arXiv subjects

Philip N. Brown

Publications and source records attributed to Philip N. Brown.

At least 19 recordsLinked to original sources

arXiv2026

Tractable Defense against Advanced Persistent Threats in Networked Settings

Recently, the theory of Boolean Dynamical Systems was proposed to study the decision theory surrounding the defense of computer networks against Advanced Persistent Threats (APTs). Boolean Dynamical Systems naturally capture four first principle primitives of APTs: the stealthy nature of attacks, limited and noisy information from automated systems like intrusion detection systems, lateral movement after the attacker penetrates into the network, and the defender's ability to secure a subset of computers at any time at the loss of resources such as system uptime. Currently, doing optimal/heuristic control in a computationally tractable manner is not possible because the emergent value function is computationally intractable (with respect to the network size). To resolve this, we propose a mean-field analysis inspired heuristic value function. We prove that our proposed heuristic is based on an exact computation of the value function under the assumption that the underlying state estimate distribution maximizes entropy. We numerically evaluate the quality of our heuristic as parameterized by the degree to which the entropy assumptions are violated.

cs.CR↗

arXiv2026

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT↗

arXiv2026

Deriving the Pure Price of Anarchy for Networked Resource Allocation Games

This work considers multi-agent coordination with arbitrary information networks among the agents using a game-theoretic approach. A system designer aims to assign local utility functions to the agents to guide their actions toward a desired system objective. The performance of the assigned local utilities is measured by the well known pure price of anarchy (pPoA) metric that equals the ratio of the system objective at the worst pure Nash equilibrium of the corresponding game to the optimal system objective. Our aim is to derive the utility functions which optimize the pPoA-based performance guarantees for any given information network and system objective. We develop a linear program that derives the optimal pPoA for any arbitrary information network and arbitrary system objective. Our work is the first to solve optimal utility design for arbitrary networks; our techniques generalize previous approaches which considered only the full-information setting. For supermodular objective functions, we prove that counterintuitively, a fully communication-denied utility design is optimal irrespective of the original information network. For submodular system objectives, an exhaustive numerical analysis suggests that the optimal utility design is robust to communication failures even for this case. When the system objective is weighted maximum coverage, the marginal contribution utility design provably optimizes the pPoA for a wide variety of information networks of interest.

cs.GT↗

arXiv2026

On the Fragility of Worst-Case Nash Equilibria in Atomic Congestion Games

Aggregate performance in smart mobility systems depends heavily on the emergent behavior of selfish, resource-sharing agents that participate within the systems. As a result, recent work has focused on how a system designer can leverage incentives to influence behavior so that system cost (e.g., traffic congestion) is minimized. These results show that worst-case equilibria can be quite inefficient compared to system-optimal allocations. However, it is unclear to what extent agents are ``satisfied'' with their decisions in these worst-case scenarios. We demonstrate that in any incentivized atomic congestion game, agents' aggregate satisfaction at equilibrium (relative to their actions in an optimal allocation) is correlated with the efficiency of the corresponding system cost, in the sense that if agents are very satisfied with their equilibrium choices, the equilibrium must be relatively efficient. Further, we show that worst-case Nash equilibria are fragile, as every agent is indifferent between their action in a worst-case equilibrium and their action in a system-optimal allocation. In summary, at equilibrium, either agents are highly satisfied with their decisions or their decisions are highly inefficient, but both cannot be true simultaneously. This work adds to recent results for other classes of games which indicate that worst-case equilibrium efficiency guarantees only occur when agents are indifferent about their decisions.

cs.GT↗

arXiv2026

ABRA: An algorithm which cannot converge to low-quality Nash equilibria

We consider a game theoretic approach to solve multi-agent coordination problems with submodular objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal. A recent work further shows that the equilibria which achieve this worst-case bound are not stable. Leveraging this, we design an Approximate Best Response Algorithm (ABRA) governed by a noise parameter and a rationality parameter. The noise allows ABRA to escape the bad equilibria and the rationality parameter balances any degradation in the objective function caused by the noise. We show for any two-player game that if ABRA converges to a Nash equilibrium, its system objective value is strictly more than 50% of optimal plus a term controlled by the noise parameter. Otherwise, ABRA converges to some recurrent class: if a recurrent class contains any action profile yielding system objective less than 50% of the optimal, the class must also contain either the optimal action profile or an action profile yielding system objective strictly more than 50\% of the optimal by the same amount in addition to a factor controlled by noise parameter. The time that ABRA spends in such action profiles can be controlled using the rationality parameter. Using numerical simulations, we show that the minimum expected objective function is typically well above half of the optimal.

