Papers

Machine learning (ML) predictions are increasingly being used to guide decision-making, giving rise to the problem of decision-focused learning (DFL) where predictors are optimized for downstream decision quality rather than accuracy alone. However, most existing work assumes a single decision-maker optimizing in isolation. This paper formalizes strategic decision-focused learning, where an ML system predicts an exogenous state that some agents observe before playing a game. For example, a park ranger may predict wildlife locations to allocate anti-poaching patrols against strategic poachers. While the exogenous state is unaffected by agent actions, predictions influence agents' strategies and the resulting equilibrium. We find that strategic considerations fundamentally change the learning problem. In particular, we show the prediction accuracy-equilibrium payoff landscape can be non-monotonic, i.e., better predictions can degrade performance. We propose algorithmic approaches to address these challenges and validate them across benchmarks in wildlife conservation and infrastructure protection. Our theory and experiments highlight the importance of accounting for strategic interactions when designing predictors.

In this paper, we derive an explicit solution of the stationary prediction with expert advice PDE for five experts. The formula is given in three regions. In the first two regions, it is the four-expert solution plus a single integral with an elementary positive density. In the third region, it is a finite sum of hyperbolic products whose coefficients are determined by one scalar quadrature. Our formula establishes that the direction $(1,0,1,0,0)$ is optimal throughout the ordered sector, and that the COMB strategy $(1,0,1,0,1)$ is optimal only on a lower dimensional subset of the sector (where $x_1=x_2$ and $x_3=x_4$). This disproves the COMB optimality conjecture of Gravin, Peres and Sivan. The verification of the Hamiltonian inequalities is a tedious task, part of which is completed with a computer assisted proof. The verification reduces to 21 scalar inequalities, which we prove using 147 exact rational Bernstein polynomial certificates. The exact certificates and their independent arithmetic checks are included in a supplement to this paper, and a Lean 4 formalization machine-checks the verification and both main theorems, apart from the viscosity characterization.

This paper studies decentralized learning of socially optimal equilibria in finite normal-form games over dynamic communication networks. Each agent observes only its own realized payoffs, does not know the game a priori, and can communicate only with time-varying neighbors using low-bandwidth messages. We propose networked decentralized optimal equilibrium learning dynamics in which agents generate randomized semantic content/discontent signals from local payoff comparisons and exchange time-stamped time-stacked tables rather than raw actions, payoff information or local estimates/parameters. The method combines table fusion with temporal majority reconstruction to mitigate dynamic communication while preserving fully decentralized operation. We establish finite-time logarithmic regret guarantees, with an in-phase exploration perturbation, for optimal equilibrium selection under utilitarian and proportional-fair social welfare objectives. Simulation results further show that the proposed approach can effectively select socially desirable equilibria over dynamic communication networks.

This paper investigates multi-agent reinforcement learning (MARL) in settings where firms compete for customers using congestible resources. We consider Bertrand competition in which firms compete by announcing prices and customers choose among firms based on both price and congestion. The relationship between price, congestion and the quantity of customers willing to accept service is governed by an unknown inverse demand curve, which firms must learn through experience. Each firm is modeled as a self-interested learning agent that chooses its price to maximize profit. A growing literature has shown that independently learning MARL agents can develop tacitly collusive behavior. We examine how such behavior emerges in markets with congestible resources. Our results provide insight into how learning dynamics, state representation, and strategic interaction jointly shape competition, with implications for both economic learning and the design of learning-enabled markets.

