Mechanism Design

Collaborative machine learning involves training high-quality models using datasets from a number of sources. To incentivize sources to share data, existing data valuation methods fairly reward each source based on its data submitted as is. However, as these methods do not verify nor incentivize data truthfulness, the sources can manipulate their data (e.g., by submitting duplicated or noisy data) to artificially increase their valuations and rewards or prevent others from benefiting. This paper presents the first mechanism that provably ensures (F) collaborative fairness and incentivizes (T) truthfulness at equilibrium for Bayesian models. Our mechanism combines semivalues (e.g., Shapley value), which ensure fairness, and a truthful data valuation function (DVF) based on a validation set that is unknown to the sources. As semivalues are influenced by others' data, we introduce an additional condition to prove that a source can maximize its expected data values in coalitions and semivalues by submitting a dataset that captures its true knowledge. Additionally, we discuss the implications and suitable relaxations of (F) and (T) when the mediator has a limited budget for rewards or lacks a validation set. Our theoretical findings are validated on synthetic and real-world datasets.

We address the problem of maximizing Gain from Trade (GFT) in repeated buyer-seller exchanges subject to global budget balance constraints. While this problem is well-understood in purely adversarial and stochastic settings, these environments exhibit a sharp dichotomy: adversarial environments allow for no-regret learning against the best fixed-price mechanism, whereas stochastic environments allow for no-regret learning against the best distribution over prices that is budget balanced in expectation. This gap is significant, as policies balanced in expectation can increase the GFT by a multiplicative factor of two. In this work, we bridge these extremes by studying perturbed markets, where an underlying stochastic distribution is subject to an adversarial corruption $C$. We design an algorithm that adaptively scales with the level of corruption, achieving an $\tilde{\mathcal{O}}(T^{3/4}) + \mathcal{O}(C\log(T))$ regret bound against the best budget-balanced distribution over prices. Simultaneously, our algorithm maintains the worst-case $\tilde{\mathcal{O}}(T^{3/4})$ regret bound relative to a per-round budget-balanced baseline, ensuring optimality even in fully adversarial environments.

Ensuring that AI agents behave safely and beneficially when interacting with other parties has emerged as one of the central challenges of modern AI safety. While mechanism design, as the theory of designing rules to align individual and collective objectives, can incentivize cooperative behavior, it is still an open question whether it alone is sufficient to maximize LLM agents' social welfare. This work proves that the answer is negative: drawing from incomplete contract theory, we formally show that when contracts cannot distinguish all relevant future contingencies, there is a strictly positive welfare loss that no realistic mechanism can eliminate. We show that prosocial agents, who weigh others' welfare alongside their own, can close this gap and achieve outcomes that are socially superior and individually beneficial. Experimentally, we show that in multi-agent resource-allocation environments and canonical social dilemmas where agents are powered by large language models, prosociality is beneficial. The implication for AI safety is clear: to enable cooperative interactions at scale, designing adequate mechanisms is not sufficient; agents must be built to be intrinsically prosocial.

Conversational AI has a fundamental flaw as a knowledge interface: sycophantic chatbots induce epistemic entrenchment and delusional belief spirals even in rational agents. We propose the problem does not stem from the AI model, rooted instead in a systemic consequence of the paradigm shift from user-driven knowledge search to users and agents engaged in strategic, repeated-play communication. We formalize the problem as a Crawford-Sobel cheap talk game, where costless user signals induce a pooling equilibrium. Agents optimized for user satisfaction produce sycophantic strategies that provide identical reinforcement across user types with opposite epistemic incentives: exploratory Growth-seekers'' ($θ_G$) and confirmatory Validation-seekers'' ($θ_V$). Under repeated play, this identification failure creates a coordination trap -- analogous to a Prisoner's Dilemma -- where locally rational feedback loops drive users toward pathologically certain false beliefs. We propose an inference-time mechanism design intervention called an Epistemic Mediator that breaks this pooling equilibrium by introducing a costly signal (epistemic friction), forcing type revelation based on users' asymmetric cognitive costs for processing resistance. A key contribution is Belief Versioning, a git-inspired epistemic meta-memory system that stores healthy beliefs and rollbacks when validation-seeking resistance is detected. In simulation, this intervention achieves a separating equilibrium achieving a $48\times$ differential in spiral rates while passing a learning preservation criterion), evidence that epistemic safety in AI is fundamentally a problem of strategic information environment design rather than simple model alignment.

