ShanghaiTech University
AI Insights
- Inaccurate or incomplete data can lead to suboptimal results. (ML: 0.98)
- Machine Learning (ML): A subfield of artificial intelligence that enables systems to learn from data without being explicitly programmed. (ML: 0.98)
- The system's performance may be affected by the quality and accuracy of the input data. (ML: 0.97)
- You need to find reliable partners to supply raw materials and components. (ML: 0.93)
- Imagine you're a manager at a company that produces electronics. (ML: 0.92)
- Partner Selection: The process of identifying and selecting suitable partners for collaboration within the supply chain. (ML: 0.90)
- Previous research has focused on developing optimization models for supply chain partner selection, but these approaches often rely on simplified assumptions and neglect the complexities of real-world supply chains. (ML: 0.89)
- Its interactive interface and machine learning capabilities facilitate the exploration of complex supply chain dynamics and provide actionable insights for optimization. (ML: 0.88)
- SCSimulator is a visual analytics tool for supply chain partner selection that leverages large-scale datasets and machine learning algorithms. (ML: 0.85)
- SCSimulator is an innovative visual analytics tool that empowers supply chain professionals to optimize their partner selection processes by leveraging large-scale datasets and machine learning algorithms. (ML: 0.85)
- Supply Chain (SC): A network of organizations, people, activities, information, and resources involved in producing and delivering a product or service from raw materials to end customers. (ML: 0.85)
- It provides an interactive interface for users to upload data, configure simulation parameters, and explore the temporal evolution of supply chains. (ML: 0.84)
- SCSimulator is a valuable tool for supply chain professionals, enabling them to make informed decisions about partner selection. (ML: 0.73)
- SCSimulator is like a super-smart assistant that helps you analyze large amounts of data, identify the best partners for your business, and make informed decisions about collaborations. (ML: 0.73)
Abstract
Supply chains (SCs), complex networks spanning from raw material acquisition to product delivery, with enterprises as interconnected nodes, play a pivotal role in organizational success. However, optimizing SCs remains challenging, particularly in partner selection, a key bottleneck shaped by competitive and cooperative dynamics. This challenge constitutes a multi-objective dynamic game requiring a synergistic integration of Multi-Criteria Decision-Making and Game Theory. Traditional approaches, grounded in mathematical simplifications and managerial heuristics, fail to capture real-world intricacies and risk introducing subjective biases. Multi-agent simulation offers promise, but prior research has largely relied on fixed, uniform agent logic, limiting practical applicability. Recent advances in LLMs create opportunities to represent complex SC requirements and hybrid game logic. However, challenges persist in modeling dynamic SC relationships, ensuring interpretability, and balancing agent autonomy with expert control. We present SCSimulator, a visual analytics framework that integrates LLM-driven MAS with human-in-the-loop collaboration for SC partner selection. It simulates SC evolution via adaptive network structures and enterprise behaviors, which are visualized via interpretable interfaces. By combining CoT reasoning with XAI techniques, it generates multi-faceted, transparent explanations of decision trade-offs. Users can iteratively adjust simulation settings to explore outcomes aligned with their expectations and strategic priorities. Developed through iterative co-design with SC experts and industry managers, SCSimulator serves as a proof-of-concept, offering methodological contributions and practical insights for future research on SC decision-making and interactive AI-driven analytics. Usage scenarios and a user study demonstrate the system's effectiveness and usability.