Participation in federated learning (FL) comes at a cost. Clients trade off privacy, communication, and compute costs for potentially greater gains in model efficacy. This paper explores this tradeoff under the aegis of individual rationality (IR) versus autarky, the basic game-theoretic requirement that the federation provide utility no worse than local training. Using the above as the design target, we examine pathwise performance of FL, as a per-round bound on cumulative surplus rather than only an asymptotic equilibrium guarantee under different degrees of client data heterogeneity. Along the learning path, clients can remain below their local-training baseline for hundreds of rounds. The natural remedy is to cap each client's per-round contribution so that this shortfall stays bounded. We prove that such a cap drives all contributions to zero, with high probability, when its tolerance is small relative to the warm-up deficit, and we observe learning collapse under it even at low heterogeneity. We then propose a design that combines a short-term participation guarantee, enforced after an announced grace window, with personalized model evaluation, while preserving the incentive properties of the underlying mechanism. We provide a theoretical basis for this approach and empirically demonstrate that, after the grace window, clients meet IR on nearly all rounds without harming overall performance under low to moderate heterogeneity; under severe heterogeneity, the design shows promising outcomes for clients compared to their local baseline at some cost in accuracy.

We resolve the matroid secretary conjecture, giving an online algorithm that accepts each element of the offline optimum with probability at least $1/4$. The algorithm only needs the number of elements in advance and independence-oracle access to subsets of already-arrived elements; it does not need to know the matroid upfront.

We study edge-weighted online bipartite matching under random arrival order, parameterized by the maximum offline degree $d$ and sampling fraction $\theta$. We analyze two sampling-based frameworks. For Deterministic Greedy Sampling, which computes prices from a fixed-size initial sample and then applies a local threshold rule, we derive an explicit worst-case competitive ratio and prove it tight within this policy family for every fixed $d\ge2$ and $\theta\in[0,1]$. The optimal sampling choice interpolates between no sampling for $d=1,2$ and a dense-limit guarantee of approximately $0.2562$, improving on the classical $1/8$ analysis while retaining linear per-arrival time. We also derive worst-case bounds on the variance of the number of matched offline agents, including order-tight behavior as $\theta\to1_-$ and an $O(\theta)$ bound as $\theta\to0_+$ for fixed $m,d$. For Black-Box Sampling–Matching, we introduce prefix-dependent reweighting followed by an arbitrary approximate offline matching solver and prove a transfer theorem whose guarantee is the offline approximation ratio times an explicit function of $d$ and $\theta$. With exact matching, the framework recovers the classical $1/e$ guarantee in the unbounded-degree limit.

We study the allocation of indivisible chores with subsidies under negative dichotomous valuations, where the marginal disutility of every chore is either zero or one. This is the chore analogue of the dichotomous goods model of Barman et al. (2022), for which a subsidy of at most one unit per agent is known to suffice for envy-freeness. We show that the same optimal guarantee holds for chores, under no structural assumption beyond binary marginals. For every instance with negative dichotomous valuations, there exists a complete allocation $A$ and a subsidy vector $p\in\{0,1\}^n$ with $\sum_{i\in N} p_i\le n-1$ such that $(A,p)$ is envy-free. Moreover, the allocation $A$ is EF1 even before subsidies are paid. The bound is tight, and the allocation and subsidies can be computed in polynomial time in the value-oracle model. We further show that the unit-subsidy guarantee cannot, in general, be maintained if Pareto optimality is also required. Our algorithm starts from an envy-free partial allocation produced by the algorithm of Tao et al. (2025), assigns the remaining chores to distinct agents in a tail strongly connected component of the terminal equality graph, and determines the subsidised agents through a backward closure in the associated equality graph.

Complementary resources are often allocated by agencies that see different coordinates of an individual's needs. If an intervention requires complementary resources, an agency may know if said person lacks its own resource; yet not know if supplying completes a useful bundle. We study allocation of $m$ divisible complementary goods when each agency observes only its own coordinate of a baseline-access profile. To isolate information from incentives, we measure the welfare cost of this split against a generous decentralized benchmark DEC: the best rule that acts on local information alone, with cooperative agencies and known population distribution and capacities. Even so, local observation alone can make optimally coordinated policies arbitrarily inefficient: a factor linear in $m$ (even with equal capacities), and a factor inverse in OPT (with but three agencies). Threshold referrals recover much of this loss: an agency reports if its value lies below a public threshold, and a clearing rule uses only the joint reports. Aggregating types by their reports captures a rectangle under the optimal half-utility survival curve. Our main tool is a profile-level charging certificate: if optimal utility is at least twice a threshold, OPT pays at least that on every deficient coordinate. This yields welfare at least ${\rm OPT}/[4(1+\ln(2/{\rm OPT}))]$ with one bit per agency; and an equal-revenue family shows this log-loss tight for one threshold. A geometric threshold ladder improves this to a constant fraction of OPT with doubly-logarithmic messages: a staircase recovers ${\rm OPT}/8$ with $\Theta(\log\log(1/{\rm OPT}))$ bits, and this is necessary within the class. The results isolate how a simple reporting language turns large local-info losses into constant-factor recovery. In short: One threshold gets a log-approximation. A staircase, with log-of-log bits, a constant-factor.