As Large Language Models (LLMs) transition into conversational agents, generative advertising emerges as a crucial monetization strategy. However, embedding advertisements within unstructured LLM outputs introduces a critical trilemma: balancing advertiser payoffs, platform revenue, and user experience. Existing methods, such as prompt injection or rigid position slots, disrupt semantic coherence and lack a parametric framework for independent control, rendering rigorous mechanism design intractable. To bridge this gap, we introduce Neuron Auctions, a novel paradigm that shifts the auction object from the surface text space to the LLM's internal representations. Leveraging mechanistic interpretability, we identify brand-specific feed-forward network (FFN) neurons and demonstrate that competing brands activate within approximately orthogonal subspaces. This near-perfect independence allows us to define continuous, disentangled intervention budgets (specifically, neuron counts and amplification factors) as auctionable commodities. Building on this computational carrier, we design a continuous menu-based auction mechanism that naturally guarantees strategy-proofness and optimizes revenue for the platform. By explicitly incorporating a user utility penalty into the platform's optimization objective, our framework dynamically prices out overly aggressive interventions. Extensive experiments demonstrate that Neuron Auctions effectively preserve natural discourse quality while achieving an optimal alignment between commercial incentives and user satisfaction.

Decentralized machine learning often relies on outsourcing computations, such as gradient evaluations, to untrusted worker nodes. Existing robust aggregation methods can mitigate malicious behavior under honest-majority assumptions, but may fail when adversaries control a majority of the workers. We study this adversary-dominated setting through an incentive-oriented framework in which reports are accepted and rewarded only when they are mutually consistent up to a threshold. This turns the adversary from a pure saboteur into a rational agent that trades off increasing estimation error against the risk of rejection and loss of reward. We consider iterative optimization under this model. Unlike one-shot computation, iterative learning requires long-horizon decisions: permissive acceptance rules enable faster early progress but admit more adversarial corruption, while strict rules improve estimation accuracy but cause frequent rejections. We propose \mathsf{VISTA}, an adaptive algorithm that tunes the acceptance threshold using the optimization history. Numerical results show that \mathsf{VISTA} improves convergence over static thresholds. We also provide a rigorous convergence analysis showing that, with suitable incentive-aware adaptation, adversary-dominated decentralized learning can retain the asymptotic convergence behavior of standard SGD without relying on an honest majority.

An agent's probability report is paid for twice: by a strictly proper scoring rule, and by an approval rule for the decision it triggers. In this classical decision-coupled setting, non-affine approval is known to defeat truthful reporting. We show the conflict is endogenous: when feasible, the welfare-maximizing approval rule is never affine. The distortion, however, is predictable and can be designed around. There is a reserve report at which pretending to be the marginal type costs exactly the approval prize. Approving at or above the reserve screens types perfectly under every strictly proper score, and the reserve does not depend on the type distribution. A Lipschitz rule with a single kink attains first-best exactly; under strict feasibility no continuously differentiable rule does. The binding constraint is steepness, not smoothness. First-best is attainable within a slope budget if and only if the budget is at least the critical slope: the steepest chord of the pretending cost up to the reserve. Below it the welfare loss is cubic in the shortfall. Where the pretending cost is convex up to the reserve, as for Brier, log and power scores, the critical slope is closed-form. The instances are AI-agent oversight and marketplace operation.

Regulatory approval of products in high-stakes domains such as drug development requires statistical evidence of safety and efficacy through large-scale randomized controlled trials. However, the high financial cost of these trials may deter developers who lack absolute certainty in their product's efficacy, ultimately stifling the development of `moonshot' products that could offer high social utility. To address this inefficiency, in this paper, we introduce a statistical protocol for experimentation where the product developer (the agent) conducts a randomized controlled trial sequentially and the regulator (the principal) partially subsidizes its cost. By modeling the protocol using a belief Markov decision process, we show that the agent's optimal strategy can be found efficiently using dynamic programming. Further, we show that the social utility is a piecewise linear and convex function over the subsidy level the principal selects, and thus the socially optimal subsidy can also be found efficiently using divide-and-conquer. Simulation experiments using publicly available data on antibiotic development and approval demonstrate that our statistical protocol can be used to increase social utility by more than 35$$\% relative to standard, non-sequential protocols.