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arXiv2026

Adverse Effects of V2V Adoption on Road Safety

Vehicle-to-vehicle (V2V) communication is expected to improve road safety and reduce congestion. However, prior work shows that V2V information sharing under partial adoption may increase congestion and decrease safety. We study whether increasing V2V adoption itself affects road safety. We propose a corrected version of an existing model and analyze its behavior under varying adoption levels. We show that, in some cases, increased V2V adoption can increase accident probability. Moreover, under an optimal signaling policy, the system can ensure that accident probability is non-increasing in the adoption level.

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arXiv2026

Carroll Mechanisms: Opportunities, Challenges, and Agenda

The purpose of Carroll Mechanisms is to facilitate autonomous group sensemaking and reasoned decisionmaking by incentivizing participants to be transparent about their reasoning process, and to empower participants who are known to be capable of changing their minds. We envision Carroll Mechanisms to be built on top of a networked combinatorial LMSR foundation and thus to inherit the desriable properties of market scoring rules and automated market-makers. While we have made great strides during Fall 2025 in building out this foundation, several significant questions remain and several major new questions have arisen as a result of this work. The purpose of this document is to document the theoretical foundation, frame these questions clearly, and propose a research plan to address the questions.

cs.GT↗

arXiv2025

Efficient State Estimation of a Networked FlipIt Model

The Boolean Kalman Filter and associated Boolean Dynamical System Theory have been proposed to study the spread of infection on computer networks. Such models feature a network where attacks propagate through, an intrusion detection system that provides noisy signals of the true state of the network, and the capability of the defender to clean a subset of computers at any time. The Boolean Kalman Filter has been used to solve the optimal estimation problem, by estimating the hidden true state given the attack-defense dynamics and noisy observations. However, this algorithm is intractable because it runs in exponential time and space with respect to the network size. We address this feasibility problem by proposing a mean-field estimation approach, which is inspired by the epidemic modeling literature. Although our approach is heuristic, we prove that our estimator exactly matches the optimal estimator in certain non-trivial cases. We conclude by using simulations to show both the run-time improvement and estimation accuracy of our approach.

cs.CR↗

arXiv2025

Game-Theoretic Cybersecurity: the Good, the Bad and the Ugly

Given the scale of consequences attributable to cyber attacks, the field of cybersecurity has long outgrown ad-hoc decision-making. A popular choice to provide disciplined decision-making in cybersecurity is Game Theory, which seeks to mathematically understand strategic interaction. In practice though, game-theoretic approaches are scarcely utilized (to our knowledge), highlighting the need to understand the deficit between the existing state-of-the-art and the needs of cybersecurity practitioners. Therefore, we develop a framework to characterize the function and assumptions of existing works as applied to cybersecurity and leverage it to characterize 80 unique technical papers. Then, we leverage this information to analyze the capabilities of the proposed models in comparison to the application-specific needs they are meant to serve, as well as the practicality of implementing the proposed solution. Our main finding is that Game Theory largely fails to incorporate notions of uncertainty critical to the application being considered. To remedy this, we provide guidance in terms of how to incorporate uncertainty in a model, what forms of uncertainty are critical to consider in each application area, and how to model the information that is available in each application area.

cs.GT↗

arXiv2025

Optimal Utility Design with Arbitrary Information Networks

We consider multi-agent systems with general information networks where an agent may only observe a subset of other agents. A system designer assigns local utility functions to the agents guiding their actions towards an outcome which determines the value of a given system objective. The aim is to design these local utility functions such that the Price of Anarchy (PoA), which equals the ratio of system objective at worst possible outcome to that at the optimal, is maximized. Towards this, we first develop a linear program (LP) that characterizes the PoA for any utility design and any information network. This leads to another LP that optimizes the PoA and derives the optimal utility design. Our work substantially generalizes existing approaches to the utility design problem. We also numerically show the robustness of proposed framework against unanticipated communication failures.