We study the fair division of indivisible goods among agents with nonnegative additive valuations. An agent's maximin share (MMS) is the value she can guarantee by partitioning the goods into as many bundles as there are agents and receiving a least-valued bundle. We prove the existence of exact MMS allocations for a valuation domain that generalizes several few-valued domains as well as weakly lexicographic valuations. For each agent, the lower-valued goods, after a positive rescaling, may take values in $\{0,1,d,d+1\}$, $\{0,1,2,2e\}$, or $\{0,1,2,3,4\}$, where $d,e\ge 2$ are integers. Above these goods, the valuation may contain arbitrarily many value classes, subject to the condition that a single good in each class is worth at least the total value of all strictly lower-valued goods. The value classes, scaling factors, and parameters may vary across agents. We give an algorithm that computes an MMS allocation in $O(nm\log^2(2+m))$ time, where $n$ is the number of agents and $m$ is the number of goods.

A principal who deploys a binary classifier with an abstention option must decide which queries the mechanism abstains on. The right choice depends on the adversary. A gaming adversary already knows the classifier and tries to manipulate features across the boundary, so the principal does best by abstaining on queries close to that boundary. The same boundary-localizing rule is the worst possible choice against a learning adversary who does not know the classifier: each abstention now tells the adversary that the boundary is nearby, which is enough to drive a binary search. We analyze this tension. The two natural defenses, abstaining at a fixed rate and abstaining near the boundary, are Blackwell-incomparable: neither can be simulated by post-processing the other's responses. The number of queries needed to reconstruct the boundary to error $\eps$ is $\tilde\Theta(d/\eps)$ under the first defense and $\Theta(d \log(1/\eps))$ under the second, where $d$ is the VC dimension of the classifier family and $\tilde\Theta$ suppresses factors polylogarithmic in $d$ and $1/\eps$. The first rate is a worst case over query distributions; no reconstruction algorithm can close the gap at the distributions that attain it. We characterize the Pareto frontier between the two defense objectives, and confirm both rates on seven binary-classification tasks spanning tabular, image, and language-model-feature inputs: label-plus-counterfactual access extracts the boundary with up to $200\times$ fewer queries than a published label-only baseline.

We study strategyproof scheduling on \(n\) unrelated machines with predictions. Each machine is controlled by an agent with privately known processing times, while the mechanism receives a public prediction of the processing-time matrix before the agents report. The objective is to minimize the makespan subject to strategyproofness. We measure performance by consistency, the approximation guarantee for correct predictions, and robustness, the worst-case guarantee for arbitrary predictions. We introduce EdgeSkip, a deterministic strategyproof member of the class of job-wise weighted mechanisms. Such mechanisms allocate each job independently using prediction-dependent weights. Using a polynomial-time \(2\)-approximate reference schedule computed from the prediction and a standard tradeoff parameter, EdgeSkip is \(4\)-consistent and \((2n-2)\)-robust, improving on the \((6,2n)\) guarantee of Balkanski, Gkatzelis, and Tan. Without computational restrictions, EdgeSkip with an optimal reference schedule is \(C\)-consistent and \(\max\{n,(n-1)C/(C-1)\}\)-robust for every \(C>1\). We prove a matching information-theoretic lower bound for all job-wise weighted mechanisms, thereby determining the exact consistency–robustness tradeoff for this class. For arbitrary deterministic strategyproof mechanisms, we establish the robustness lower bound \(\max\{n,C/(C-1)\}\) for every \(C>1\). We also study an error-tolerant variant and improve upon prior guarantees. Experiments demonstrate that our mechanisms achieve good empirical performance.