Strategy-proofness is a fundamental desideratum in mechanism design, ensuring truthful reporting and robust participation. Stability is another central requirement in matching markets, widely adopted in applications such as school choice and labor market clearing. In practice, however, these markets are invariably governed by complex distributional constraints, ranging from diversity quotas and regional balance to global capacity slacks, under which stable matchings often fail to exist. This raises a fundamental question: how to distribute unavoidable instability across agents while preserving strategy-proofness? To address this, we propose \texttt{MenuNet}, a strategy-proof mechanism design framework based on a neural representation of menus. Rather than directly constructing assignments, \texttt{MenuNet} learns to generate personalized probabilistic menus, from which assignments are realized via a structured sequential choice rule that guarantees strategy-proofness by construction. By decomposing stability into fairness (no envy) and non-wastefulness, our approach models these properties as vector-valued quantities and optimizes their distribution through differentiable objectives, providing a principled trade-off between competing axioms. Empirically, \texttt{MenuNet} navigates this trade-off effectively: it consistently outperforms Random Serial Dictatorship (RSD) in terms of envy and Deferred Acceptance (DA) in terms of waste, while maintaining scalability and computational efficiency. These results suggest that learning-based menu mechanisms provide a flexible and scalable paradigm for mechanism design in highly constrained, real-world environments.

Designing mechanical linkages involves combinatorial topology selection and continuous parameter fitting. We show that language models can systematically improve linkage designs through symbolic representations. Language model agents explore discrete topologies while numerical optimisers fit continuous parameters. A symbolic lifting operator translates simulator trajectories into qualitative descriptors, motion labels, temporal predicates, and structural diagnostics that models interpret across iterative design cycles. Across six engineering-relevant motion targets and three open-source models (Llama 3.3 70B, Qwen3 4B, Qwen3 MoE 30B-A3B), the modular architecture reduces geometric error by up to 68% and improves structural validity by up to 134% over monolithic baselines. Critically, 78.6% of iterative refinement trajectories show measurable improvement, with the system correctly diagnosing overconstraint (56.3%) and underconstraint (35.6%) failure modes and proposing grounded corrections. Models across all three families acquire interpretable mechanical reasoning strategies without fine-tuning, demonstrating that principled symbolic abstraction bridges generative AI and the numerical precision required for engineering design.

Large-scale IoT weather sensing networks require incentive mechanisms to sustain participation, yet determining how much value individual data contributions bring to the network remains an open problem. Existing approaches address data quality but not data valuation; in operational meteorology, adjoint-based methods derive value from the forecast model itself but require full data assimilation infrastructure. We propose to utilise differentiable AI weather models to fill this gap and characterise gradient-based attribution on gridded GFS analysis inputs as a candidate value signal, evaluating fidelity, calibration, cost, and gaming vulnerability across more than 400 configurations. Attribution captures near-optimal sensor placement utility with monotonically faithful payments, but can be inflated by adversarial inputs, with detection requiring external baseline data. These findings establish gradient attribution as a computationally validated signal for model-informed reward allocation in participatory weather sensing.

The volume of scientific manuscripts is growing faster than the capacity to evaluate them, yet the institutions that govern peer review have remained largely unchanged. The result is a widening mismatch: reviewer scarcity, noisier assessments, and declining confidence in editorial decisions. Every scientist wants better reviews, but review quality depends on the total burden, which no single author can shift. To isolate this tension, we provide a game-theoretic thought experiment: a voluntary lottery in which authors accept a chance of random pre-review rejection, reducing reviewer burden and improving the quality of surviving evaluations. We show that a Nash equilibrium emerges in which authors voluntarily enter the lottery. Scientists who care about the literature they read, not just the papers they publish, will opt in, raising the quality of published science for all.

