Dynamic pricing is the dominant mechanism for managing demand in private ride-hailing platforms, yet its potential application in publicly operated shared autonomous vehicle (SAV) services remains largely theoretical and under-investigated. This paper repositions dynamic pricing within a unified performance framework that links control mechanisms, such as reinforcement learning (RL) and market design, to operational levers for demand shaping and fleet allocation, and to outcomes across economic, operational, accessibility, and environmental dimensions. Using strict inclusion criteria, we systematically review 49 peer-reviewed studies and integrate their findings into a coherent account of how dynamic pricing affects system performance. Analytical, control, RL and market design models report revenue and reliability gains. Separate studies employing these models also document affordability and sustainability trade-offs when fares rise or rebalancing increases vehicle kilometre travel. Overall, the findings suggest that pricing outcomes depend on how fares interact with matching, rebalancing, and charging policies.

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