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Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. . That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth ...
In the mathematics of social science, and especially game theory, a moving-knife procedure is a type of solution to the fair division problem. The canonical example is the division of a cake using a knife.
The research in strategic fair division has two main branches. One branch is related to game theory and studies the equilibria in games created by fair division algorithms: The Nash equilibrium of the Dubins-Spanier moving-knife protocol; [2] The Nash equilibrium and subgame-perfect equilibrium of generalized-cut-and-choose protocols; [3]
It was the first example of a continuous procedure in fair division. The knife is passed over the cake from the left end to the right. Any player may say stop when they think / of the cake is to the left of the knife, the cake is cut and the player who spoke gets that piece. Repeat with the remaining cake and players, the last player gets the ...
But if they instead they slaughter the ox, they divide the profit in proportion. This is discussed in the Babylonian Talmud (just after the estate division problem). [4] Ibn Ezra's problem. This is a later problem of estate division that was solved in a different way. A man with an estate of 120 dies bequeathing 120, 60, 40 and 30 to his four sons.
Truthful cake-cutting is the design of truthful mechanisms for fair cake-cutting. The currently known algorithms and impossibility results are shown here. The main cases in which it is unknown whether a deterministic truthful fair mechanism exists are: [10] There are 3 or more agents with piecewise-uniform valuations, without free disposal.
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Fair division among groups [1] (or families [2]) is a class of fair division problems, in which the resources are allocated among groups of agents, rather than among individual agents. After the division, all members in each group consume the same share, but they may have different preferences; therefore, different members in the same group ...