Geodesic
Nash equilibria in mixed stationary strategies for $m$-player mean payoff games on networks
Contributions to game theory and management, Tome 11 (2018), pp. 103-112.

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We consider a class of non-zero-sum mean payoff games on networks that extends the two-player zero-sum mean payoff game introduced by Ehrenfeucht and Mycielski. We show that for the considered class of games there exist Nash equilibria in mixed stationary strategies and propose an approach for determining the optimal strategies of the players.
Keywords: mean payoff game, pure stationary strategy, mixed stationary strategy, Nash equilibria. 
@article{CGTM_2018_11_a7,
     author = {Dmitrii Lozovanu and Stefan Pickl},
     title = {Nash equilibria in  mixed stationary strategies for $m$-player mean payoff games on networks},
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     volume = {11},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2018_11_a7/}
}
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Dmitrii Lozovanu; Stefan Pickl. Nash equilibria in  mixed stationary strategies for $m$-player mean payoff games on networks. Contributions to game theory and management, Tome 11 (2018), pp. 103-112. http://geodesic.mathdoc.fr/item/CGTM_2018_11_a7/

[1] Alpern S., “Cycles in extencsive form perfect information games”, Journal of Mathematical Analysis and Applications, 159 (1991), 1–17 | DOI | MR | Zbl

[2] Dasgupta P., Maskin E., “The existence of an equilibrium in discontinuous economic games”, The Review of Economic Studies, 53 (1986), 1–26 | DOI | MR | Zbl

[3] Ehrenfeucht A., Mycielski J., “Positional strategies for mean payoff games”, International Journal of Game Theory, 8 (1979), 109–113 | DOI | MR | Zbl

[4] Gurvich V., Karzanov A., Khachiyan L., “Cyclic games and an algorithm to find minimax cicle means in directed graphs”, USSR Computational Mathematics and Mathematical Physics, 28 (1988), 85–91 | DOI | MR | Zbl

[5] Lozovanu D., “Stationary Nash equilibria for average stochastic positional games”, Static amd Dynamic Game Theory: Foundations and Applications, eds. Petrosyan L., Mazalov V., Zenkevich N., Springer, 2018 (to appear) | MR

[6] Lozovanu D., Pickl S., “Nash equilibria conditions for cyclic games with $m$ players”, Electronic Notes in Discrete Mathematics, 28 (2006), 85–91 | MR

[7] Lozovanu D., Pickl S., Optimization of Stochastic Discrete Systems and Control on Complex Networks, Springer, 2015 | MR | Zbl

[8] Lozovanu D., Pickl S., “Determining the optimal strategies for zero-sum average stochastic positional games”, Electronic Notes in Discrete Mathematics, 55 (2016), 155–159 | DOI | Zbl

[9] Zwick U., Paterson M., “The complexity of mean payoffs on graphs”, Theoretical Computer Science, 158 (1996), 343–359 | DOI | MR | Zbl