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. 
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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/

[1] Mazalov V. V., Mencher A. E., Tokareva Yu. S., Peregovory. Matematicheskaya teoriya, Lan, SPb., 2012

[2] Baston V., Garnaev A., “A Non-Zero-Sum War of Attrition”, Mathematical Methods of Operations Research, 45 (1997), 197–211 | DOI | MR | Zbl

[3] Brams S. J., Taylor A. D., Fair Division: from Cake-Cutting to Dispute Resolution, Cambridge Univ. Press, 1996, 272 pp. | MR | Zbl

[4] Brams S. J., Taylor A. D., “An envy-free cake division protocol”, American Mathematical Monthly, 102:1 (1995), 9–18 | DOI | MR | Zbl

[5] Dubins L. E., Spanier E. H., “How to cut a cake fairly”, American Mathematical Monthly, 68 (1961), 1–17 | DOI | MR | Zbl

[6] Hamers H., “A Silent Duel over a Cake”, Mathematical Methods of Operations Research, 43 (1993), 119–127 | DOI | MR

[7] Mazalov V. V., Banin M. V., “$N$-person best-choice game with voting”, Game Theory and Applications, 9 (2003), 45–53 | MR

[8] Mazalov V. V., Sakaguchi M., Zabelin A. A., “Multistage arbitration game with random offers”, Game Theory and Applications, 8 (2002), 95–106 | MR

[9] Rubinstein A., “Perfect Equilibrium in a Bargaining Model”, Econometrica, 50:1 (1982), 97–109 | DOI | MR | Zbl

[10] Sakaguchi M., “Best-choice game where arbitration comes in”, Game Theory and Applications, 9 (2003), 141–149 | MR

[11] Steinhaus H., “The problem of fair division”, Econometrica, 16 (1948), 101–104

[12] Stromquist W., “How to cut a cake fairly”, American Mathematical Monthly, 87:8 (1980), 640–644 | DOI | MR | Zbl