{"product_id":"the-pre-kernel-as-a-tractable-solution-for-cooperative-games-an-exercise-in-algorithmic-game-theory-von-holger-ingmar-meinhardt","title":"The Pre-Kernel as a Tractable Solution for Cooperative Games","description":"\n                                \n                \u003cp\u003eThis present book provides an alternative approach to study the pre-kernel solution of transferable utility games based on a generalized conjugation theory from convex analysis. Although the pre-kernel solution possesses an appealing axiomatic foundation that lets one consider this solution concept as a standard of fairness, the pre-kernel and its related solutions are regarded as obscure and too technically complex to be treated as a real alternative to the Shapley value. Comprehensible and efficient computability is widely regarded as a desirable feature to qualify a solution concept apart from its axiomatic foundation as a standard of fairness. We review and then improve an approach to compute the pre-kernel of a cooperative game by the indirect function. The indirect function is known as the Fenchel-Moreau conjugation of the characteristic function. Extending the approach with the indirect function, we are able to characterize the pre-kernel of the grand coalition simply by the solution sets of a family of quadratic objective functions.\u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783662513149\"\u003e\u003ch3\u003eAn Exercise in Algorithmic Game Theory\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642395482\"\u003e\u003ch3\u003eAn Exercise in Algorithmic Game Theory\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783662513149","offer_id":39429769592925,"sku":"9783662513149","price":53.49,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783642395482","offer_id":51579977606,"sku":"9783642395482","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/7dbd551a-3f25-4bcc-aa56-ff8e1d9062ca.jpg?v=1775886452","url":"https:\/\/shop.autorenwelt.de\/en\/products\/the-pre-kernel-as-a-tractable-solution-for-cooperative-games-an-exercise-in-algorithmic-game-theory-von-holger-ingmar-meinhardt","provider":"Autorenwelt Shop","version":"1.0","type":"link"}