When algorithmic predictions inform people's decisions, the models we deploy are performative and actively shape the data we see. This feedback loop between algorithms and their broader environments introduces a challenge in the mechanics of social prediction: If different predictive models induce different distributions, is it possible to efficiently learn a prediction rule that is optimal for the distribution that it induces? Formally, this solution concept is known as performative stability. A core challenge in learning a performatively stable predictor is that, unlike supervised learning where distributions are fixed, the learner must deploy different predictors and observe their induced distributions. The main contribution of our work is a new algorithmic procedure that, in the high-accuracy regime, finds a performatively stable model in nearly the minimum number of model deployments without making any assumptions regarding how predictions shape distributions. In particular, our procedure succeeds at finding a randomized performatively stable predictor using exponentially fewer model deployments than prior approaches. Our second main contribution is a structural result showing how this recent randomized notion of stability achieved by our algorithm can be derandomized into a single predictor satisfying the prior deterministic notion if one is willing to assume that the loss is well-conditioned and that performative effects are weak, as in early work in this area. On a technical level, our results come from building on an underexplored technical connection between performative stability and expected variational inequalities.

We study fair and efficient allocations of indivisible chores under binary additive costs, with a focus on unequal entitlements and best-of-both-worlds guarantees. While binary valuations have been extensively studied for goods, their chore counterpart remains much less understood. A notable exception is due to Tao et al. (TCS 2025), who established that EFX and fPO are compatible for binary chores with equal entitlements. We revisit binary chores under unequal entitlements and establish the computation of allocations that satisfy WEFX and fPO. Our key technical contribution is a new lexicographic potential function tailored to chores: any allocation minimizing this potential ensures both WEFX and fPO. This potential further guides a polynomial-time local-search algorithm for computing allocations with such fairness and efficiency guarantees. For best-of-both-worlds guarantees, we show that unequal entitlements create a sharp obstruction: even with two agents and identical binary additive costs, no lottery can simultaneously satisfy ex-ante WEF and ex-post WEF1. In contrast, for equal entitlements, we construct in polynomial time a lottery that is ex-ante EF and fPO, while every realization is both EFX and fPO.

If AI and automation make reproducible goods cheap, do scarcity rents disappear or migrate? We give a closed general-equilibrium answer that separates a low unit price from economic abundance. Agents consume an automated good, a fixed-supply good, and a numeraire; their purchasing power comes from resource endowments and ownership of scarce assets. The equilibrium of a heterogeneous economy exists, is unique, and is globally stable. Aggregate scarcity rent obeys an exact accounting identity: it rises with automation if and only if real expenditure on the automated good falls. In a symmetric economy this sign is determined by whether the curvature of marginal utility is above or below one. Thus marginal cost converging to zero is insufficient: demand rebound can absorb the released resources. After automated demand is fixed or sufficiently satiated, each agent's access share is an exact convex combination of net purchasing-power and scarce-asset ownership shares. This yields a concentration decomposition with a covariance term, showing why equalizing one asset can increase access inequality when ownership sources were offsetting. A compute extension distinguishes a fixed productive input, whose rent can vanish, from a binding throughput constraint, whose rent persists. Numerical experiments reproduce the sign reversals, ownership effects, and institutional frontiers, and imply eight falsifiable restrictions. The results replace a binary “post-scarcity” claim with a testable condition on expenditure, capacity, and ownership.

