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Fair Division
Fair division is a concept in game theory and economics that deals with the problem of dividing a set of resources or goods among several people who have an entitlement to them, so that each person receives their due share or fair share. The key idea is to allocate resources in a way that each participant feels they have received what is rightfully theirs, based on their own valuation of the goods.
Key aspects of fair division:
- Players and resources: There are multiple parties (players) entitled to a share of a set of resources (goods, assets, etc.).
- Subjective valuation: Each player may value the items differently, so fairness is based on each player's own assessment of their share.
- No external arbitration: Ideally, the division is done by the players themselves without needing a third party, since only the players truly know how they value the goods.
- Types of goods: The problem can involve divisible goods (like land, cake, or pizza) or indivisible goods (like paintings, cars, or jewelry).
- Fair share: When dividing among (N) parties, a fair share is typically (1/N) of the whole, but defined by each party's own valuation.
- Fair division methods: These are procedures or algorithms designed to ensure each party receives a share they consider fair. The classic example is the "divide and choose" method, where one person divides and the other chooses.
- Additional fairness criteria: Beyond basic fairness, divisions can also be evaluated for properties like:
- Envy-freeness: No one prefers someone else's share over their own.
- Pareto optimality: No other division could make someone better off without making someone else worse off.
- Equitability: Each party feels they received an equal proportion relative to their valuation.
Applications:
Fair division problems arise in many real-world contexts such as inheritance division, divorce settlements, business profit sharing, allocation of natural resources, and even airport traffic management.
In summary, fair division is the study and practice of dividing resources among multiple parties so that each party believes they have received a just and equitable portion, based on their own preferences and valuations. It is a foundational problem in game theory, economics, and dispute resolution.