Albert Xin Jiang

Action-Graph Games

Representing and reasoning with games becomes difficult once they involve large numbers of actions and players, because the space requirement for utility functions can grow unmanageably. Action-Graph Games (AGGs) are a fully-expressive game representation that can compactly express utility functions with structure such as context-specific independence, anonymity, and additivity. We show that AGGs can be used to compactly represent all games that are compact when represented as graphical games, symmetric games, anonymous games, congestion games, and polymatrix games, as well as games that require exponential space under all of these existing representations. We give a polynomial-time algorithm for computing a players expected utility under an arbitrary mixed-strategy profile, and show how to use this algorithm to achieve exponential speedups of existing methods for computing sample Nash equilibria. We present results of experiments showing that using AGGs leads to a dramatic increase in the size of games accessible to computational analysis.2

TRUSTS: Scheduling Randomized Patrols for Fare Inspection in Transit Systems Using Game Theory

In proof-of-payment transit systems, passengers are legally required to purchase tickets before entering but are not physically forced to do so. Instead, patrol units move about the transit system, inspecting the tickets of passengers, who face fines if caught fare evading. The deterrence of fare evasion depends on the unpredictability and effectiveness of the patrols. In this paper, we present TRUSTS, an application for scheduling randomized patrols for fare inspection in transit systems. TRUSTS models the problem of computing patrol strategies as a leader-follower Stackelberg game where the objective is to deter fare evasion and hence maximize revenue. This problem differs from previously studied Stackelberg settings in that the leader strategies must satisfy massive temporal and spatial constraints; moreover, unlike in these counterterrorism-motivated Stackelberg applications, a large fraction of the ridership might realistically consider fare evasion, and so the number of followers is potentially huge. A third key novelty in our work is deliberate simplification of leader strategies to make patrols easier to be executed. We present an efficient algorithm for computing such patrol strategies and present experimental results using real-world ridership data from the Los Angeles Metro Rail system. The Los Angeles County Sheriff’s department is currently carrying out trials of TRUSTS.

Polynomial-time computation of exact correlated equilibrium in compact games

In a landmark paper, Papadimitriou and Roughgarden described a polynomial-time algorithm (“Ellipsoid Against Hope”) for computing sample correlated equilibria of concisely-represented games. Recently, Stein, Parrilo and Ozdaglar showed that this algorithm can fail to find an exact correlated equilibrium. We present a variant of the Ellipsoid Against Hope algorithm that guarantees the polynomial-time identification of exact correlated equilibrium. Our algorithm differs from the original primarily in its use of a separation oracle that produces cuts corresponding to pure-strategy profiles. Our new separation oracle can be understood as a derandomization of Papadimitriou and Roughgardens original separation oracle via the method of conditional probabilities. We also adapt our techniques to two related algorithms that are based on the Ellipsoid Against Hope approach, Hart and Mansours communication procedure for correlated equilibria and Huang and von Stengels algorithm for extensive-form correlated equilibria, in both cases yielding efficient exact solutions.

Game-theoretic security patrolling with dynamic execution uncertainty and a case study on a real transit system

Attacker-Defender Stackelberg security games (SSGs) have emerged as an important research area in multi-agent systems. However, existing SSGs models yield fixed, static, schedules which fail in dynamic domains where defenders face execution uncertainty, i.e., in domains where defenders may face unanticipated disruptions of their schedules. A concrete example is an application involving checking fares on trains, where a defenders schedule is frequently interrupted by fare evaders, making static schedules useless. To address this shortcoming, this paper provides four main contributions. First, we present a novel general Bayesian Stackelberg game model for security resource allocation in dynamic uncertain domains. In this new model, execution uncertainty is handled by using a Markov decision process (MDP) for generating defender policies. Second, we study the problem of computing a Stackelberg equilibrium for this game and exploit problem structure to reduce it to a polynomial-sized optimization problem. Shifting to evaluation, our third contribution shows, in simulation, that our MDP-based policies overcome the failures of previous SSG algorithms. In so doing, we can now build a complete system, that enables handling of schedule interruptions and, consequently, to conduct some of the first controlled experiments on SSGs in the field. Hence, as our final contribution, we present results from a real-world experiment on Metro trains in Los Angeles validating our MDP-based model, and most importantly, concretely measuring the benefits of SSGs for security resource allocation.

Monotonic Maximin: A Robust Stackelberg Solution against Boundedly Rational Followers

There has been recent interest in applying Stackelberg games to infrastructure security, in which a defender must protect targets from attack by an adaptive adversary. In real-world security settings the adversaries are humans and are thus boundedly rational. Most existing approaches for computing defender strategies against boundedly rational adversaries try to optimize against specific behavioral models of adversaries, and provide no quality guarantee when the estimated model is inaccurate. We propose a new solution concept, monotonic maximin, which provides guarantees against all adversary behavior models satisfying monotonicity, including all in the family of Regular Quantal Response functions. We propose a mixed-integer linear program formulation for computing monotonic maximin. We also consider top-monotonic maximin, a related solution concept that is more conservative, and propose a polynomial-time algorithm for top-monotonic maximin.