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arXiv2024

Conditions for Altruistic Perversity in Two-Strategy Population Games

Self-interested behavior from individuals can collectively lead to poor societal outcomes. These outcomes can seemingly be improved through the actions of altruistic agents, which benefit other agents in the system. However, it is known in specific contexts that altruistic agents can actually induce worse outcomes compared to a fully selfish population -- a phenomenon we term altruistic perversity. This paper provides a holistic investigation into the necessary conditions that give rise to altruistic perversity. In particular, we study the class of two-strategy population games where one sub-population is altruistic and the other is selfish. We find that a population game can admit altruistic perversity only if the associated social welfare function is convex and the altruistic population is sufficiently large. Our results are a first step in establishing a connection between properties of nominal agent interactions and the potential impacts from altruistic behaviors.

cs.GT↗

arXiv2024

Altruism Improves Congestion in Series-Parallel Nonatomic Congestion Games

Self-interested routing polices from individual users in a system can collectively lead to poor aggregate congestion in routing networks. The introduction of altruistic agents, whose goal is to benefit other agents in the system, can seemingly improve aggregate congestion. However, it is known in that in some network routing problems, altruistic agents can actually worsen congestion compared to that which would arise in the presence of a homogeneously selfish population. This paper provides a thorough investigation into the necessary conditions for altruists to be guaranteed to improve total congestion. In particular, we study the class of series-parallel non-atomic congestion games, where one sub-population is altruistic and the other is selfish. We find that a game is guaranteed to have improved congestion in the presence of altruistic agents (even if only a small part of the total population) compared to the homogeneously selfish version of the game, provided the network is symmetric, where all agents are given access to all paths in the network, and the series-parallel network for the game does not have sub-networks which emulate Braess's paradox -- a phenomenon we refer to as a Braess-resistant network. Our results appear to be the most complete characterization of when behavior that is designed to improve total congestion (which we refer to as altruism) is actually guaranteed to do so.

cs.GT↗

arXiv2024

A Unified Toll Lane Framework for Autonomous and High-Occupancy Vehicles in Interactive Mixed Autonomy

In this study, we introduce a toll lane framework that optimizes the mixed flow of autonomous and high-occupancy vehicles on freeways, where human-driven and autonomous vehicles of varying commuter occupancy share a segment. Autonomous vehicles, with their ability to maintain shorter headways, boost traffic throughput. Our framework designates a toll lane for autonomous vehicles with high occupancy to use free of charge, while others pay a toll. We explore the lane choice equilibria when all vehicles minimize travel costs, and characterize the equilibria by ranking vehicles by their mobility enhancement potential, a concept we term the mobility degree. Through numerical examples, we demonstrate the framework's utility in addressing design challenges such as setting optimal tolls, determining occupancy thresholds, and designing lane policies, showing how it facilitates the integration of high-occupancy and autonomous vehicles. We also propose an algorithm for assigning rational tolls to decrease total commuter delay and examine the effects of toll non-compliance. Our findings suggest that self-interest-driven behavior mitigates moderate non-compliance impacts, highlighting the framework's resilience. This work presents a pioneering comprehensive analysis of a toll lane framework that emphasizes the coexistence of autonomous and high-occupancy vehicles, offering insights for traffic management improvements and the integration of autonomous vehicles into existing transportation infrastructures.