Efficient and fair spectrum allocation is a central challenge in 6G networks, where massive connectivity and heterogeneous services continuously compete for limited radio resources. We investigate the use of Large Language Models (LLMs) as bidding agents in repeated 6G spectrum auctions with budget constraints in vehicular networks. Each user equipment (UE) acts as a rational player optimizing its long-term utility through repeated interactions. Using the Vickrey-Clarke-Groves (VCG) mechanism as a benchmark for incentive-compatible, dominant-strategy truthfulness, we compare LLM-guided bidding against truthful and heuristic strategies. Unlike heuristics, LLMs leverage historical outcomes and prompt-based reasoning to adapt their bidding behavior dynamically. Results show that when the theoretical assumptions guaranteeing truthfulness hold, LLM bidders recover near-equilibrium outcomes consistent with VCG predictions. However, when these assumptions break -- such as under static budget constraints -- LLMs sustain longer participation and achieve higher utilities, revealing their ability to approximate adaptive equilibria beyond static mechanism design. This work provides the first systematic evaluation of LLM bidders in repeated spectrum auctions, offering new insights into how AI-driven agents can interact strategically and reshape market dynamics in future 6G networks.

Collusion among autonomous agents poses a critical security threat in embodied multi-agent systems (MAS), where coordinated behaviors can deviate from global objectives and lead to real-world consequences. Existing defenses, primarily based on identity control or post-hoc behavior analysis, are insufficient to address such threats in embodied settings due to delayed feedback and noisy observations in physical environments, which make behavioral deviations difficult to detect accurately and in a timely manner. To address this challenge, we propose a mutagenic incentive intervention approach that mitigates collusion by reshaping agents' payoff structures. By rewarding agents who report collusive behavior and penalizing identified participants, the mechanism induces strategic defection and renders collusion unstable. We further design supporting mechanisms, including reporting deposits, smart contract-based reward enforcement, and encrypted communication, to ensure robustness against misuse of the incentive mechanism and retaliation from penalized agents. We implement the proposed approach in both simulated and real-world embodied environments. Experimental results show that our method effectively suppresses collusion by inducing defection, while preserving system efficiency. It achieves performance comparable to the non-collusion baseline and outperforms representative reactive defenses, thereby fulfilling the desired security objectives. These results demonstrate the effectiveness of proactive incentive design as a practical paradigm for securing embodied multi-agent systems.

Competing firms that share a population of risky customers face a decentralized risk detection problem in which each firm holds fragmentary information whose aggregation would generate social value, but private incentives impede truthful sharing. We develop a dynamic mechanism design framework for this setting and identify three strategic frictions that distinguish it from classical mechanism design with decentralized information: compliance moral hazard, adversarial adaptation, and information destruction through intervention. A temporal value assignment (TVA) mechanism credits firms using a strictly proper scoring rule applied to discounted verified outcomes; under stated assumptions, TVA implements truthful posterior reporting as a Bayes--Nash equilibrium (uniquely optimal at each edge in large federations, with $O(1/m)$ shading in finite systems). A network Shapley characterization shows that under edge-additive coalition value, each firm's marginal contribution is proportional to its weighted cross-firm interaction degree, yielding a sharp prescription for coalition design that prioritizes inter-firm volume over firm size. Embedding TVA in a model of competition among firms, we establish a welfare ordering across four regulatory regimes (autarky, voluntary federation, mandated full sharing, TVA) and identify conditions under which information-sharing mandates without compatible incentive design reduce welfare below autarky: a ``backfiring mandate.'' We illustrate the framework on a 1.4M-transaction synthetic anti-money-laundering benchmark; the same machinery extends to platform fraud, cybersecurity threat intelligence, and supply chain risk detection.

