Multiple access game with imperfect information
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 4, pp. 3-17.

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We propose a model of data transmission in the network of a special topology, in which two players (nodes of the network) tend to send as many randomly appeared data packages as they can through a common node. We assume that the player does not have complete information on the number of data packages of the other player for possible transfer to the destination node. To solve the game, we propose to use cooperative and noncooperative approaches, according to which the cooperative solution and Nash equilibrium are found. To compare the players' payoffs in the cooperative solution and the Nash equilibrium, the price of anarchy is calculated.
Mots-clés : data transmission
Keywords: multiple access, stochastic game, imperfect information.
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Vladimir M. Bure; Elena M. Parilina. Multiple access game with imperfect information. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 4, pp. 3-17. http://geodesic.mathdoc.fr/item/MGTA_2017_9_4_a0/

[1] Bellman R., Dinamicheskoe programmirovanie, Izd-vo inostrannoi literatury, M., 1960

[2] Bure V. M., Parilina E. M., “Stokhasticheskie modeli peredachi dannykh v setyakh s razlichnymi topologiyami”, Upravlenie bolshimi sistemami, 68, 2017, 6–29

[3] Parilina E. M., “Kooperativnaya igra peredachi dannykh v besprovodnoi seti”, Matematicheskaya teoriya igr i ee prilozheniya, 1:4 (2009), 93–110

[4] Chirkova Yu. V., “Tsena anarkhii v igre balansa zagruzki sistemy obsluzhivaniya s tremya mashinami”, Matematicheskaya teoriya igr i ee prilozheniya, 6:4 (2014), 85–96

[5] Abramson N. M., “The aloha system: Another Alternative for Computer Communications”, Proceedings of the November 17–19, 1970, Fall Joint Computer Conference, AFIPS '70 (Fall), ACM, New York, NY, USA, 1970, 281–285

[6] Altman E., El Azouzi R., Jiménez T., “Slotted Aloha as a game with partial information”, Computer Networks, 45:6 (2004), 701–713 | DOI

[7] Bazenkov N. I., “Double best response dynamics in topology formation game for ad hoc networks”, Automation and Remote Control, 76:2 (2015), 323–335 | DOI | MR

[8] Buttyan L., Hubaux J.-P., Security and Cooperation in Wireless Networks: Thwarting Malicious and Selfish Behavior in the Age of Ubiquitous Computing, Cambridge University Press, New York, 2007

[9] Fink A. M., “Equilibrium in a stochastic $n$-person game”, Journal of Science of the Hiroshima University, A-I 28 (1964), 89–93 | MR

[10] Inaltekin H., Wicker S. B., “The Analysis of Nash Equilibria of the One-Shot Random-Access Game for Wireless Networks and the Behavior of Selfish Nodes”, IEEE/ACM Transactions on Networking, 16:5 (2008), 1094–1107 | DOI

[11] Koutsoupias E., Papadimitriou C., “Worst-case equilibria”, Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, 1999, 404–413 | MR

[12] MacKenzie A. B., Wicker S. B., “Selfish users in Aloha: a game-theoretic approach”, IEEE 54th Vehicular Technology Conference. VTC Fall 2001, Proceedings (Atlantic City, NJ), v. 3, 2001, 1354–1357 | DOI

[13] Marbán S., van de Ven P., Borm P., Hamers H., “ALOHA networks: a game-theoretic approach”, Math Meth Oper Res., 78:2 (2013), 221–242 | DOI | MR

[14] Parilina E. M., Tampieri A., “Stability and cooperative solution in stochastic games”, Theory and Decision, 2017 (to appear) | DOI

[15] Petrosjan L. A., Baranova E. M., “Cooperative Stochastic Games in Stationary Strategies”, Game Theory and Applications, 11 (2006), 7–17 | MR

[16] Sagduyu Y. E., Ephremides A., “A game-theoretic look at simple relay channel”, Wireless Networks, 12:5 (2006), 545–560 | DOI

[17] Shapley L. S., “Stochastic games”, Proc. Natl. Acad. Sci. USA, 39 (1953), 1095–1100 | DOI | MR

[18] Takahashi M., “Stochastic games with infinitely many strategies”, Journal of Science of the Hiroshima University, A-I 28 (1964), 95–99 | MR

[19] https://www.wolfram.com/mathematica/