eess.SY↗

arXiv2023

Strategically revealing capabilities in General Lotto games

Can revealing one's competitive capabilities to an opponent offer strategic benefits? In this paper, we address this question in the context of General Lotto games, a class of two-player competitive resource allocation models. We consider an asymmetric information setting where the opponent is uncertain about the resource budget of the other player, and holds a prior belief on its value. We assume the other player, called the signaler, is able to send a noisy signal about its budget to the opponent. With its updated belief, the opponent then must decide to invest in costly resources that it will deploy against the signaler's resource budget in a General Lotto game. We derive the subgame perfect equilibrium to this extensive-form game. In particular, we identify necessary and sufficient conditions for which a signaling policy improves the signaler's resulting performance in comparison to the scenario where it does not send any signal. Moreover, we provide the optimal signaling policy when these conditions are met. Notably we find that for some scenarios, the signaler can effectively double its performance.

cs.GT↗

arXiv2023

Avoiding Unintended Consequences: How Incentives Aid Information Provisioning in Bayesian Congestion Games

When users lack specific knowledge of various system parameters, their uncertainty may lead them to make undesirable deviations in their decision making. To alleviate this, an informed system operator may elect to signal information to uninformed users with the hope of persuading them to take more preferable actions. In this work, we study public and truthful signalling mechanisms in the context of Bayesian congestion games on parallel networks. We provide bounds on the possible benefit a signalling policy can provide with and without the concurrent use of monetary incentives. We find that though revealing information can reduce system cost in some settings, it can also be detrimental and cause worse performance than not signalling at all. However, by utilizing both signalling and incentive mechanisms, the system operator can guarantee that revealing information does not worsen performance while offering similar opportunities for improvement. These findings emerge from the closed form bounds we derive on the benefit a signalling policy can provide. We provide a numerical example which illustrates the phenomenon that revealing more information can degrade performance when incentives are not used and improves performance when incentives are used.

cs.GT↗

arXiv2022

Valid Utility Games with Information Sharing Constraints

The use of game theoretic methods for control in multiagent systems has been an important topic in recent research. Valid utility games in particular have been used to model real-world problems; such games have the convenient property that the value of any decision set which is a Nash equilibrium of the game is guaranteed to be within 1/2 of the value of the optimal decision set. However, an implicit assumption in this guarantee is that each agent is aware of the decisions of all other agents. In this work, we first describe how this guarantee degrades as agents are only aware of a subset of the decisions of other agents. We then show that this loss can be mitigated by restriction to a relevant subclass of games.

cs.GT↗

arXiv2022

A Coupling Approach to Analyzing Games with Dynamic Environments

The theory of learning in games has extensively studied situations where agents respond dynamically to each other by optimizing a fixed utility function. However, in real situations, the strategic environment varies as a result of past agent choices. Unfortunately, the analysis techniques that enabled a rich characterization of the emergent behavior in static environment games fail to cope with dynamic environment games. To address this, we develop a general framework using probabilistic couplings to extend the analysis of static environment games to dynamic ones. Using this approach, we obtain sufficient conditions under which traditional characterizations of Nash equilibria with best response dynamics and stochastic stability with log-linear learning can be extended to dynamic environment games. As a case study, we pose a model of cyber threat intelligence sharing between firms and a simple dynamic game-theoretic model of social precautions in an epidemic, both of which feature dynamic environments. For both examples, we obtain conditions under which the emergent behavior is characterized in the dynamic game by performing the traditional analysis on a reference static environment game.

cs.GT↗

arXiv2022

On Partial Adoption of Vehicle-to-Vehicle Communication: When Should Cars Warn Each Other of Hazards?

The emerging technology of Vehicle-to-Vehicle (V2V) communication over vehicular ad hoc networks promises to improve road safety by allowing vehicles to autonomously warn each other of road hazards. However, research on other transportation information systems has shown that informing only a subset of drivers of road conditions may have a perverse effect of increasing congestion. In the context of a simple (yet novel) model of V2V hazard information sharing, we ask whether partial adoption of this technology can similarly lead to undesirable outcomes. In our model, drivers individually choose how recklessly to behave as a function of information received from other V2V-enabled cars, and the resulting aggregate behavior influences the likelihood of accidents (and thus the information propagated by the vehicular network). We fully characterize the game-theoretic equilibria of this model. Our model indicates that for a wide range of our parameter space, V2V information sharing surprisingly increases the equilibrium frequency of accidents relative to no V2V information sharing, and that it may increase equilibrium social cost as well.

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