arXiv subjects

Jason R. Marden

Publications and source records attributed to Jason R. Marden.

At least 19 recordsLinked to original sources

arXiv2026

Deceptive Stochastic Patrolling via Markov Chain Lifting

In this paper we propose lifted Markov Chains (MCs) as a new paradigm for deriving patrol strategies for mobile agents on an environment represented as a graph. Lifted MCs operate on a state space that can be larger than the set of nodes of the graph, and a projection operation maps the MC state to the corresponding node of the graph. We prove bounds on the performance improvement of lifted MCs over non-lifted MCs, where the performance is measured by the Kemeny constant, and show a corresponding monotonicity for the Stackelberg game capture probability and return-time entropy. These bounds yield a result of independent interest that relates the Kemeny constant and the MC conductance for general MCs. We also provide a tractable method for optimizing lifted MCs on general graphs with edge weights encoding travel times. Simulation results on randomly generated and real-world graphs verify that lifted MCs achieve substantial improvements, particularly on sparse graphs.

eess.SY↗

arXiv2026

Playing with Peaks: A Game-Theoretic Comparison of Electricity Pricing Mechanisms

As electricity consumption grows, reducing peak demand--the maximum load on the grid--has become critical for preventing infrastructure strain and blackouts. Pricing mechanisms that incentivize consumers with flexible loads to shift consumption away from high-demand periods have emerged as effective tools, yet different mechanisms are used in practice with unclear relative performance. This work compares two widely implemented approaches: anytime peak pricing (AP), where consumers pay for their individual maximum consumption, and coincident peak pricing (CP), where consumers pay for their consumption during the system-wide peak period. To compare these mechanisms, we model the electricity market as a strategic game and characterize the peak demand in equilibrium under both AP and CP. Our main result demonstrates that with perfect information, equilibrium peak demand under CP never exceeds that under AP; on the other hand, with imperfect information, the coordination introduced by CP can backfire and induce larger equilibrium peaks than AP. These findings demonstrate that potential gains from coupling users' costs (as done in CP) must be weighed against these miscoordination risks. We conclude with preliminary results indicating that progressive demand cost structures--rather than per-unit charges--may mitigate these risks while preserving coordination benefits, achieving desirable performance in both deterministic and stochastic settings.

cs.GT↗

arXiv2026

On the Fragility of Efficiency: Uncoupled Learning with a Deviant

An important question in learning in games is whether players can learn to achieve efficient outcomes, those that maximize the sum of their utilities, without communication or coordination. Completely uncoupled learning algorithms, which use only each player's own past actions and utilities, can guarantee this in broad classes of games, but they typically require every player to follow the same algorithm. In this work, we ask whether one can design welfare-maximizing learning algorithms that are robust to a deviant player. To study this question, we take a well-studied welfare-maximizing learning algorithm as a testbed and consider what happens when every player except one follows it. First, we consider a deviant player who either (i) always plays the same action or (ii) selects their action uniformly at random. We show that such a player can significantly alter the long-run behavior of this algorithm, leading to states that are far from welfare-maximizing, and that no completely uncoupled learning algorithm is robust to such a player in every game. Next, we consider a strategic deviant player who acts in their own interest and show that this player can adopt a different learning algorithm to shift the long-run outcome in their favor. Moreover, we show that under any completely uncoupled welfare-maximizing learning algorithm, there is a game in which some player benefits from switching to a different completely uncoupled learning algorithm. These results show that completely uncoupled welfare-maximizing learning is fragile, even to a single deviant player, suggesting that robustness may require communication or coordination.