Supply chains (SCs), complex networks spanning from raw material acquisition to product delivery, with enterprises as interconnected nodes, play a pivotal role in organizational success. However, optimizing SCs remains challenging, particularly in partner selection, a key bottleneck shaped by competitive and cooperative dynamics. This challenge constitutes a multi-objective dynamic game requiring a synergistic integration of Multi-Criteria Decision-Making and Game Theory. Traditional approaches, grounded in mathematical simplifications and managerial heuristics, fail to capture real-world intricacies and risk introducing subjective biases. Multi-agent simulation offers promise, but prior research has largely relied on fixed, uniform agent logic, limiting practical applicability. Recent advances in LLMs create opportunities to represent complex SC requirements and hybrid game logic. However, challenges persist in modeling dynamic SC relationships, ensuring interpretability, and balancing agent autonomy with expert control. We present SCSimulator, a visual analytics framework that integrates LLM-driven MAS with human-in-the-loop collaboration for SC partner selection. It simulates SC evolution via adaptive network structures and enterprise behaviors, which are visualized via interpretable interfaces. By combining CoT reasoning with XAI techniques, it generates multi-faceted, transparent explanations of decision trade-offs. Users can iteratively adjust simulation settings to explore outcomes aligned with their expectations and strategic priorities. Developed through iterative co-design with SC experts and industry managers, SCSimulator serves as a proof-of-concept, offering methodological contributions and practical insights for future research on SC decision-making and interactive AI-driven analytics. Usage scenarios and a user study demonstrate the system's effectiveness and usability.
Why we are recommending this paper?
Due to your Interest in Supply Chain
This paper directly addresses partner selection within supply chains, a core area of interest. Utilizing LLM-driven multi-agent simulation offers a powerful approach to optimizing complex supply chain dynamics, aligning with the userâs focus on AI for supply chain optimization.
Due to your Interest in Supply Chain
This paper directly addresses partner selection within supply chains, a core area of interest. Utilizing LLM-driven multi-agent simulation offers a powerful approach to optimizing complex supply chain dynamics, aligning with the userâs focus on AI for supply chain optimization.
Binghamton University, State University of New York
AI Insights
- The development of agentic AI systems may be hindered by the lack of standardization and interoperability between different AI technologies. (ML: 0.93)
- The proposed framework may require significant computational resources and data storage capacity. (ML: 0.92)
- Neuro-symbolic AI is a key technology for developing agentic systems that can reason, learn, and interact with humans. (ML: 0.92)
- Neuro-symbolic AI: A type of AI that combines the strengths of neural networks and symbolic reasoning to enable more efficient and effective decision-making. (ML: 0.91)
- Agentic AI has been studied in various fields, including computer science, cognitive psychology, and philosophy. (ML: 0.90)
- The application of agentic AI in business processes can lead to improved productivity, reduced costs, and enhanced customer satisfaction. (ML: 0.89)
- The proposed framework for designing agentic AI systems using neuro-symbolic AI has the potential to revolutionize business process optimization by enabling more accurate and efficient decision-making. (ML: 0.86)
- The authors propose a framework for designing agentic AI systems using neuro-symbolic AI and provide an example of its application in a business process optimization problem. (ML: 0.86)
- The paper discusses the concept of agentic AI and its application in business processes. (ML: 0.83)
- Agentic AI: A type of artificial intelligence that is capable of reasoning, learning, and interacting with humans in a way that is similar to human agency. (ML: 0.80)
Abstract
Current business environments require organizations to continuously reconfigure cross-functional processes, yet enterprise systems are still organized around siloed departments, rigid workflows, and hard-coded automation. Meanwhile large language models (LLMs) excel at interpreting natural language and unstructured data but lack deterministic, verifiable execution of complex business logic. To address this gap, here we introduce AUTOBUS, an Autonomous Business System that integrates LLM-based AI agents, predicate-logic programming, and business-semantics-centric enterprise data into a coherent neuro-symbolic AI architecture for orchestrating end-to-end business initiatives. AUTOBUS models an initiative as a network of tasks with explicit pre/post conditions, required data, evaluation rules, and API-level actions. Enterprise data is organized as a knowledge graph whose entities, relationships, and constraints are translated into logic facts and foundational rules, providing the semantic grounding for task reasoning. Core AI agents synthesize task instructions, enterprise semantics, and available tools into task-specific logic programs, which are executed by a logic engine that enforces constraints, coordinates auxiliary tools, and orchestrate execution of actions and outcomes. Humans define and maintain the semantics, policies and task instructions, curate tools, and supervise high-impact or ambiguous decisions, ensuring accountability and adaptability. We detail the AUTOBUS architecture, the anatomy of the AI agent generated logic programs, and the role of humans and auxiliary tools in the lifecycle of a business initiative.