Online fair division captures allocation problems in which indivisible resources arrive over time and must be assigned before future resources are known. Understanding what fairness remains achievable when allocation decisions are immediate and irrevocable is a fundamental question in this setting. We study deterministic online allocation among $n$ agents with nonnegative additive valuations, where the number of goods is unknown and the adversary can adapt to previous allocation decisions. We focus on proportionality up to one good (PROP1) and examine how advance information affects the achievable guarantees. Without additional future information, we give a deterministic algorithm that guarantees $\Omega(\frac{1}{\log(nm)})$-PROP1 after every round, where $m$ is the number of goods at termination. We complement this result by showing that, for every $n$ and sufficiently large $m$, every deterministic algorithm has an adaptive instance with $m$ goods on which its allocation has PROP1 approximation guarantee $O(\frac{\log \log m}{\log m})$. Thus, when the number of agents is fixed, our upper and lower bounds on the competitive ratio differ by at most an $O(\log\log m)$ factor. These results answer an open question proposed by Choo et al. on whether a nontrivial deterministic approximation for PROP1 can be obtained. We also study the setting where the algorithm knows the predictions of the maximum item value for every agent. When the predictions are accurate, we give a deterministic $\frac{1}{2}$-PROP1 algorithm, improving the $\frac{1}{n}$ guarantee of Choo et al. to a constant. We further establish an explicit upper bound below one on the competitive ratio, even for two agents with accurate predictions. Finally, we give a single deterministic algorithm that guarantees $\frac{1}{2}$-PROP1 when predictions are accurate and $\Omega(\frac{1}{\log (nm)})$-PROP1 for arbitrary predictions.

In an approval-based committee election, a committee of size $k$ is selected from a set of candidates to represent voters of total weight $n$, each of whom has positive weight and approves a subset of the candidates. A size-$k$ committee is $\lambda$-stable if, for every nonempty subset $T$ of candidates, the total weight of voters who strictly prefer $T$ is less than $\lambda$ times the proportional share $n|T|/k$. Whether there exists a committee that is exactly stable, corresponding to $\lambda=1$, remains a major open problem in approval-based committee voting. Thus, a natural objective is to identify small values of $\lambda>1$ for which $\lambda$-stability can always be guaranteed. We prove that weighted sequential Phragmén, a classical and natural rule, always returns a $2$-stable committee of size $k$. Since the $\lambda$-core is the set of all $\lambda$-stable committees, our result implies that the $2$-core is always nonempty. This improves upon the previously best-known guarantee, due to Gao, Sun, and Vondrák~[EC~2026], that a $3.651$-stable committee always exists.

The chance-constrained correlated equilibrium concept provides a robust coordination technique for self-interested agents whose costs are uncertain to a central coordinator, but the number of joint actions considered in its computation grows exponentially with the number of agents. We propose an exact-one resource-assignment restriction for games in which agents compete for shared resources and simultaneous use of a resource is undesirable or unsafe. The restriction allows each resource to be assigned to exactly one agent, reducing the number of joint actions considered from O(2^(nr)) to O(n^r) for n agents and r resources. The resulting problem is solved over the restricted joint action set while retaining all incentive constraints associated with unilateral deviations. We show that the feasible set of the restricted problem is exactly the convex hull of the chance-constrained pure Nash equilibria contained in the exact-one assignment set, yielding a necessary and sufficient condition for nonemptiness. We further derive a sufficient condition under which all chance-constrained pure Nash equilibria of the unrestricted game are retained by the restriction. Numerical experiments in a vertiport departure-corridor coordination scenario demonstrate a 99.81% reduction in median computation time relative to the unrestricted formulation while achieving equivalent coordination performance.

We study NFT-based reward mechanisms in which a user can create multiple identities and submit fraudulent claims that mature a reward subject to vesting. We assume that the issuer stochastically verifies claims during the vesting period and that identities can be linked into clusters so that the detection of one identity submitting a fraudulent claim causes the whole cluster to be forfeited through a penalty. A farmer's payoff is then non-linear in the number of identities: rewards increase linearly, while the probability of avoiding detection decreases geometrically. We characterise the optimal farming scale in the continuous relaxation of the problem. This allows us to derive a sufficient condition for deterrence and then consider the issuer's choice of reward vesting and claim verification. Vesting reduces the probability that a fraudulent claim is paid but also affects genuine participants, while verification is costly for the issuer. We characterise the sufficient deterrence frontier for the issuer in terms of auditing cost, vesting schedule, and penalty value. When small amounts of audit capacity can be added at negligible marginal cost, vesting alone is not optimal. We also distinguish the role of penalties from that of cluster-level auditing. Finally, we discuss the implications for NFT reward programmes on high-throughput ledgers, such as Hedera.