cs.GT↗

arXiv2026

Holding the Cold: Retention-Aware Inventory Control for Industrial Refrigeration

Industrial refrigeration consumes substantial electricity, and compressors are the dominant energy consumers in these systems, making their operation central to improving energy efficiency. Compressors are most efficient when operated at full capacity, but the cooling they provide at full capacity can exceed the facility's immediate needs. This motivates pre-cooling, where compressors operate at full capacity and the excess cooling is stored as thermal inventory for future heat loads. However, stored cooling is inherently lossy: colder spaces attract additional heat from their surroundings, creating a tradeoff between maximizing compressor efficiency and avoiding cooling that dissipates before it can be used. We study this tradeoff through a retention factor, defined as the fraction of thermal inventory that survives after one minute, with the goals of understanding how retention affects the value of pre-cooling and designing effective control policies that account for this lossiness. We formulate compressor control as a stochastic inventory problem, solve for an optimal policy via dynamic programming alongside two simpler alternatives, and evaluate the performance of these policies using models fit from real industrial refrigeration facility data. Our results show that (i) pre-cooling can provide substantial energy savings when thermal inventory is sufficiently persistent, but that failing to account for retention can make aggressive pre-cooling increasingly costly as losses grow, and (ii) structurally simple policies that account for lossiness can still achieve near-optimal performance in lossy systems.

eess.SY↗

arXiv2026

Forming Alliances in the Fog of War: A General Lotto Perspective

Agents competing against a common opponent can often gain an edge by forming alliances, but deciding whether to do so is difficult when they lack precise knowledge about their opponent or ally. We study how uncertainty affects opportunities for alliance formation in the coalitional General Lotto game, in which two players compete aganist a shared adversary by allocating their resource budgets over separate sets of valued contests. When all agents know one another's budgets, it is known that a budget transfer from one player to the other can benefit both players. We ask whether such alliances survive when the players know the relevant budgets only up to a multiplicative factor. Under two models, one in which the players are uncertain about the adversary's budget and one in which they are uncertain about each other's budgets, we characterize exactly which games admit a transfer that benefits both players in every game consistent with what they conjecture to be possible. In both models, we show that such robust transfers exist in a set of games of positive measure for every level of uncertainty. These results suggest that alliances can remain worthwhile even when allies are largely in the dark.

cs.GT↗

arXiv2026

Move Over, Prisoner's Dilemma: Colonel Blotto has arrived

The Prisoner's Dilemma, zero-sum games, LQR team problems, and differential games have shaped game theory in controls for decades, but the field's most pressing adversarial challenges demand a richer framework, and its name is Colonel Blotto. Strategic adversarial constraints represent a fundamental consideration in control systems, from cybersecurity defense to infrastructure protection. Colonel Blotto games, despite their direct relevance to such applications, remain underutilized in the controls community relative to other game-theoretic approaches. This article aims to close that gap for the controls community. Indeed, theoretical advances within the last two decades have spurred a resurgence of interest and enabled their applications across several domains. In this article, we introduce the Colonel Blotto framework, survey key analytical and computational results, and demonstrate how problems spanning cybersecurity, network defense, and multi-agent systems fit naturally within this structure. Three research directions are examined in depth: interdependent contest objectives that capture networked vulnerabilities, alternate winning rules that model partial rewards and structural asymmetries, and multi-agent competitive environments involving coalition formation and strategic concessions. Taken together, these directions reveal a framework that is both practically deployable and rich enough to capture the strategic complexity inherent in adversarial resource allocation.

cs.GT↗

arXiv2026

Learning Empirical Evidence Equilibria under Weak Environmental Coupling

Strategic multi-agent systems are fundamentally characterized by decentralization, uncertainty, and ambiguity. Agents operating under limited observations will often need to make decisions based on simplified internal models of the environment, reflecting bounded rationality in both computational capacity and environmental knowledge. The Empirical Evidence Equilibrium (EEE) framework explicitly accounts for these limitations by modeling each agent as forming a potentially misspecified belief derived from signals obtained through partial observations of the environment. The resulting equilibrium concept captures the system's steady state under bounded rationality and decentralization. In this work, we study games in which the environment dynamics are driven jointly by exogenous factors and agents' actions. We analyze agent behavior under Q-value iteration where each agent independently forms a belief model, computes Q-values, and derives a greedy strategy, yet the collective actions of all agents jointly shape the environment each agent faces at the next stage. We prove that despite this decentralization, an EEE emerges from the joint dynamics when the coupling between agents' actions and the environment is sufficiently weak. We further extend this result to softmax policies, establishing a contraction result under a sufficient coupling condition.