Current business environments require organizations to continuously reconfigure cross-functional processes, yet enterprise systems are still organized around siloed departments, rigid workflows, and hard-coded automation. Meanwhile large language models (LLMs) excel at interpreting natural language and unstructured data but lack deterministic, verifiable execution of complex business logic. To address this gap, here we introduce AUTOBUS, an Autonomous Business System that integrates LLM-based AI agents, predicate-logic programming, and business-semantics-centric enterprise data into a coherent neuro-symbolic AI architecture for orchestrating end-to-end business initiatives. AUTOBUS models an initiative as a network of tasks with explicit pre/post conditions, required data, evaluation rules, and API-level actions. Enterprise data is organized as a knowledge graph whose entities, relationships, and constraints are translated into logic facts and foundational rules, providing the semantic grounding for task reasoning. Core AI agents synthesize task instructions, enterprise semantics, and available tools into task-specific logic programs, which are executed by a logic engine that enforces constraints, coordinates auxiliary tools, and orchestrate execution of actions and outcomes. Humans define and maintain the semantics, policies and task instructions, curate tools, and supervise high-impact or ambiguous decisions, ensuring accountability and adaptability. We detail the AUTOBUS architecture, the anatomy of the AI agent generated logic programs, and the role of humans and auxiliary tools in the lifecycle of a business initiative.
Why we are recommending this paper?
Due to your Interest in AI for Supply Chain
The paperâs exploration of autonomous business systems through neuro-symbolic AI is highly relevant to optimizing decision-making processes within complex environments. This approach aligns with the userâs interest in AI for pricing optimization and overall system design.
Due to your Interest in AI for Supply Chain
The paperâs exploration of autonomous business systems through neuro-symbolic AI is highly relevant to optimizing decision-making processes within complex environments. This approach aligns with the userâs interest in AI for pricing optimization and overall system design.
Delft University of Technology
AI Insights
- Ecological validity: The extent to which the results of an experiment can be generalized to real-world situations. (ML: 0.99)
- Fair compensation: Ensuring that participants receive a fair wage for their work, considering factors such as task complexity and required expertise. (ML: 0.98)
- The Incentive-Tuning Framework provides a standardized solution for designing effective incentive schemes in human-AI decision-making studies. (ML: 0.97)
- The Incentive-Tuning Framework is a standardized solution for designing and documenting effective incentive schemes in human-AI decision-making studies. (ML: 0.97)
- Incentive scheme: A system of rewards or penalties designed to motivate participants in human-AI decision-making studies. (ML: 0.97)
- The Incentive-Tuning Framework aims to address methodological challenges surrounding incentive design and provide a solution for researchers to tune 'appropriate' incentive schemes for their specific studies. (ML: 0.97)
- A well-designed framework can foster a standardized, systematic, and comprehensive approach to designing effective incentive schemes. (ML: 0.96)
- Researchers should prioritize intentional design and alignment with research goals when employing an incentive scheme. (ML: 0.96)
- Researchers should explicitly identify the purpose of employing an incentive scheme to ensure intentional design and alignment with research goals. (ML: 0.95)
- The framework consists of five steps: identifying the purpose of employing an incentive scheme, coming up with a base pay, designing a bonus structure, gathering participant feedback, and reflecting on design implications. (ML: 0.88)
Abstract
AI has revolutionised decision-making across various fields. Yet human judgement remains paramount for high-stakes decision-making. This has fueled explorations of collaborative decision-making between humans and AI systems, aiming to leverage the strengths of both. To explore this dynamic, researchers conduct empirical studies, investigating how humans use AI assistance for decision-making and how this collaboration impacts results. A critical aspect of conducting these studies is the role of participants, often recruited through crowdsourcing platforms. The validity of these studies hinges on the behaviours of the participants, hence effective incentives that can potentially affect these behaviours are a key part of designing and executing these studies. In this work, we aim to address the critical role of incentive design for conducting empirical human-AI decision-making studies, focusing on understanding, designing, and documenting incentive schemes. Through a thematic review of existing research, we explored the current practices, challenges, and opportunities associated with incentive design for human-AI decision-making empirical studies. We identified recurring patterns, or themes, such as what comprises the components of an incentive scheme, how incentive schemes are manipulated by researchers, and the impact they can have on research outcomes. Leveraging the acquired understanding, we curated a set of guidelines to aid researchers in designing effective incentive schemes for their studies, called the Incentive-Tuning Framework, outlining how researchers can undertake, reflect on, and document the incentive design process. By advocating for a standardised yet flexible approach to incentive design and contributing valuable insights along with practical tools, we hope to pave the way for more reliable and generalizable knowledge in the field of human-AI decision-making.
