How to Fairly Split Group Project Scores Using Shapley Value and LOTB
This article explains cooperative game theory concepts—Last‑On‑The‑Bus Value and Shapley Value—and demonstrates how they can be used to fairly allocate scores among group project members by evaluating each participant’s marginal contributions across all possible joining orders.
What is Cooperative Game Theory?
Before evaluating contributions we need to understand cooperative games, which study how a group of players can fairly distribute the total payoff of a joint task.
Last‑On‑The‑Bus Value (LOTB)
The LOTB measures the marginal increase in total value when a player joins an already formed coalition as the last member.
In the example of three students A, B, C producing a report worth 100 points, if C joins the coalition of A and B and raises the score from 70 to 100, C’s LOTB is 30 points.
Shapley Value – A Fair Allocation Method
The Shapley value averages each player’s marginal contribution over all possible joining orders, providing a comprehensive and equitable assessment.
Given the value table:
{} = 0
{A} = 30
{B} = 20
{C} = 40
{A,B} = 70
{A,C} = 90
{B,C} = 80
{A,B,C} = 100
Calculating the Shapley value for the three members yields:
A: 33.33 points
B: 23.33 points
C: 43.33 points
The Shapley value is widely used beyond classroom projects, such as profit sharing in companies and voting power allocation in parliaments.
Cooperative game theory helps allocate collaborative outcomes fairly by considering all possible contribution orders.
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