cs.GT↗

arXiv2026

Incentive Design in Competitive Resource Allocation: Exploiting Valuation Asymmetry in Tullock Contests

In competitive resource allocation, a central coordinator may seek to gain an advantage not by directly controlling subordinate agents, but by strategically manipulating the information they receive. We study this problem within the framework of multi-player Tullock contests, where the coordinator influences subordinate players by designing their reported valuations of the contested prize, a mechanism that preserves the Tullock structure of the subordinates' objectives and thereby enables tractable equilibrium analysis. We first characterize the Nash equilibrium of the general multi-player Tullock contest, establishing how valuations and per-unit costs jointly determine equilibrium bids and payoffs. We then derive the optimal reported valuations for a coordinator managing two subordinates against a single opponent, and show that the structure of the optimal solution extends to contests with an arbitrary number of subordinates, reducing the coordinator's optimization to a two-variable problem regardless of system size.

cs.GT↗

arXiv2026

Beyond Arbitrary Allocations: Security Values in Constrained General Lotto Games

Resource allocation problems across multiple contests are ubiquitous in adversarial settings, from military operations to market competition. While Colonel Blotto and General Lotto games have provided valuable theoretical foundations for such problems, their equilibrium characterizations typically permit resources to be arbitrarily allocated across all contests -- a flexibility that rarely aligns with practical constraints. This paper introduces a novel constrained variant of the General Lotto game where one player is restricted to allocating resources to only a single contest. In this model we provide lower and upper bounds on the security values for this constrained player, quantifying how the inability to distribute resources across multiple contests fundamentally changes optimal strategic behavior and performance guarantees. These findings contribute to a broader understanding of how operational constraints shape strategic outcomes in competitive resource allocation, with implications for decision-makers facing similar constraints in practice.

cs.GT↗

arXiv2026

Dynamic Adversarial Resource Allocation: the dDAB Game

This work introduces the dynamic Defender-Attacker Blotto (dDAB) game, extending the classical static Blotto game to a dynamic resource allocation setting over graphs. In the dDAB game, a defender is required to maintain numerical superiority against attacker resources across a set of key nodes in a connected graph. The engagement unfolds as a discrete-time game, where each player reallocates its resources in turn, with resources allowed to move at most one hop per time step. The primary goal is to determine the necessary and sufficient amount of defender resources required to guarantee sustained defense, along with the corresponding strategies. To address the central challenge arising from graph-constrained resource reallocation, we conduct a reachability analysis, starting with simplified settings where attacker resources act as a single cohesive group. We then extend the framework to allow attacker resources to split and merge arbitrarily, and construct defender strategies using superposition principles. A set-based dynamic programming algorithm is developed to compute the optimal strategies, as well as the minimum amount of defender resources to ensure successful defense. The effectiveness of our approach is demonstrated through numerical simulations and hardware experiments on the Georgia Tech Robotarium platform.

cs.MA↗

arXiv2026

Alliance Mechanisms in General Lotto Games

How do different alliance mechanisms compare? In this work, we analyze various methods of forming an alliance in the Coalitional General Lotto game, a simple model of competitive resource allocation. In the game, Players 1 and 2 independently compete against a common Adversary by allocating their limited resource budgets towards separate sets of contests; an agent wins a contest by allocating more resources towards it than their opponent. In this setting, we study three alliance mechanisms: budget transfers (resource donation), contest transfers (contest redistribution), and joint transfers (both simultaneously). For all three mechanisms, we study when they present opportunities for collective improvement (the sum of the Players' payoffs increases) or mutual improvement (both Players' individual payoffs increase). In our first result, we show that all three are fundamentally different with regards to mutual improvement; in particular, mutually beneficial budget and contest transfers exist in distinct, limited subsets of games, whereas mutually beneficial joint transfers exist in almost all games. However, in our second result, we demonstrate that all three mechanisms are equivalent when it comes to collective improvement; that is, collectively beneficial budget, contest, and joint transfers exist in almost all game instances, and all three mechanisms achieve the same maximum collective payoff. Together, these results demonstrate that differences between mechanisms depend fundamentally on the objective of the alliance.

