Shapley Settlement
Allocation of system costs and revenues according to marginal contribution.
Overview
One of the central questions in electricity market design is deceptively simple:
How should generators be compensated fairly?
Today's electricity markets largely answer this question based on how much energy a generator produces. Every generator dispatched during a settlement period receives the same wholesale market price regardless of where it is located, when it generated, or how useful it was to the wider electricity system.
This is increasingly difficult to justify.
As electricity systems become more distributed and more dependent on weather-driven renewable generation, not all megawatt-hours are equally valuable. Electricity produced at the wrong location or the wrong time may contribute little to meeting demand, while electricity produced where and when the system is constrained can be enormously valuable.
The challenge therefore becomes:
How do we measure the value that each generator contributes to the electricity system?
FP-AMM addresses this using the Shapley Value, a concept from cooperative game theory developed by Lloyd Shapley in 1953.
Rather than rewarding participants simply for what they produce, the Shapley Value rewards them according to the value they contribute to the system as a whole.
The central idea
Imagine removing one generator from the electricity system.
How much worse would the system become?
Now imagine removing a different generator.
The impact may be completely different.
A generator located behind a transmission constraint may be critical to serving local demand, while another generator producing the same amount of energy elsewhere may have little effect because many alternatives already exist.
The Shapley Value captures exactly this intuition.
Instead of asking:
How much energy did this generator produce?
it asks:
How much value does the system lose if this generator is unavailable?
Importantly, that question is evaluated across every possible combination of generators, ensuring that each participant is rewarded according to their average marginal contribution rather than a single arbitrary scenario.
Why use the Shapley Value?
The Shapley Value possesses several mathematical properties that make it uniquely attractive for settlement problems.
It guarantees that:
- Participants making identical contributions receive identical rewards.
- Participants that contribute nothing receive nothing.
- The total reward is distributed exactly—no money is created or destroyed.
- Independent value streams can be combined consistently.
These properties make it one of the few allocation mechanisms that is both mathematically rigorous and widely accepted as a fair method of distributing shared value.
Shapley Settlement in FP-AMM
Within FP-AMM, the Shapley Value is not used to determine energy prices.
Instead, it is used to distribute revenues associated with the long-term value that generators provide to the electricity system.
Rather than paying every generator the same regardless of its contribution, FP-AMM compensates generators according to their system value.
System value reflects questions such as:
- How much additional demand can this generator reliably serve?
- Does it generate when electricity is scarce?
- Is it located where the network most needs generation?
- Does it reduce congestion?
- Does it improve overall system reliability?
Generators that consistently provide greater value to consumers receive greater compensation.
Those that contribute less receive correspondingly less.
This creates investment incentives that align naturally with the needs of the electricity system rather than rewarding energy production alone.
In this section
The following pages introduce the Shapley Value progressively.
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A Simple Shapley Example introduces the mathematics using a familiar taxi fare example.
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Applying Shapley to Electricity Markets demonstrates how the same principles can be used to compensate generators according to their contribution to serving demand.
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Nested Shapley Settlement introduces the hierarchical approximation developed for FP-AMM that makes Shapley settlement computationally tractable for national-scale electricity systems.