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This platform explores the ubiquitous problem of dividing resources fairly. Browse the collection of algorithms below, study fair division theory, or use the algorithm simulator to try running the procedures yourself!

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Divisible Resources

Algorithms for resources that can be cut and divided continuously, like cake or land

Divide-and-Choose Procedure

2 Players Discrete 2 RW Queries

The fundamental fair division procedure for two players.

Fairness Properties

Proportional Envy-free Strategy-proof

Study Algorithm

Austin Moving Knife Procedure

2 Players Continuous $\infty$ RW Queries

An extension of Divide-and-Choose employing a moving-knife mechanism.

Fairness Properties

Equitable Envy-free Strategy-proof

Study Algorithm

Steinhaus Lone-Divider Procedure

3 Players Discrete 8-10 RW Queries

A rudimentary procedure enabling basic fair division among three players.

Fairness Properties

Proportional

Study Algorithm

Selfridge-Conway Procedure

3 Players Discrete 7-17 RW Queries

The first envy-free procedure for three players

Fairness Properties

Envy-free

Study Algorithm

Stromquist Moving Knife Procedure

3 Players Continuous $\infty$ RW Queries

A continuous procedure for envy-free division between three parties

Fairness Properties

Envy-free

Study Algorithm

Banach-Knaster Last-Diminisher Procedure

N Players Discrete O(N²) RW Queries

An elegant procedure ensuring proportionality for $N$ players

Fairness Properties

Proportional

Study Algorithm

Brams-Taylor Procedure

N Players Discrete $\Omega$(N) RW Queries

Uses sophisticated iterative trimming and reallocation mechanisms.

Fairness Properties

Envy-free

Study Algorithm

Coming Soon!

Indivisible Resources

Algorithms for discrete items that cannot be divided, like houses or artwork

Knaster Sealed Bids Procedure

N Players Discrete Items Auction O(N) Rounds

A truthful auction mechanism using sealed bids and monetary transfers

Fairness Properties

Proportional* Strategy-proof

*With monetary compensation

Study Algorithm

Lucas Markers Method

N Players Linear Arrangement Marker Placement O(N²)

A procedure for linearly arranged goods using a 'marking' mechanism.

Fairness Properties

Proportional Strategy-proof Remainder-efficient

Works for both continuous and discrete goods in linear arrangement

Study Algorithm

Coming Soon!