Recent work shows that LLM-based pricing agents can produce supracompetitive outcomes in repeated oligopoly environments without being explicitly instructed to collude. We reproduce the qualitative prompt-sensitivity effect of Fish et al. using DeepSeek-V3.1: the P1 prompt produces significantly higher prices and profits than P2, although our outcomes are less monopoly-like than the original GPT-4 results. We then evaluate three regulatory interventions: a prompt-only warning, a Harrington-inspired expected-damages payoff regulator, and an active random entrant. The prompt-only regulator reduces but does not eliminate above-Nash pricing. The Harrington regulator brings P1 outcomes close to the duopoly Nash benchmark and removes the statistically significant P1–P2 gap. The active entrant produces the strongest effect, pushing both prompts below the appropriate random-entrant Nash benchmark. Overall, our experiments provide preliminary evidence that interventions that alter incentives or market participation can reduce supracompetitive pricing more effectively than prompt warnings alone.

Block building is an essential skill in speedcubing competitions. However, there is currently no systematic method to understand or analyze block-building techniques. Rewatching gameplay reveals only the outcome, not the underlying mechanism. This paper presents a systematic approach, the "AK-cubie method" (or "cubie method" for short), for constructing near-optimal block-building move sequences within a short computation time. Speedcubers can use the accompanying software to train their look-ahead and block-building skills. We hope this work will contribute to breaking the 2-second world record in the near future.

We study learning-augmented mechanism design for locating a single facility in $\mathbb{R}^d$ to minimize the sum of the agents' $\ell_p$ distances to the facility. We analyze the coordinate-wise median with predictions (CMP) mechanism, which adds $cn$ virtual agents at a predicted optimal facility location to the $n$ reported locations and returns their coordinate-wise median. The parameter $c\in[0,1)$ represents confidence in the prediction; CMP is known to be strategyproof when both are fixed independently of the reports. We determine its approximation guarantees under correct predictions (consistency) and arbitrary predictions (robustness) in two settings. First, for $d=2$, we establish exact guarantees for every $p\in[1,+\infty]$. For $1<p<+\infty$, the consistency and robustness are respectively $\Bigl(1+\bigl(\frac{1-c}{1+c}\bigr)^{\frac{p}{p-1}}\Bigr)^{\frac{p-1}{p}}$ and $\Bigl(1+\bigl(\frac{1+c}{1-c}\bigr)^{\frac{p}{p-1}}\Bigr)^{\frac{p-1}{p}}$. We use the median condition in each coordinate to compare the mechanism's cost with the optimal cost, and establish tightness using instances with agents at only three distinct locations. Second, for $1<p<+\infty$, we obtain dimension-independent consistency and robustness upper bounds valid for every $d\ge1$. For each fixed $p$ and $c$, we construct families of instances whose ratios approach the respective upper bounds as $d\to\infty$, proving asymptotic tightness. We also establish exact guarantees for $p=1$ in every dimension and asymptotically tight bounds for $p=+\infty$. Our high-dimensional results recover the prediction-free bounds of Gravin and Jia (STOC 2025) when $c=0$ and their learning-augmented bounds in arbitrary-dimensional Euclidean spaces when $p=2$.