AI has revolutionised decision-making across various fields. Yet human judgement remains paramount for high-stakes decision-making. This has fueled explorations of collaborative decision-making between humans and AI systems, aiming to leverage the strengths of both. To explore this dynamic, researchers conduct empirical studies, investigating how humans use AI assistance for decision-making and how this collaboration impacts results. A critical aspect of conducting these studies is the role of participants, often recruited through crowdsourcing platforms. The validity of these studies hinges on the behaviours of the participants, hence effective incentives that can potentially affect these behaviours are a key part of designing and executing these studies. In this work, we aim to address the critical role of incentive design for conducting empirical human-AI decision-making studies, focusing on understanding, designing, and documenting incentive schemes. Through a thematic review of existing research, we explored the current practices, challenges, and opportunities associated with incentive design for human-AI decision-making empirical studies. We identified recurring patterns, or themes, such as what comprises the components of an incentive scheme, how incentive schemes are manipulated by researchers, and the impact they can have on research outcomes. Leveraging the acquired understanding, we curated a set of guidelines to aid researchers in designing effective incentive schemes for their studies, called the Incentive-Tuning Framework, outlining how researchers can undertake, reflect on, and document the incentive design process. By advocating for a standardised yet flexible approach to incentive design and contributing valuable insights along with practical tools, we hope to pave the way for more reliable and generalizable knowledge in the field of human-AI decision-making.
Why we are recommending this paper?
Due to your Interest in AI for Pricing
This work investigates collaborative decision-making between humans and AI, a critical area for leveraging the strengths of both. The focus on incentive design directly relates to optimizing human behavior within AI-driven systems, aligning with the userâs interest in AI for supply chain optimization.
Due to your Interest in AI for Pricing
This work investigates collaborative decision-making between humans and AI, a critical area for leveraging the strengths of both. The focus on incentive design directly relates to optimizing human behavior within AI-driven systems, aligning with the userâs interest in AI for supply chain optimization.
