Fair Division - Shapley Value, Fair Division, Sperner's Lemma, Necklace Splitting Problem, Proportional, Equity, Entitlement, Divide and Choose (Paperback)

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Shapley Value, Fair Division, Sperner's Lemma, Necklace Splitting Problem, Proportional, Equity, Entitlement, Divide and Choose, Exact Division, Selfridge-conway Discrete Procedure, Envy-Free, Spite, Stromquist Moving-Knife Procedure, Strategyproof, Adjusted Winner Procedure, Weakly Additive, Airport Problem, Moving-Knife Procedure, Hobby-rice Theorem, Surplus Procedure, Chore Division. Excerpt: In problems of fair division, the adjusted winner procedure is used to partition a bundle of goods between two players in such a way as to minimize envy and maximize efficiency and equitability . The procedure is used in divorce settlements and illustrates the concept of Nash equilibria . The method is also interesting from an ethical perspective as it appears to encourage honesty . Method Each player is given the list of goods and an equal number of points to distribute among them. He or she assigns a value to each good and submits it sealed to an arbiter. The arbiter, or a computer program, assigns each item to the high bidder. Then, if players' total point values are unequal, the player with the higher total gives its least valuable asset to the other player; this is repeated, with splitting of a divisible asset if necessary, until the players have equal point values. (Ibid.) As patented, this method does not handle multiple identical assets with diminishing marginal utility . Software Patent This algorithm is patented in the United States. Some concerns have been raised that this patent is overly broad. References (URLs online) Websites (URLs online) A hyperlinked version of this chapter is at In mathematics and especially game theory, the airport problem is a type of fair division problem in which it is decided how to distribute the cost of an airport runway among different playe...