Geodesic
Stochastic design in cake division problem
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 3, pp. 33-50

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Stochastic procedure of fair cake division for $n$-person is constructed. We consider multistage model which characterized by finite horizon and non-cooperative behavior of players and arbitration procedure which applies random offers with Dirichlet distribution. The optimal behavior of the players is derived. Nash equilibrium is found in the class of threshold strategies. The value of the game is derived in analytical form.
Keywords: cake division model, random offers, multistage procedure, threshold strategy, Dirichlet distribution, Nash equilibrium. 
@article{MGTA_2012_4_3_a2,
     author = {Vladimir V. Mazalov and Tatyana E. Nosalskaya},
     title = {Stochastic design in cake division problem},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {33--50},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2012_4_3_a2/}
}
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Vladimir V. Mazalov; Tatyana E. Nosalskaya. Stochastic design in cake division problem. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 3, pp. 33-50. http://geodesic.mathdoc.fr/item/MGTA_2012_4_3_a2/