We study strategyproof mechanisms for locating a single facility on a circle so as to serve a set of strategic agents under the utilitarian social cost objective. We analyze a simple parity-dependent mechanism that randomizes between the Random Dictator (RD) mechanism and the Proportional Circle Distance (PCD) mechanism. For an odd number \(n\) of agents, this mechanism mixes RD and PCD with equal probability, as originally proposed by Rogowski and Dziubiński (IJCAI 2025). For even \(n\), it mixes RD with a random-deletion extension of PCD, in which one agent is removed uniformly at random before PCD is applied to the remaining agents. Our main result shows that this mechanism is strategyproof and achieves an approximation ratio of \(\frac32\) for every \(n\ge 3\). This improves the \(\frac74\) upper bound of Rogowski and Dziubiński, which applied only to odd \(n\), and extends the guarantee to even numbers of agents. Finally, we establish a computer-assisted lower bound of \(1.088187\ldots\) on the approximation ratio of any randomized strategyproof mechanism, improving on the previous lower bound of \(1.0456\) due to Meir (SAGT 2019).

While Reinforcement Learning from Human Feedback (RLHF) is the standard paradigm for aligning large language models with human preferences, its effectiveness in pluralistic settings has been called into question. Notably, recent work by Gölz et al. (2025) demonstrated that the distortion – defined as the multiplicative gap between the average user utility of the RLHF policy and the optimal average utility – can scale exponentially with the Bradley-Terry temperature parameter $\beta$ when users have heterogeneous preferences. In this work, we present a fine-grained analysis of the distortion of RLHF with reward clipping and demonstrate that such exponential degradation is not a fundamental property of the algorithm but rather a consequence of distribution mismatch between the distribution generating preference data ($\mu$) and the KL reference policy ($\pi_{\mathrm{ref}}$). To this end, we establish tight upper and lower bounds on the distortion of RLHF across multiple regimes of the KL regularization strength. We show that in a representative regime, under the Bradley-Terry model, the distortion is $\tilde{\Theta}(\beta B + \beta)$, where $B$ is an upper bound on the log density ratio between $\mu$ and $\pi_{\mathrm{ref}}$. In particular, when there is no distribution mismatch (i.e., $\mu = \pi_{\mathrm{ref}}$), RLHF achieves the optimal distortion of $O(\beta)$ up to a constant. Our results suggest that, to reasonably maximize average utility with RLHF, it is preferable to use on-policy sampled preference data or to fine-tune before RLHF on data from a source close to $\mu$.

We consider universally truthful randomized mechanisms for the problem of scheduling $m$ jobs on $n$ unrelated machines. We prove a lower bound on the expected approximation ratio of every such mechanism whose probability distribution has discrete support. We show that no universally truthful randomized mechanism in this class can achieve approximation ratio smaller than $n/12 - o(n)$ with respect to the optimal makespan. We match this, up to a constant factor, by a mechanism with approximation ratio $n/2 + o(n)$.

Arm TrustZone for Armv8-M isolates Secure and Non-secure software, but developers must still coordinate peripheral attribution, interrupt routing, initialization, and gateway interfaces across separately built firmware images. Inconsistent assumptions between these images can compile successfully and emerge only as faults on the target device. We present MicroHasTEE, a multiparty programming framework that expresses both firmware applications as participants in one typed Haskell program. MicroHasTEE represents peripheral authority with type-level capability ledgers and uses indexed setup computations to track resource acquisition, configuration, transfer, and finalization. Domain-specific effect types restrict peripheral operations and interrupt callbacks to the participant that holds the corresponding authority, while typed callable handles describe the Secure services available to Non-secure code. MicroHs compiles the shared program twice to produce separate bare-metal Secure and Non-secure firmware images. We implement MicroHasTEE for an STM32U5 Nucleo board, including TrustZone configuration, peripheral drivers, and a serialized gateway for cross-domain Haskell calls. For programs expressed through its interface, MicroHasTEE rejects inconsistent resource use, attribution changes after configuration, callbacks in the wrong domain, and calls to unregistered Secure services. A door-lock case study demonstrates feasibility, with firmware images occupying 232.7 KiB and 228.4 KiB of flash and approximately 220 KiB of SRAM per domain.

