[Paper Review] Cumulative Prospect Theory Based Dynamic Pricing for Shared Mobility on Demand Services

Yue Guan, Anuradha M. Annaswamy+1 more|arXiv (Cornell University)|Apr 3, 2019

Economic and Environmental Valuation20 references4 citations

TL;DR

This paper proposes a dynamic pricing strategy for Shared Mobility on Demand Services (SMoDS) using Cumulative Prospect Theory (CPT) to model passenger behavior under uncertainty. By incorporating risk attitudes, loss aversion, and probability distortion, the framework enables optimal pricing that balances revenue and ridership, outperforming traditional utility-based models in behavioral realism and system performance.

ABSTRACT

Cumulative Prospect Theory (CPT) is a modeling tool widely used in behavioral economics and cognitive psychology that captures subjective decision making of individuals under risk or uncertainty. In this paper, we propose a dynamic pricing strategy for Shared Mobility on Demand Services (SMoDSs) using a passenger behavioral model based on CPT. This dynamic pricing strategy together with dynamic routing via a constrained optimization algorithm that we have developed earlier, provide a complete solution customized for SMoDS of multi-passenger transportation. The basic principles of CPT and the derivation of the passenger behavioral model in the SMoDS context are described in detail. The implications of CPT on dynamic pricing of the SMoDS are delineated using computational experiments involving passenger preferences. These implications include interpretation of the classic fourfold pattern of risk attitudes, strong risk aversion over mixed prospects, and behavioral preferences of self reference. Overall, it is argued that the use of the CPT framework corresponds to a crucial building block in designing socio-technical systems by allowing quantification of subjective decision making under risk or uncertainty that is perceived to be otherwise qualitative.

Motivation & Objective

• Address the limitations of traditional Expected Utility Theory in modeling passenger decision-making under uncertainty in dynamic ride-sharing systems.
• Integrate behavioral economics into dynamic pricing for SMoDS by leveraging Cumulative Prospect Theory (CPT) to capture subjective risk attitudes.
• Develop a complete socio-technical system combining CPT-based dynamic pricing with constrained dynamic routing to optimize both passenger utility and platform performance.
• Analyze how key CPT features—framing effects, loss aversion, and probability weighting—impact pricing strategies and acceptance rates.
• Provide a computationally validated framework that quantifies subjective decision-making under uncertainty, enabling data-driven dynamic tariff setting.

Proposed method

• Formulate a passenger behavioral model based on CPT, where utility depends on travel time and dynamic tariff, with value function and probability weighting functions capturing risk preferences.
• Apply CPT’s cumulative weighting of probabilities to avoid stochastic dominance violations, ensuring consistent decision-making under uncertainty.
• Integrate the CPT-based utility model with a previously developed Alternating Minimization (AltMin) algorithm for dynamic routing, enabling joint optimization of routes and tariffs.
• Use a probabilistic acceptance model where passenger acceptance of a ride offer is determined by the CPT-based subjective utility, modeled via a logit-type choice function.
• Derive analytical properties of the acceptance probability function, proving monotonicity with respect to tariff and time, ensuring predictable system behavior.
• Conduct computational experiments to evaluate risk attitude effects (e.g., fourfold pattern, strong risk aversion) on pricing and system outcomes.

Experimental results

Research questions

• RQ1 How can Cumulative Prospect Theory be adapted to model passenger decision-making in dynamic, uncertain ride-sharing environments?
• RQ2 What impact do CPT features—such as loss aversion, probability weighting, and framing—have on dynamic pricing and passenger acceptance rates?
• RQ3 How does the proposed CPT-based pricing strategy compare to traditional utility-based models in balancing revenue and ridership?
• RQ4 What are the implications of the fourfold pattern of risk attitudes for dynamic pricing in SMoDS platforms?
• RQ5 How can dynamic pricing be integrated with dynamic routing to achieve system-wide optimization under behavioral constraints?

Key findings

• The CPT-based model captures the fourfold pattern of risk attitudes, showing increased risk aversion in high-probability gains and low-probability losses, which aligns with empirical behavioral patterns.
• Passengers exhibit strong risk aversion in mixed prospects, particularly when facing potential losses, which significantly affects their acceptance of dynamic tariffs.
• The model demonstrates that loss aversion and probability distortion lead to lower acceptance rates for high tariffs, even when expected utility is positive.
• The proposed dynamic pricing strategy ensures that the probability of passenger acceptance decreases monotonically with increasing tariff, enabling predictable system control.
• Computational experiments confirm that CPT-based pricing outperforms standard utility models in matching real-world behavioral preferences and improving platform revenue and ridership balance.
• The framework enables the platform to achieve a desired average waiting time by dynamically adjusting tariffs based on behavioral feedback, validated through analytical and simulation results.