Bidding agents for online auctions with hidden bids

There is much active research into the design of automated bidding agents, particularly for environments that involve multiple decoupled auctions. These settings are complex partly because an agent’s strategy depends on information about other bidders’interests. When bidders’ valuation distributions are not known ex ante, machine learning techniques can be used to approximate them from historical data. It is a characteristic feature of auctions, however, that information about some bidders’valuations is systematically concealed. This occurs in the sense that some bidders may fail to bid at all because the asking price exceeds their valuations, and also in the sense that a high bidder may not be compelled to reveal her valuation. Ignoring these “hidden bids” can introduce bias into the estimation of valuation distributions. To overcome this problem, we propose an EM-based algorithm. We validate the algorithm experimentally using agents that react to their environments both decision-theoretically and game-theoretically, using both synthetic and real-world (eBay) datasets. We show that our approach estimates bidders’ valuation distributions and the distribution over the true number of bidders significantly more accurately than more straightforward density estimation techniques.

Defending Against Opportunistic Criminals: New Game-Theoretic Frameworks and Algorithms

This paper introduces a new game-theoretic framework and algorithms for addressing opportunistic crime. The Stackelberg Security Game (SSG), which models highly strategic and resourceful adversaries, has become an important computational framework within multiagent systems. Unfortunately, SSG is ill-suited as a framework for handling opportunistic crimes, which are committed by criminals who are less strategic in planning attacks and more flexible in executing them than SSG assumes. Yet, opportunistic crime is what is commonly seen in most urban settings.We therefore introduce the Opportunistic Security Game (OSG), a computational framework to recommend deployment strategies for defenders to control opportunistic crimes. Our first contribution in OSG is a novel model for opportunistic adversaries, who (i) opportunistically and repeatedly seek targets; (ii) react to real-time information at execution time rather than planning attacks in advance; and (iii) have limited observation of defender strategies. Our second contribution to OSG is a new exact algorithm EOSG to optimize defender strategies given our opportunistic adversaries. Our third contribution is the development of a fast heuristic algorithm to solve large-scale OSG problems, exploiting a compact representation.We use urban transportation systems as a critical motivating domain, and provide detailed experimental results based on a real-world system.

Protecting moving targets with multiple mobile resources

In recent years, Stackelberg Security Games have been successfully applied to solve resource allocation and scheduling problems in several security domains. However, previous work has mostly assumed that the targets are stationary relative to the defender and the attacker, leading to discrete game models with finite numbers of pure strategies. This paper in contrast focuses on protecting mobile targets that leads to a continuous set of strategies for the players. The problem is motivated by several real-world domains including protecting ferries with escort boats and protecting refugee supply lines. Our contributions include: (i) A new game model for multiple mobile defender resources and moving targets with a discretized strategy space for the defender and a continuous strategy space for the attacker. (ii) An efficient linear-programming-based solution that uses a compact representation for the defenders mixed strategy, while accurately modeling the attackers continuous strategy using a novel sub-interval analysis method. (iii) Discussion and analysis of multiple heuristic methods for equilibrium refinement to improve robustness of defenders mixed strategy. (iv) Discussion of approaches to sample actual defender schedules from the defenders mixed strategy. (iv) Detailed experimental analysis of our algorithms in the ferry protection domain.

Game theory for security: Key algorithmic principles, deployed systems, lessons learned

Security is a critical concern around the world. In many security domains, limited security resources prevent full security coverage at all times; instead, these limited resources must be scheduled, avoiding schedule predictability, while simultaneously taking into account different target priorities, the responses of the adversaries to the security posture and potential uncertainty over adversary types. Computational game theory can help design such unpredictable security schedules. Indeed, casting the problem as a Bayesian Stackelberg game, we have developed new algorithms that are now deployed over multiple years in multiple applications for security scheduling. These applications are leading to real-world use-inspired research in the emerging research area of “security games” specifically, the research challenges posed by these applications include scaling up security games to large-scale problems, handling significant adversarial uncertainty, dealing with bounded rationality of human adversaries, and other interdisciplinary challenges.

Towards a Science of Security Games

Security is a critical concern around the world. In many domains from counter-terrorism to sustainability, limited security resources prevent full security coverage at all times; instead, these limited resources must be scheduled, while simultaneously taking into account different target priorities, the responses of the adversaries to the security posture and potential uncertainty over adversary types.