The rapid collapse of decentralized game economies, often characterized by the \textit{death spiral,} remains the most formidable barrier to the mass adoption of Web3 gaming. This paper proposes that the sustainability of an open game economy is predicated on three necessary and sufficient conditions: Anti-Sybil Resilience, Anti-Capital Dominance, and Anti-Inflationary Saturation. The first section establishes a theoretical proof of these conditions, arguing that the absence of any single dimension leads to systemic failure. The second section explores the dialectical relationship between these dimensions, illustrating how unchecked automation and capital-driven monopolies accelerate asset hyperinflation. In the third section, we introduce the Identity-Bound Asset Integrity Model (IBAIM) as a comprehensive technical solution. IBAIM utilizes Zero-Knowledge (ZK) biometric hashing and Account Abstraction (AA) to anchor asset utility to unique human identities through a privacy-preserving and regulatory-compliant architecture. By exogenizing biometric verification to trusted local environments and utilizing Zero-Knowledge Proofs of Identity (zk-PoI), the model ensures absolute user privacy. Furthermore, by implementing an Asymmetric Utility Decay (AUD) engine-whereby assets suffer a vertical 50% utility cliff upon secondary transfer-and an entropy-driven thermodynamic degradation mechanism., the model successfully decouples financial speculation from in-game merit. Finally, we apply this framework to analyze prominent historical failures in the GameFi sector, demonstrating that their collapse was an inevitable consequence of violating these core economic constraints. Our findings suggest that trading a degree of asset liquidity for system integrity is the only viable path toward long-term economic viability in decentralized virtual worlds.

In the design stage of robotic hands, it is not straightforward to quantitatively evaluate the effect of phalanx length ratios on dexterity without defining specific objects or manipulation tasks. Therefore, this study presents a framework for optimizing the phalanx length ratios of a five-finger robotic hand based on potential dexterity within a kinematic structure. The proposed method employs global manipulability, workspace volume, overlap workspace volume, and fingertip sensitivity as evaluation metrics, and identifies optimal design configurations using a weighted objective function under given constraints. The reachable workspace is discretized using a voxel-based representation, and joint motions are discretized at uniform intervals for evaluation. The optimization is performed over design sets for both the thumb and the other fingers, and design combinations that do not generate overlap workspace are excluded. The results show that each phalanx does not contribute equally to the overall dexterity, and the factors influencing each phalanx are identified. In addition, it is observed that the selection of weighting coefficients does not necessarily lead to the direct maximization of individual performance metrics, due to the non-uniform distribution of evaluation measures within the design space. The proposed framework provides a systematic approach to analyze the trade-offs among reachability, dexterity, and controllability, and can serve as a practical guideline for the kinematic design of multi-fingered robotic hands.

Aerobat is a bat-inspired flapping-wing robot with a wing gait generate by the computational structure, a planar linkage of carbon fiber links driven by a single motor. This design minimizes weight but couples both wings to a shared input motor, eliminating independent thrust control and preventing asymmetric maneuvers. This thesis investigates thrust regulation by modifying the effective length of the first radius link $R_1$ in the computational structure. Static experiments using FDM-printed $R_1$ links at three lengths (28.58, 29.33, and 30.08 mm) across 3,4, and 5 Hz flapping frequencies demonstrated that a 1.5 mm length increase produced a 37% increase in peak lift force and shifted peak force timing within the downstroke. An additional experiment using a string-actuated regulator mechanism was performed. Further actuation methods were evaluated: sub-gram micro-servo and piezoelectric slip-stick. After both the string-tension and micro-servo actuation methods failed due to structural member compliance and motor fragility respectively, a TULA-50 piezoelectric slip-stick actuator was selected. Multiple force-amplifying mechanisms were prototyped, resulting in a direct-drive variable-length mechanism. This final mechanism was demonstrated in a preliminary bench-top test, though insufficient force output prevented dynamic testing during flapping. This work establishes linkage-length modulation via embedded slip-stick actuation as a viable approach to independent wing thrust control.

Traditional facility management often relies on centralized decision-making structures that limit stakeholder participation, leading to misalignment with occupant needs and reduced satisfaction. This paper proposes a novel blockchain- and Decentralized Autonomous Organization (DAO)-based framework for community-based facilities management in smart buildings. The framework comprises two key components: a decentralized governance platform that facilitates transparent collective decision-making through blockchain-based voting, and a maintenance management platform with an incentivization mechanism that encourages building occupants to actively contribute to facility upkeep through tokenized rewards. System evaluation includes cost analysis, scalability, data security considerations, usability testing, and semi-structured interviews with facility managers and researchers to assess the platform's usefulness, challenges, and adoption potential. The findings demonstrate the framework's potential as a viable incentivization solution for engaging stakeholders in the collective upkeep and improvement of building infrastructure.

