Automated Abstractions for Patrolling Security Games

Recently, there has been a significant interest in studying security games to provide tools for addressing resource allocation problems in security applications. Patrolling security games (PSGs) constitute a special class of security games wherein the resources are mobile. One of the most relevant open problems in security games is the design of scalable algorithms to tackle realistic scenarios. While the literature mainly focuses on heuristics and decomposition techniques (e.g., double oracle), in this paper we provide, to the best of our knowledge, the first study on the use of abstractions in security games (specifically for PSGs) to design scalable algorithms. We define some classes of abstractions and we provide parametric algorithms to automatically generate abstractions. We show that abstractions allow one to relax the constraint of patrolling strategies' Markovianity (customary in PSGs) and to solve large game instances. We additionally pose the problem to search for the optimal abstraction and we develop an anytime algorithm to find it

Endogenous Cartel Formation with Heterogeneous Firms and Differentiated Products

Real-world collusive agreements do not necessarily include all firms that are active in the cartelized industry. Often, cartels are formed by asymmetric firms offering products that are not completely homogenous. This article endogenizes the process of cartel formation in a simulation model where firms are asymmetric in marginal costs and offer differentiated products. After a cartel is formed, it may be destabilized if the evolution of costs produces a sufficiently asymmetric cost-structure. In this case, the cartelists use price wars to stabilize the collusive agreement. Cartels arise as the outcome of a dynamic formation game in mixed strategies. This game is complex because of firms' asymmetry and the multitude of possible cartel-compositions. I show that the Nash-equilibrium of this game can be obtained efficiently by a Differential Evolution stochastic optimization algorithm. It turns out that large firms gain more from colluding than small firms. Nevertheless, large firms choose a lower probability of joining the cartel

Understanding Financial Market Behavior through Empirical Game-Theoretic Analysis

Financial market activity is increasingly controlled by algorithms, interacting through electronic markets. Unprecedented information response times, autonomous operation, use of machine learning and other adaptive techniques, and ability to proliferate novel strategies at scale are all reasons to question whether algorithmic trading may produce dynamic behavior qualitatively different from what arises in trading under direct human control. Given the high level of competition between trading firms and the significant financial incentives to trading, it is desirable to understand the effect incentives have on the behavior of agents in financial markets. One natural way to analyze this effect is through the economic concept of a Nash equilibrium, a behavior profile of every agent such that no individual stands to gain by doing something different. Some of the incentives traders face arise from the complexities of modern market structure. Recent studies have turned to agent-based modeling as a way to capture behavioral response to this structure. Agent-based modeling is a simulation paradigm that allows studying the interaction of agents in a simulated environment, and it has been used to model various aspects of financial market structure. This thesis builds on recent agent-based models of financial markets by imposing agent rationality and studying the models in equilibrium. I use empirical game-theoretic analysis, a methodology for computing approximately rational behavior in agent-based models, to investigate three important aspects of market structure. First, I evaluate the impact of strategic bid shading on agent welfare. Bid shading is when agents demand better prices, lower if they are buying or higher if they are selling, and is typically associated with lower social welfare. My results indicate that in many market environments, strategic bid shading actually improves social welfare, even with some of the complexities of financial markets. Next, I investigate the optimal clearing interval for a proposed market mechanism, the frequent call market. There is significant evidence to support the idea that traders will benefit from trading in a frequent call market over standard continuous double auction markets. My results confirm this statement for a wide variety of market settings, but I also find a few circumstances, particularly when large informational advantages exist, or when markets are thin, that call markets consistently hurt welfare, independent of frequency. I conclude with an investigation on the effect of trend following on market stability. Here I find that the presence of trend followers alters a market’s response to shock. In the absence of trend followers, shocks are small but have a long recovery. When trend followers are present, they alter background trader behavior resulting in more severe shocks that recover much more quickly. I also develop a novel method to efficiently evaluate the effect of shock anticipation on equilibrium. While anticipation of shocks does make markets more stable, trend followers continue to be profitable.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144031/1/ebrink_1.pd

Economics of Conflict and Terrorism

This book contributes to the literature on conflict and terrorism through a selection of articles that deal with theoretical, methodological and empirical issues related to the topic. The papers study important problems, are original in their approach and innovative in the techniques used. This will be useful for researchers in the fields of game theory, economics and political sciences

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

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