cs.GT↗

arXiv2025

Cooling Under Convexity: An Inventory Control Perspective on Industrial Refrigeration

Industrial refrigeration systems have substantial energy needs, but optimizing their operation remains challenging due to the tension between minimizing energy costs and meeting strict cooling requirements. Load shifting--strategic overcooling in anticipation of future demands--offers substantial efficiency gains. This work seeks to rigorously quantify these potential savings through the derivation of optimal load shifting policies. Our first contribution establishes a novel connection between industrial refrigeration and inventory control problems with convex ordering costs, where the convexity arises from the relationship between energy consumption and cooling capacity. Leveraging this formulation, we derive three main theoretical results: (1) an optimal algorithm for deterministic demand scenarios, along with proof that optimal trajectories are non-increasing (a valuable structural insight for practical control); (2) performance bounds that quantify the value of load shifting as a function of cost convexity, demand variability, and temporal patterns; (3) a computationally tractable load shifting heuristic with provable near-optimal performance under uncertainty. Numerical simulations validate our theoretical findings, and a case study using real industrial refrigeration data demonstrates an opportunity for improved load shifting.

math.OC↗

arXiv2025

Allocation of Heterogeneous Resources in General Lotto Games

The allocation of resources plays an important role in the completion of system objectives and tasks, especially in the presence of strategic adversaries. Optimal allocation strategies are becoming increasingly more complex, given that multiple heterogeneous types of resources are at a system planner's disposal. In this paper, we focus on deriving optimal strategies for the allocation of heterogeneous resources in a well-known competitive resource allocation model known as the General Lotto game. In standard formulations, outcomes are determined solely by the players' allocation strategies of a common, single type of resource across multiple contests. In particular, a player wins a contest if it sends more resources than the opponent. Here, we propose a multi-resource extension where the winner of a contest is now determined not only by the amount of resources allocated, but also by the composition of resource types that are allocated. We completely characterize the equilibrium payoffs and strategies for two distinct formulations. The first consists of a weakest-link/best-shot winning rule, and the second considers a winning rule based on a weighted linear combination of the allocated resources. We then consider a scenario where the resource types are costly to purchase, and derive the players' equilibrium investments in each of the resource types.

econ.TH↗

arXiv2025

The Price of Simplicity: Analyzing Decoupled Policies for Multi-Location Inventory Control

What is the performance cost of using simple, decoupled control policies in inherently coupled systems? Motivated by industrial refrigeration systems, where centralized compressors exhibit economies of scale yet traditional control employs decoupled room-by-room temperature regulation, we address this question through the lens of multi-location inventory control. Here, a planner manages multiple inventories to meet stochastic demand while minimizing costs that are coupled through nonlinear ordering functions reflecting economies of scale. Our main contributions are: (i) a surprising equivalence result showing that optimal stationary base-stock levels for individual locations remain unchanged despite the coupling when restricting attention to decoupled strategies; (ii) tight performance bounds for simple decoupled policies relative to optimal coupled policies, revealing that the worst-case ratio depends primarily on the degree of nonlinearity in the cost function and scales with the number of locations for systems with fixed costs; and (iii) analysis of practical online algorithms that achieve competitive performance without solving complex dynamic programs. Numerical simulations demonstrate that while decoupled policies significantly outperform their worst-case guarantees in typical scenarios, they still exhibit meaningful suboptimality compared to fully coordinated strategies. These results provide actionable guidance for system operators navigating the trade-off between control complexity and operational efficiency in coupled systems.

