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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.
Steven J. Brams (born November 28, 1940, in Concord, New Hampshire) is an American game theorist and political scientist at the New York University Department of Politics. . Brams is best known for using the techniques of game theory, public choice theory, and social choice theory to analyze voting systems and fair divi
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 slaughter the ox, the profit is divided proportionally. 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.
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]
In fair division problems, spite is a phenomenon that occurs when a player's value of an allocation decreases when one or more other players' valuation increases. Thus, other things being equal, a player exhibiting spite will prefer an allocation in which other players receive less than more (if more of the good is desirable).
Then, for each subject, a new population of 20 divisions was created using a genetic algorithm. This procedure continued for 15 iterations until a best surviving allocation was found. The results were compared to five provably-fair division algorithms: Sealed Bid Knaster, Adjusted Winner, Adjusted Knaster, Division by Lottery and Descending Demand.