Geodesic
A new equilibrium in cyclic games on graphs
Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 94-99.

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We prove that there exists an equilibrium for stationary strategies in cyclic games where the game on vertices of a graph lasts until it reaches a cycle, and the payment of one player to the other equals the sum of the maximal and minimal costs of the edges of this cycle. 
@article{DM_1997_9_4_a9,
     author = {V. N. Lebedev},
     title = {A new equilibrium in cyclic games on graphs},
     journal = {Diskretnaya Matematika},
     pages = {94--99},
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     volume = {9},
     number = {4},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a9/}
}
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V. N. Lebedev. A new equilibrium in cyclic games on graphs. Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 94-99. http://geodesic.mathdoc.fr/item/DM_1997_9_4_a9/