math.OC↗

arXiv2025

Trial-and-Error Learning in Decentralized Matching Markets

Two-sided matching markets, environments in which two disjoint groups of agents seek to partner with one another, arise in several contexts. In static, centralized markets where agents know their preferences, standard algorithms can yield a stable matching. However, in dynamic, decentralized markets where agents must learn their preferences through interaction, such algorithms cannot be used. Our goal in this paper is to identify achievable stability guarantees in decentralized matching markets where (i) agents have limited information about their preferences and (ii) no central entity determines the match. Surprisingly, our first result demonstrates that these constraints do not preclude stability--simple "trial and error" learning policies guarantee convergence to a stable matching without requiring coordination between agents. Our second result shows that more sophisticated policies can direct the system toward a particular group's optimal stable matching. This finding highlights an important dimension of strategic learning: when agents can accurately model others' policies, they can adapt their own behavior to systematically influence outcomes in their favor--a phenomenon with broad implications for learning in multi-agent systems.

cs.GT↗

arXiv2025

Learning Optimal Stable Matches in Decentralized Markets with Unknown Preferences

Matching algorithms have demonstrated great success in several practical applications, but they often require centralized coordination and plentiful information. In many modern online marketplaces, agents must independently seek out and match with another using little to no information. For these kinds of settings, can we design decentralized, limited-information matching algorithms that preserve the desirable properties of standard centralized techniques? In this work, we constructively answer this question in the affirmative. We model a two-sided matching market as a game consisting of two disjoint sets of agents, referred to as proposers and acceptors, each of whom seeks to match with their most preferable partner on the opposite side of the market. However, each proposer has no knowledge of their own preferences, so they must learn their preferences while forming matches in the market. We present a simple online learning rule that guarantees a strong notion of probabilistic convergence to the welfare-maximizing equilibrium of the game, referred to as the proposer-optimal stable match. To the best of our knowledge, this represents the first completely decoupled, communication-free algorithm that guarantees probabilistic convergence to an optimal stable match, irrespective of the structure of the matching market.

cs.GT↗

arXiv2024

Battlefield Transfers in Coalitional Blotto Games

In competitive resource allocation environments, agents often choose to form alliances; however, for some agents, doing so may not always be beneficial. Is there a method of forming alliances that always reward each of their members? We study this question using the framework of the coalitional Blotto game, in which two players compete against a common adversary by allocating their budgeted resources across disjoint sets of valued battlefields. On any given battlefield, the agent that allocates a greater amount of resources wins the corresponding battlefield value. Existing work has shown the surprising result that in certain game instances, if one player donates a portion of their budget to the other player, then both players win larger amounts in their separate competitions against the adversary. However, this transfer-based method of alliance formation is not always mutually beneficial, which motivates the search for alternate strategies. In this vein, we study a new method of alliance formation referred to as a joint transfer, whereby players publicly transfer battlefields and budgets between one another before they engage in their separate competitions against the adversary. We show that in almost all game instances, there exists a mutually beneficial joint transfer that strictly increases the payoff of each player.

cs.GT↗

arXiv2024

The Value of Compromising Strategic Intent in General Lotto Games

Resource allocation in adversarial environments is a fundamental challenge across various domains, from corporate competition to military strategy. This article examines the impact of compromising an opponent's strategic intent in the context of General Lotto games, a class of resource allocation problems. We consider a scenario where one player, termed the "Breaker", has access to partial information about their opponent's strategy through a binary sensor. This sensor reveals whether the opponent's allocated resources exceed a certain threshold. Our analysis provides a comprehensive characterization of equilibrium strategies and payoffs for both players under this information structure. Through numerical studies, we demonstrate that the information provided by the sensor can significantly improve the Breaker's performance.

cs.GT↗