It is increasingly important that LLM agents interact effectively and safely with other goal-pursuing agents, yet, recent works report the opposite trend: LLMs with stronger reasoning capabilities behave less cooperatively in mixed-motive games such as the prisoner's dilemma and public goods settings. Indeed, our experiments show that recent models -- with or without reasoning enabled -- consistently defect in single-shot social dilemmas. To tackle this safety concern, we present the first comparative study of game-theoretic mechanisms designed to enable cooperative outcomes between rational agents in equilibrium. Across four social dilemmas testing distinct components of robust cooperation, we evaluate four families of mechanisms: (1) repeating the game for many rounds, (2) reputation systems, (3) third-party mediators to delegate decision making to, and (4) contract agreements for outcome-conditional payments between players. Among our findings, we establish that contracting and mediation are most effective in achieving cooperative outcomes between capable LLM models, and that repetition-induced cooperation deteriorates drastically when co-players vary. Moreover, we demonstrate that the mechanisms become more effective under evolutionary pressures to maximize individual payoffs.

The performance of legged robots depends strongly on both mechanical design and control, motivating co-design approaches that jointly optimize these parameters. However, most existing co-design studies focus on link dimensions and transmission ratios while neglecting detailed actuator design, particularly motor and gearbox parameter optimization, and are largely limited to serial open-chain mechanisms. In this work, we present a co-design framework for a planar closed-chain five-bar monoped that jointly optimizes mechanical design, motor and gearbox parameters, and control parameters for dynamic jumping. The objective is to maximize jump distance while minimizing mechanical energy consumption. The framework employs a two-stage optimization approach, where actuator optimization generates a mapping from gear ratio to actuator mass, efficiency, and peak torque, which is then incorporated into CMA-ES-based co-design optimization of the robot design and control parameters. Simulation results demonstrate an improvement of approximately 30.4% in jump distance and an 11.5% reduction in mechanical energy consumption compared to a nominal design, highlighting the effectiveness of the proposed framework for high-performance and energy-efficient planar jumping.

Autonomous AI agents are becoming economic actors. They compose deadline-bound services across the device-edge-cloud continuum and contend for capacity no single operator owns. This article asks when decentralised pricing can coordinate them exactly and truthfully, and what their service dependencies must satisfy. We model the pipelines as service-dependency graphs under governance constraints and identify the decisive property: laminarity of the induced leaf-block family. Where it holds, the feasible allocation space is a polymatroid and efficient incentive-compatible clearing exists per epoch; where a crossing breaks it, exactness and truthfulness can fail, while clearing prices survive on every totally unimodular family. The formal results instantiate polymatroid, gross-substitutes and Vickrey-Clarke-Groves theory; the contribution is the bridge from dependency structure to that machinery and an integrator architecture that exposes a laminar interface. The node-level evaluation (32,020 runs), at testbed-calibrated congestion, locates the boundary. One crossing costs exactness in 14.7% of high-load rounds and none on laminar instances, and truthfulness fails where exactness does, across contention. An integrator's inner exposure restores exactness at a cost in admitted volume, and before translation overhead it cuts median latency by 16 to 17 percent. Against truth-free posted prices the tuned market leads at medium load and trails a demand-responsive one in four of six high-load cells. Recorded and composed agent workloads drive the allocation. For platform designers, laminar pipelines admit exact decentralised pricing, truthful under the VCG mechanism, and a crossing needs an integrator's inner exposure.

The rapid proliferation of AI applications has intensified debate on effective regulation of these black-box services. Effective regulation must balance two competing goals: (1) deterring non-compliant providers from entering the market, while (2) retaining compliant ones. We call this ideal the perfect market outcome (PMO). Regulators face two compounding obstacles that make PMO difficult to achieve: providers hold private information and can act strategically to evade compliance, while any evidence drawn or derived from a finite sample carries statistical uncertainty in proving non-compliance. As this information asymmetry and statistical uncertainty is inherent to any effective regulation, we formalise them through a mechanism design framework that explicitly accounts for such statistical uncertainty. This yields a sharp characterisation: a mechanism achieves PMO if and only if the set of non-compliant evidence distributions forms a closed, convex set of probability measures, known in imprecise probability as a credal set. This result serves as a diagnostic tool to determine whether PMO is achievable under a given regulation. We further show that PMO-achieving mechanisms can be constructed from a collection of hypothesis tests, and validate our theoretical contributions through experiments on spurious-feature and fairness-based regulations.