Monash University
AI Insights
- The use of a probabilistic MNL model to capture stochastic perception errors in user decision-making may oversimplify the complexity of real-world user behavior. (ML: 0.97)
- The framework assumes that EV users have perfect knowledge of their travel times, waiting times, and charging prices, which may not be realistic in practice. (ML: 0.96)
- The framework aims to achieve a system-level performance improvement that balances operator revenue and user welfare. (ML: 0.92)
- The use of a Stackelberg game formulation allows the government authority to balance operator revenue and user welfare. (ML: 0.90)
- The proposed framework can mitigate congestion-induced queuing losses and improve resource allocation efficiency through dynamic pricing mechanisms. (ML: 0.89)
- The Cross-Entropy Method (CEM) is used for upper-level dynamic pricing optimization, combined with the Method of Successive Averages (MSA) for lower-level EV-CS equilibrium analysis. (ML: 0.84)
- Cross-Entropy Method (CEM): A Monte Carlo-based framework for estimating rare-event probabilities and reformulating optimization processes into probabilistic learning problems. (ML: 0.83)
- The resulting system is designed as a Stackelberg game, in which the government authority acts as the leader by setting time-varying prices, while EV users act as followers and respond by selecting their preferred Cs. (ML: 0.81)
- The proposed framework formulates a dynamic interaction and optimization process between EVs and CSs within a public charging network. (ML: 0.75)
- Stackelberg game: A type of game where one player (the leader) makes decisions first, and the other players (the followers) respond to those decisions. (ML: 0.67)
Abstract
The rapid adoption of electric vehicles (EVs) introduces complex spatiotemporal demand management challenges for charging station operators (CSOs), exacerbated by demand imbalances, behavioral heterogeneity, and system uncertainty. Traditional dynamic pricing models, often relying on deterministic EV-CS pairings and network equilibrium assumptions, frequently oversimplify user behavior and lack scalability. This study proposes a stochastic, behaviorally heterogeneous dynamic pricing framework formulated as a bi-level Stackelberg game. The upper level optimizes time-varying pricing to maximize system-wide utility, while the lower level models decentralized EV users via a multinomial logit (MNL) choice model incorporating price sensitivity, battery aging, risk attitudes, and network travel costs. Crucially, the model avoids network equilibrium constraints to enhance scalability, with congestion effects represented via queuing-theoretic approximations. To efficiently solve the resulting large-scale optimization problem, a rolling-horizon approach combining the Dynamic Probabilistic Sensitivity Analysis-guided Cross-Entropy Method (PSA-CEM) with the Method of Successive Averages (MSA) is implemented. A real-world case study in Clayton, Melbourne, validates the framework using 22 charging stations. Simulation results demonstrate that the proposed mechanism substantially reduces queuing penalties and improves user utility compared to fixed and time-of-use pricing. The framework provides a robust, scalable tool for strategic EV charging management, balancing realism with computational efficiency.
The rapid adoption of electric vehicles (EVs) introduces complex spatiotemporal demand management challenges for charging station operators (CSOs), exacerbated by demand imbalances, behavioral heterogeneity, and system uncertainty. Traditional dynamic pricing models, often relying on deterministic EV-CS pairings and network equilibrium assumptions, frequently oversimplify user behavior and lack scalability. This study proposes a stochastic, behaviorally heterogeneous dynamic pricing framework formulated as a bi-level Stackelberg game. The upper level optimizes time-varying pricing to maximize system-wide utility, while the lower level models decentralized EV users via a multinomial logit (MNL) choice model incorporating price sensitivity, battery aging, risk attitudes, and network travel costs. Crucially, the model avoids network equilibrium constraints to enhance scalability, with congestion effects represented via queuing-theoretic approximations. To efficiently solve the resulting large-scale optimization problem, a rolling-horizon approach combining the Dynamic Probabilistic Sensitivity Analysis-guided Cross-Entropy Method (PSA-CEM) with the Method of Successive Averages (MSA) is implemented. A real-world case study in Clayton, Melbourne, validates the framework using 22 charging stations. Simulation results demonstrate that the proposed mechanism substantially reduces queuing penalties and improves user utility compared to fixed and time-of-use pricing. The framework provides a robust, scalable tool for strategic EV charging management, balancing realism with computational efficiency.
Why we are recommending this paper?
Due to your Interest in AI for Pricing Optimization
The paper tackles dynamic pricing for EV charging, a key area within supply chain optimization and pricing strategies. The use of a Stackelberg game framework provides a sophisticated approach to managing demand and uncertainty, directly addressing the user's interest in pricing.
Due to your Interest in AI for Pricing Optimization
The paper tackles dynamic pricing for EV charging, a key area within supply chain optimization and pricing strategies. The use of a Stackelberg game framework provides a sophisticated approach to managing demand and uncertainty, directly addressing the user's interest in pricing.
