Read e-book online Kooperative Spiele und Märkte PDF

By J. Rosenmüller (auth.)

ISBN-10: 3540055509

ISBN-13: 9783540055501

ISBN-10: 3642806333

ISBN-13: 9783642806339

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1st etwa 1 E 6 +1 > Ek+1 > E1 C5 so set zen wir uk +1 1st 1st 2 , - 44 - Man sieht nun leicht, daB die Folge u1 , u 2 , ••• che durchlauft. Wir setzen (9) u(x) .. u i alle dyadischen Bru- falls XE Ei Dann gilt offenbar fUr x, y ~+ x~ y genau dann, wenn u(x)~ u(y). Vermoge (5), (6) und (9) ist daher eine Nutzenfunktion auf Qm+ festgelegt, die wir nun mit Hilfe der Stetigkeit auf ~m+ fortsetzen werden. FUr x e Rm+ sei (10) u(x) .. +, x~Y1 = inf (,u (z) I z 6: Qm+, z ~ x } Die zweite Gleichheit folgt aus den bisher festgestellten Tatsachen uber u und ~.

Kann x durch x lk A lk ~ lke angenommen werden, sonst ersetzt man x lke. Daher gilt: lim u i (x It.... ). lk - 54 Mithin ist ii optimal in B: und (p,X) also Gleichgewicht. 8. 1st w.... , Rm+, (~2, A) mit stetigem, konvexen, vertraglichen (~), so gibt es stets ein Gleichgewicht. A. 0 ~ u i , 1) Beweis. Sei u: ~+ ~ 0,1 irgendeine stetige, strikt konkave Funktion. FUr jedes nattirliche list (20) ui . U sei aus .... gewonnen, indem u i durch ui ersetzt wird. (pI, Xl) sei Gleichgewicht in~lund lk lk P "p,X +X.

FOO S\ - 1) falls 1 E S sonst. Der Shapley Wert dieses Spieles laBt sich so berechnen: zunachst ist (n2 1 ) I ~ (v(S~) - v(SI - {11» 'Ir( 1) = k f(k - 1) Wir hoffen. keinen allzu groBen Fehler zu machen. wenn wir dies durch (15) CP1"" ~ n Sf (t) dt o ersetzen. • n alle gleichberechtigt sind, ist n' mithin mithin CP1 + (n - 1)-P2 "~(n) = v(n) .. fen -1). Also hat man (16) 4! i = fen - 1) n - 1 -4'1 Grob gesprochen erhalt also der GroBgrundbesitzer eine Auszahlun~. die proportional zur Flache unter der Kurve f(l) ist; entsprechend teilen sich die Landarbeiter eine Auszahlung, die proportional zur Flache tiber der Kurve f(l) ist.

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Kooperative Spiele und Märkte by J. Rosenmüller (auth.)


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