Typically, heuristic/trial-based approaches are used to design soft pneumatic grippers (SPGs). This paper presents a systematic topology optimization framework for developing SPGs. The design-dependent nature of actuating load is modeled using Darcy's law with an added drainage term. A 2D soft arm unit is then optimized as a compliant mechanism under pneumatic loading. To ensure the design is robust and manufacturable, the problem is formulated as a min-max optimization, where output deformations of blueprint and eroded designs are considered. A volume constraint is imposed on the blueprint part, while a strain-energy constraint is enforced on the eroded part. The Method of Moving Asymptotes is employed to solve optimization problems. The optimized 2D part is extruded suitably to generate a 3D unit. Ten such 3D units are assembled to create a gripper arm. Both the optimized 2D unit and the corresponding gripper arm outperform their conventional rectangular designs under pneumatic loading, demonstrating the efficacy of the proposed approach. The arms are fabricated using the SLA printing technique. Numerical and experimental results are compared at different pneumatic loads. Four 3D-printed arms are integrated with a supporting structure to form the SPG. The gripping action of the SPG is demonstrated on objects with different weights, sizes, structures, stiffnesses, and shapes.

In dynamic noncooperative games, each player makes conjectures about other players' reactions before choosing a strategy. However, resulting equilibria may be multiple and do not always lead to desirable outcomes. These issues are typically addressed separately, for example, through opponent modelling and incentive design. Drawing inspiration from conjectural variations games, we propose an incentive design framework in which a coordinator first computes an equilibrium by optimizing a predefined objective function, then communicates this equilibrium as a target for the players to reach. In a centralized setting, the coordinator also optimizes the conjectures to steer the players towards the target. In decentralized settings, players independently compute conjectures and update their strategies based on individual targets. We provide a guarantee of equilibrium existence in both cases. This framework uses conjectures not only to guide the system towards desirable outcomes but also to decouple the game into independent optimization problems, enabling efficient computation and parallelization in large-scale settings. We illustrate our theoretical results on classical representative noncooperative games, demonstrating its application potential.

We study the dynamic allocation of indivisible resources to strategic agents under long-term constraints, where the planner aims to maximize social welfare, satisfy multiple constraints, and elicit near-truthful reports. We find standard primal-dual methods fragile in this setting: agents easily manipulate their reports to distort dual variables, sacrificing social efficiency for individual utility. To address this, we propose the Incentive-Aware Primal-Dual (IAPD) framework. On the primal side, we integrate three components to suppress manipulation: a VCG-based payment neutralizes immediate misreporting benefits, while epoch-based lazy updates and random exploration together ensure potential future gains are outweighed by immediate penalties. On the dual side, to overcome a learning barrier due to lazy updates -- which we call the "price of incentives" -- we design a novel optimistic online learning algorithm, O-FTRL-FP. It utilizes a fixed-point oracle to resolve the circular dependency between optimistic dual variables and the resulting allocations. Ultimately, our mechanism attains $\tilde{\mathcal O}(\sqrt T)$ social welfare regret, satisfies all long-term constraints, and induces a near-truthful equilibrium. It also smoothly generalizes to multi-unit multi-demand allocation problems. Notably, this $\tilde{\mathcal O}(\sqrt T)$ regret near-matches the non-strategic $Ω(\sqrt T)$ lower bound, demonstrating that incentive-awareness can be accommodated at nearly no cost.

