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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.
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 ...
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 ...
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]
For two agents with additive valuations, the answer is yes: we can round a connected envy-free cake-cutting (e.g., found by divide and choose). For n {\displaystyle n} agents with additive valuations, we can find an "EF minus 2" allocation by rounding a connected envy-free cake-cutting, and there also exists an EF2 allocation (proof using a ...
A division is called product-envy-free if, for each group, the product of agents' values of the group share is at least the product of their values of the share of any other group. Democratic fairness requires that, in each group, a certain fraction of the agents agree that the division is fair; preferredly this fraction should be at least 1/2.
The procedure was designed by Steven Brams and Alan D. Taylor, and published in their book on fair division [2]: 65–94 and later in a stand-alone book. [3]: 69–88 Adjusted Winning was previously patented in the United States, but expired in 2016. [4]