concepts from Game Theory to both the analysis and design of rational{exchange protocols. In our opinion, signi¯cant contributions have been made in both directions: ² In terms of the formal analysis of these schemes, our work has focused on the proposal of two extensions to an existing formalism. The viability and e®ec- tiveness of our proposals is corroborated by the application of both formalisms to the analysis and veri¯cation of several exchange schemes. ² With regard to the design of rational protocols, our approach is based on applying heuristic search to automate the process, and to generate exchange protocols which can be proven rational within an underlying game theoretical framework. Experimental work is carried out to illustrate the proposed methodology in a particular three-entity exchanging scenario as well as in several randomized environments. Di®erent heuristic techniques are implemented and their results compared, measuring success rates and the average number of protocols eval- uated until an optimal solution is obtained. Furthermore, as a result of this experimental work, a whole family of multi{party rational exchange protocols is presented. ____________________________________________________________________Durante siglos el comportamiento racional de la especie humana ha sido extensamente estudiado por filósofos, sociólogos, psicólogos, etc. Considerado siempre como un concepto abstracto, a mediados del siglo veinte el desarrollo de la Teoría de Juegos proporcionó, por primera vez, un marco matemático para la definición formal del comportamiento racional de las entidades participantes de un juego. A partir de entonces la Teoría de Juegos se ha convertido en el modelo matemático que sustenta importantes resultados en campos tan diversos como la Biología, la Economía, la Inteligencia Artificial o la Criptografía. Este trabajo se encuentra englobado dentro del campo de la Criptografía Racional. La Criptografía Racional nace de la aplicación de los resultados teóricos sobre juegos al campo de la Criptografía. Nielsen et al. en [Nielsen et al., 2007] establecen una relación de los avances más significativos llevados a cabo hasta el momento en esta área de reciente creación. En particular, especialmente relevantes para esta tesis serían los trabajos de Syverson [Syverson, 1998] y Buttyán et al. [Buttyán, 2001] centrados respectivamente en el diseño y análisis formal de protocolos seguros de intercambio racional

Spillovers and strategic interaction in immigration policy

Asylum policies are interdependent across countries: Policy choices in one country can affect refugee flows into neighbouring countries and may provoke policy changes there, in an a priori unknown direction. We formulate a dynamic model of refugees' location choices and of the strategic interaction among destinations that we fit to Syrian refugee migration to Europe. We find that south and southeastern European countries view recognition rates as strategic substitutes, whereas the same policies can be strategic complements in northern Europe. Our findings have implications for frameworks that use cross-country variation to estimate effects of policy changes on migration

Mechanism Design and Analysis Using Simulation-Based Game Models.

As agent technology matures, it becomes easier to envision electronic marketplaces teeming with autonomous agents. Since agents are explicitly programmed to (nearly) optimally compete in these marketplaces, and markets themselves are designed with specific objectives in mind, tools are necessary for systematic analyses of strategic interactions among autonomous agents. While traditional game-theoretic approaches to the analysis of multi-agent systems can provide much insight, they are often inadequate, as they rely heavily on analytic tractability of the problem at hand; however, even mildly realistic models of electronic marketplaces contain enough complexity to render a fully analytic approach hopeless. To address questions not amenable to traditional theoretical approaches, I develop methods that allow systematic computational analysis of game-theoretic models in which the players' payoff functions are represented using simulations (i.e., simulation-based games). I develop a globally convergent algorithm for Nash equilibrium approximation in infinite simulation-based games, which I instantiate in the context of infinite games of incomplete information. Additionally, I use statistical learning techniques to improve the quality of Nash equilibrium approximation based on data collected from a game simulator. I also derive probabilistic confidence bounds and present convergence results about solutions of finite games modeled using simulations. The former allow an analyst to make statistically-founded statements about results based on game-theoretic simulations, while the latter provide formal justification for approximating game-theoretic solutions using simulation experiments. To address the broader mechanism design problem, I introduce an iterative algorithm for search in the design space, which requires a game solver as a subroutine. As a result, I enable computational mechanism design using simulation-based models of games by availing the designer of a set of solution tools geared specifically towards games modeled using simulations. I apply the developed computational techniques to analyze strategic procurement and answer design questions in a supply-chain simulation, as well as to analyze dynamic bidding strategies in sponsored search auctions. Indeed, the techniques I develop have broad potential applicability beyond electronic marketplaces: they are geared towards any system that features competing strategic players who respond to incentives in a way that can be reasonably predicted via a game-theoretic analysis.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60786/1/yvorobey_1.pd