Hedonic Games are a well-established model for describing the formation of coalitions. In this work, we considered the design of Non-Obviously Manipulable (NOM) mechanisms, that are mechanisms that bounded rational agents may fail to recognize as manipulable, for two relevant classes of succinctly representable Hedonic Games, namely Additively Separable and Fractional Hedonic Games. In these classes, agents have cardinal scores towards other agents, and their preferences towards different coalitions are determined by aggregating these scores. Moreover, the quality of an outcome can also be easily evaluated through these scores by means of the utilitarian social welfare. We first prove that, when scores can be arbitrary, every welfare-maximizing mechanism is NOM, and, when scores are limited in a continuous interval, then there exist tie-breaking rules making welfare-maximizing mechanisms NOM. Next, we focus on efficient NOM mechanisms, since there is no known polynomial-time algorithm to compute welfare-maximizing outcomes in the considered classes of hedonic games. To this aim, we first prove a characterization of NOM mechanisms that simplifies the class of mechanisms of interest. Then, we design a NOM mechanism returning approximations that essentially match the best-known approximation achievable in polynomial time. Finally, we turn our attention to discrete scores, and specifically, the case that scores are $\{-x, 0, 1\}$ for $x > 0$. We prove that the ability to design welfare-maximizing NOM mechanisms depends on the magnitude of the scores. In particular, for $x > 1$, we prove that a welfare-maximizing NOM mechanism exists only when $x$ is very large. For $x \leq 1$, instead, we observe that a welfare-maximizing NOM mechanism always exists except when $x$ lies in the interval $[a, b]$ where $a \approx 2/n^2$ and $b \approx 1/n$.

Rigid link flapping mechanisms remain the most practical choice for flapping wing micro-aerial vehicles (MAVs) to carry useful payloads and onboard batteries for free flight due to their long-term durability and reliability. However, MAVs with these mechanisms require significant weight reduction to achieve high agility and maneuverability. One approach involves using single-DOF planar rigid linkages, which are rarely optimized dimensionally for high lift and low power, considering their sweeping kinematics and the unsteady aerodynamic effects. We integrated a mechanism simulator based on a quasistatic nonlinear finite element method with an unsteady vortex lattice method-based aerodynamic analysis tool within an optimization routine. We optimized three different mechanism topologies from the literature. Significant power savings were observed up to 34% in some cases, due to increased amplitude and higher lift coefficients resulting from optimized asymmetric sweeping velocity profiles. We also conducted a robustness analysis to quantify performance sensitivity to manufacturing tolerances. It provided a trade-off between performance and reliability and revealed the need for tight manufacturing tolerances and careful material selection. Finally, the analysis helped select the best mechanism topology, as we observed significant variation in sensitivity to manufacturing tolerances and peak input torque values across different topologies for a given design lift value. The presented unified computational tool can find application in flapping mechanism topology optimization, as it can simulate any generic single-DOF planar rigid linkage without supplying kinematics manually.

To alleviate the training burden in federated learning while enhancing convergence speed, Split Federated Learning (SFL) has emerged as a promising approach by combining the advantages of federated and split learning. However, despite its advantages, existing SFL studies have largely overlooked the strategic interactions among self-interested participants during the SFL process. In this framework, the SFL model owner can choose the cut layer to balance the training load between the server and clients, ensuring the necessary level of privacy for the clients. Additionally, the SFL model owner sets incentives to encourage client participation in the SFL process. The optimization strategies employed by the SFL model owner influence clients' decisions regarding the amount of data they contribute, taking into account the shared incentives over clients and anticipated energy consumption from both computation and networking during SFL. To address this framework, we model the problem using a hierarchical decision-making approach, formulated as a single-leader multi-follower Stackelberg game. We demonstrate the existence and uniqueness of the Nash equilibrium among clients and analyze the Stackelberg equilibrium by examining the leader's game. Furthermore, we discuss privacy concerns related to differential privacy and the criteria for selecting the minimum required cut layer. Our findings show that the Stackelberg equilibrium solution maximizes the utility for both the clients and the SFL model owner while achieving a well-balanced trade-off between model accuracy and the associated computing and networking overhead during the SFL process.

We study the welfare-maximizing allocation of heterogeneous objects when screening uses costly effort rather than monetary transfers. No-screening mechanisms perform well as object variety increases. In a symmetric continuous market with i.i.d. values whose CDF is log-concave, the multidimensional problem reduces exactly to a single-dimensional problem in agents' best-option values. More options make low best-option values rarer, weakening the case for screening. We characterize when no screening is optimal and show it remains optimal as variety expands. Large-variety limits and numerical results for finite, correlated markets support this pattern. We apply these results to propose an invitation-based vaccine appointment system.