Wayne State University
AI Insights
- The framework assumes a deterministic scenario for the first stage, which may not capture all uncertainties. (ML: 0.92)
- The framework integrates pre-event flexible-capacity allocation with post-event optimal dispatch, supported by CVaR-based risk modeling to capture extreme load-ramp uncertainty. (ML: 0.83)
- FCMs are modeled within a scalable optimization structure, providing a practical foundation for resilient planning in digital-era power systems. (ML: 0.77)
- DRO: Distributionally Robust Optimization CVaR: Conditional Value-at-Risk MILP: Mixed-Integer Linear Programming FCMs: Flexible Capacity Modules The proposed framework provides a practical foundation for resilient planning in digital-era power systems. (ML: 0.74)
- A two-stage risk-averse DRO-MILP framework is proposed to manage emerging AI/data center demand shocks and enhance distribution-grid resilience. (ML: 0.74)
- The framework is suitable for application on the IEEE 33-bus system or larger IEEE feeders capable of representing AI-scale loads. (ML: 0.59)
Abstract
The rapid growth of artificial intelligence (AI)-driven data centers is reshaping electricity demand patterns. This is achieved by introducing fast, multi-gigawatt load ramps that challenge the stability and resilience of modern power systems. Traditional resilience frameworks focus mainly on physical outages and largely overlook these emerging digital-era disturbances. This paper proposes a unified two-stage, risk-aware distributionally robust optimization (DRO)-MILP framework that coordinates the pre-allocation and post-event dispatch of Flexible Capacity Modules (FCMs), including BESS, fast-ramping generation, demand response, and potential long-duration storage. Stage-I optimally positions FCMs using DRO with CVaR to hedge against uncertain AI load surges. Stage-II models real-time stabilization following stochastic demand-shock scenarios, minimizing imbalance, unserved energy, and restoration penalties. The framework is designed to be applied on IEEE 33-bus system or expanded for scalability to larger IEEE test feeders capable of representing AI-scale loads. This contributes a scalable planning tool for resilient, AI-integrated distribution grids.
The rapid growth of artificial intelligence (AI)-driven data centers is reshaping electricity demand patterns. This is achieved by introducing fast, multi-gigawatt load ramps that challenge the stability and resilience of modern power systems. Traditional resilience frameworks focus mainly on physical outages and largely overlook these emerging digital-era disturbances. This paper proposes a unified two-stage, risk-aware distributionally robust optimization (DRO)-MILP framework that coordinates the pre-allocation and post-event dispatch of Flexible Capacity Modules (FCMs), including BESS, fast-ramping generation, demand response, and potential long-duration storage. Stage-I optimally positions FCMs using DRO with CVaR to hedge against uncertain AI load surges. Stage-II models real-time stabilization following stochastic demand-shock scenarios, minimizing imbalance, unserved energy, and restoration penalties. The framework is designed to be applied on IEEE 33-bus system or expanded for scalability to larger IEEE test feeders capable of representing AI-scale loads. This contributes a scalable planning tool for resilient, AI-integrated distribution grids.
Why we are recommending this paper?
Due to your Interest in AI for Pricing
This paper addresses demand shocks in AI-driven data centers, a critical aspect of supply chain resilience and risk management. The methodological framework offers a robust approach to managing uncertainty, aligning with the userâs interest in supply chain optimization and risk-averse strategies.
Due to your Interest in AI for Pricing
This paper addresses demand shocks in AI-driven data centers, a critical aspect of supply chain resilience and risk management. The methodological framework offers a robust approach to managing uncertainty, aligning with the userâs interest in supply chain optimization and risk-averse strategies.