Marginal-contribution pricing makes the social objective an exact potential, but does not ensure that every stable assignment is efficient. We study indivisible clients with heterogeneous workloads, arbitrary nonnegative assignment costs, and private eligibility menus over a fixed number of shared servers and optional local execution. Each server's social cost is its occupancy multiplied by its aggregate workload and a server-specific coefficient. For every fixed server cap $M$, we prove that the price of anarchy over this class is $\Theta_M(\kappa^{1-2^{-M}})$ as the workload-ratio cap $\kappa$ grows. The upper bound applies to every equilibrium and every feasible comparison, without an acyclic-comparison or strongly-connected-component restriction. Its proof combines a common-multiplier certificate, a source-weighted residual inequality and an ordered moment recurrence. A matching chain family has a realization by mobile unmanned aerial vehicle (UAV) clients and fixed ground servers, with positive altitude, positive-width coverage and an explicitly paid wireless baseline. We prove exact waypoint elimination and give an input-computable component refinement. Scheduling and congestion identities delimit which established bounds transfer. Exact enumeration of 2,800 synthetic games identifies inefficient equilibria, while 270 primary-parameterized synthetic instance-budget records evaluate incremental latency relative to a feasible multistart reference. Tightness concerns the heterogeneity exponent for fixed $M$, not matching leading constants or measured frequency of the worst-case configurations.

We consider an agent acting against a general non-Markovian environment. The agent maintains its agent states, but is free to choose a transition kernel across those states and optimize its state-feedback control policies. We study the bi-level agent design problem that optimizes the transition kernel and the policy it induces, given said kernel with offline data of observations and actions obtained via a behavioral policy. For general environments, we show that a soft $Q$-learning algorithm converges almost surely to the fixed point of a soft Bellman equation defined by the stationary averages that the behavioral policy and the chosen kernel induce, and we delineate what separates the resulting policy from an optimal one. In partially observed Markov decision problems, we analyze convergence properties of parametrized transition kernel design via zero-th order and Bayesian optimization techniques.

The security and liveness of Proof-of-Work (PoW) blockchains fundamentally depend on the economic rationality of miners. Existing incentive-driven denial-of-service attacks, such as BDoS, can deter rational miners from participating, but require the attacker to continuously absorb substantial economic losses and are therefore difficult to sustain in high-value networks. Meanwhile, prior infiltration-based withholding attacks are designed to extract revenue rather than to directly disrupt chain liveness. We present PDoS, a hybrid attack that combines block header signal deterrence with parasitic revenue extraction. PDoS disrupts blockchain liveness while exploiting the victim pool's share-reward mechanism to subsidize the attack cost, thereby lowering the adversarial hash-power threshold required to induce rational miners to shut down. We further show a counterintuitive result: in high-fee or high-MEV environments, higher block value can make PoW systems less secure by increasing the attacker's parasitic revenue and pushing the attack across the break-even point into a self-sustaining, or even profitable, regime. To the best of our knowledge, PDoS is the first attack to demonstrate that disrupting PoW blockchain liveness can be economically self-sustaining and even profitable.

Many stochastic systems in operations and economics exhibit feedback between their long-run state distribution and the transition law governing their dynamics. In this paper, we develop a computational framework for stationary equilibria in such measure-dependent Markov systems when this feedback operates through a finite-dimensional aggregate. We show that the original stationary-equilibrium problem can be reduced to a finite-dimensional self-consistency equation, separating steady-state analysis of the underlying Markov system from equilibrium computation. We use properties of the resulting self-consistency map to guide the choice among fixed-point iteration, relaxed fixed-point iteration, and minimization of the fixed-point residual. The last approach requires derivatives of the self-consistency map, which are typically unavailable in closed form. We therefore develop finite-time infinitesimal perturbation analysis estimators for these derivatives, with error bounds that separate Monte Carlo error from finite-time bias. We illustrate the framework through a strategic $G/G/c$ queue and an opinion-dynamics model, showing how different structural properties lead naturally to different equilibrium-computation methods.