Interactive module

Envy-Free Allocation

Cut a cake so nobody prefers someone else’s piece.

Rule ledger

caseAva likes cream, Ben loves chocolate, and Chloe wants fruit.

rulev_i(A_i) >= v_i(A_j) for every pair i, j

questionWhen one strategy changes alone, whose payoff or fairness changes first?

Cake Cut Fairness

Cream

Chocolate

Fruit

Ava own value

Ben own value

Chloe own value

Cut line 134%Cut line 268%

Envy-free check

No envy detected

How to read this result

Fairness here is not equal physical size. It is whether each person, using their own preferences, would still prefer someone else's piece.

Formula

v_i(A_i) >= v_i(A_j) for every pair i, j

Fairness is judged by each person’s own preferences, not by physical size alone.

Step-by-step Explanation

Scenario

Ava likes cream, Ben loves chocolate, and Chloe wants fruit.

Why This Matters

Envy-freeness helps reason about fair chores, inheritance, scheduling, and shared resources.

Beginner-Friendly Summary

An allocation is envy-free when every person values their own bundle at least as much as every other bundle.

Try changing the strategy and watch which result changes first.