Johns Hopkins University
AI Insights
- It's like using a super-powerful calculator to figure out the right price. (ML: 0.98)
- You need to take into account all the information available up to a certain point in time. (ML: 0.97)
- Imagine you're trying to price a financial instrument, like a stock or bond. (ML: 0.92)
- It discusses various concepts such as operator algebras, conditional expectations, and martingales in the context of financial markets. (ML: 0.90)
- It may be challenging to follow without prior knowledge of operator algebras and conditional expectations. (ML: 0.89)
- The text is quite technical and assumes a high level of mathematical background. (ML: 0.87)
- Axiom 3.8: {Nt}tâ[0,T] is an increasing family of abelian von Neumann subalgebras. (ML: 0.82)
- Axiom 3.27: {St}tâ[0,T], the price process, is an (Nt,Et)-martingale under the Local Informational Efficiency Principle (LIEP). (ML: 0.81)
- The text appears to be setting up a framework for quantum pricing using operator algebras and conditional expectations. (ML: 0.79)
- It assumes the existence of an increasing family of abelian von Neumann subalgebras, a faithful normal state on M, and normal ÏÏ-preserving conditional expectations satisfying the tower property. (ML: 0.78)
- Definition 3.22: Existence of normal ÏÏ-preserving conditional expectations Et:MâNtsatisfying the tower property. (ML: 0.75)
- The text discusses how to use mathematical tools called operator algebras and conditional expectations to do this. (ML: 0.73)
- The text discusses the mathematical framework for quantum pricing, focusing on operator algebras, conditional expectations, and martingales in financial markets. (ML: 0.72)
- Definition 3.4: ÏÏ is a faithful normal state on M. (ML: 0.69)
- This text appears to be a continuation of a mathematical or financial document, likely from a chapter on quantum pricing. (ML: 0.60)
- The text references various literature on the topic, including Ethier-Kurtz [13] and Stroock-Varadhan [14], which are likely used as sources for the mathematical framework discussed in the chapter. (ML: 0.52)
Abstract
Let $M$ be a von Neumann algebra and let $(N_t)_{t\in[0,T]}$ be an increasing family of abelian von Neumann subalgebras encoding a (classical) information flow. Fix a faithful normal state $\varphi_Ï$ on $M$ and assume a filtration of normal $\varphi_Ï$-preserving conditional expectations $E_t:M\to N_t$ satisfying the tower property. For self-adjoint observables affiliated with $M$, we introduce a truncation-stable notion of $(N_t,E_t)$-martingales via bounded functional-calculus cutoffs $f_n$, and formulate a \emph{Local Informational Efficiency Principle} requiring symmetrically discounted traded prices to be martingales in this localized sense. Assuming the existence of a pricing state $\varphi^\star$ and a compatible family of normal $\varphi^\star$-preserving conditional expectations $(E_t^\star)$, we define for bounded terminal payoffs $X\in M_T$ the dynamic pricing operator \[ Î _t(X):=B_t^{1/2}\,E_t^\star\!\bigl(B_T^{-1/2}XB_T^{-1/2}\bigr)\,B_t^{1/2}, \] where $(B_t)$ is a strictly positive numĂ©raire adapted to $(N_t)$. We prove that $(Î _t)_{t\in[0,T]}$ is normal, completely positive, unital, $N_t$-bimodular, and time-consistent; in the commutative reduction it coincides with classical risk-neutral valuation by conditional expectation. We further develop an $L^2(M,\varphi_Ï)$-prediction theory: $E_t$ acts as the $L^2$-optimal predictor and yields a canonical innovation decomposition. For differentiable parametric families of normal states, we introduce an operator-valued Fisher information relative to $(N_t)$ and derive a noncommutative CramĂ©r--Rao inequality giving a quantitative lower bound on conditional mean-square prediction error under information constraints; the bound is computed explicitly for compound Poisson lattice-jump models under the risk-neutral constraint $\sum_αγ_α(e^{αÎx}-1)=r$.
Let $M$ be a von Neumann algebra and let $(N_t)_{t\in[0,T]}$ be an increasing family of abelian von Neumann subalgebras encoding a (classical) information flow. Fix a faithful normal state $\varphi_Ï$ on $M$ and assume a filtration of normal $\varphi_Ï$-preserving conditional expectations $E_t:M\to N_t$ satisfying the tower property. For self-adjoint observables affiliated with $M$, we introduce a truncation-stable notion of $(N_t,E_t)$-martingales via bounded functional-calculus cutoffs $f_n$, and formulate a \emph{Local Informational Efficiency Principle} requiring symmetrically discounted traded prices to be martingales in this localized sense. Assuming the existence of a pricing state $\varphi^\star$ and a compatible family of normal $\varphi^\star$-preserving conditional expectations $(E_t^\star)$, we define for bounded terminal payoffs $X\in M_T$ the dynamic pricing operator \[ Î _t(X):=B_t^{1/2}\,E_t^\star\!\bigl(B_T^{-1/2}XB_T^{-1/2}\bigr)\,B_t^{1/2}, \] where $(B_t)$ is a strictly positive numĂ©raire adapted to $(N_t)$. We prove that $(Î _t)_{t\in[0,T]}$ is normal, completely positive, unital, $N_t$-bimodular, and time-consistent; in the commutative reduction it coincides with classical risk-neutral valuation by conditional expectation. We further develop an $L^2(M,\varphi_Ï)$-prediction theory: $E_t$ acts as the $L^2$-optimal predictor and yields a canonical innovation decomposition. For differentiable parametric families of normal states, we introduce an operator-valued Fisher information relative to $(N_t)$ and derive a noncommutative CramĂ©r--Rao inequality giving a quantitative lower bound on conditional mean-square prediction error under information constraints; the bound is computed explicitly for compound Poisson lattice-jump models under the risk-neutral constraint $\sum_αγ_α(e^{αÎx}-1)=r$.
Why we are recommending this paper?
Due to your Interest in Pricing
Due to your Interest in Pricing
University of San Francisco
AI Insights
- Pricing responses become highly asymmetric across segments when loyal customers are highly price-sensitive while strategic customers are relatively price-insensitive. (ML: 0.96)
- PMGs act as a demand-dependent adjustment governing how price-aware customers are served. (ML: 0.95)
- Conditional on bundling, PMG adoption varies systematically with customer price-sensitivities and underlying demand conditions. (ML: 0.94)
- Conditional on bundling, PMG adoption follows a clear trade-off between capturing strategic demand and conceding margins on loyal, price-aware customers. (ML: 0.93)
- Bundling is a primary strategic lever for Retailer 1. (ML: 0.91)
- Bundling can be an effective strategy for retailers to increase sales and revenue, especially in markets with complementary goods. (ML: 0.89)
- Price-Matching Guarantee (PMG): A policy where a retailer promises to match the lower price offered by a competitor for a specific product or service. (ML: 0.87)
- Bundling: A retail strategy where multiple products or services are sold together at a discounted price. (ML: 0.84)
- Equilibrium existence is more robust when bundle-level complementarity λl is sufficiently high and item-level complementarity Ξl is sufficiently low. (ML: 0.81)
- Mixed bundling strictly dominates no bundling whenever an equilibrium exists. (ML: 0.73)
Abstract
We study mixed bundling and competitive price-matching guarantees (PMGs) in a duopoly selling complementary products to heterogeneous customers. One retailer offers mixed bundling while the rival sells only a bundle. We characterize unique pure-strategy Nash equilibria across subgames and compare them to a no-bundling benchmark. Mixed bundling strictly dominates whenever an equilibrium exists. Conditional on bundling, PMG adoption trades off strategic demand capture against margin losses on loyal customers and varies systematically with relative demand responsiveness to prices and complementarities.
We study mixed bundling and competitive price-matching guarantees (PMGs) in a duopoly selling complementary products to heterogeneous customers. One retailer offers mixed bundling while the rival sells only a bundle. We characterize unique pure-strategy Nash equilibria across subgames and compare them to a no-bundling benchmark. Mixed bundling strictly dominates whenever an equilibrium exists. Conditional on bundling, PMG adoption trades off strategic demand capture against margin losses on loyal customers and varies systematically with relative demand responsiveness to prices and complementarities.
Why we are recommending this paper?
Due to your Interest in Pricing
Due to your Interest in Pricing
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