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An Extended Basic System of Equilibria and the Technique of the Solution of Noncooperative Games

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Abstract

A basic system of equilibria for noncooperative games is suggested and studied and the technique of its use is set out for seeking the game equilibria that are most suitable for all players.

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REFERENCES

  1. Vorob'ev, N.N., Osnovy teorii igr. Bezkoalitsionnye igry (Basics of the Theory of Games. Noncooperative Games), Moscow: Nauka, 1984.

    Google Scholar 

  2. Roos, C.F., Generalized Lagrange Problems in the Calculus of Variations, Trans. Am. Math. Soc., 1928, vol. 30, pp. 360-384.

    Google Scholar 

  3. Nash, J., Non-Cooperative Games, Ann. Math., 1951, vol. 54, no. 2, pp. 286-295.

    Google Scholar 

  4. Smol'yakov, E.R., Ravnovesnye modeli pri nesovpadayushchikh interesakh uchastnikov (Equilibrium Models with Noncoincident Interests of Participants), Moscow: Nauka, 1986.

    Google Scholar 

  5. Smol'yakov, E.R., Teoriya antagonizmov i differentsial'nye igry (The Theory of Antagonisms and Differential Games), Moscow: Editorial URSS, 2000.

    Google Scholar 

  6. Smol'yakov, E.R., Existence of the Infinite System of Notions of the Noncooperative Equilibrium, Dokl. Ross. Akad. Nauk, 2000, vol. 374, no. 2, pp. 173-176.

    Google Scholar 

  7. Smol'yakov, E.R., Methods of Search for the Always Existing “Strongest” Saddle Point in Two-Person Zero-Sum Games, Avtom. Telemekh., 2000, no. 12, pp. 53-62.

  8. Smol'yakov, E.R., Search for the Always Existing Strongest Equilibrium in Noncooperative Games, Differ. Uravnen., 2000, vol. 36, no. 12, pp. 1658-1664.

    Google Scholar 

  9. Smol'yakov, E.R., On the Search for a Saddle Point in Noncooperative Games, Zh. Vychisl. Mat. Mat. Fiz., 1999, vol. 39, no. 6, pp. 897-905.

    Google Scholar 

  10. Smol'yakov, E.R., Saddle Points and Active Equilibria in Differential Games with Dependent Strategies, Dokl. Ross. Akad. Nauk, 1999, vol. 365, no. 3, pp. 325-328.

    Google Scholar 

  11. Smol'yakov, E.R., Methods of Search for All Types of Solutions in Two-Person Zero-Sum Differential Games with Dependent Strategies, Differ. Uravnen., 1998, vol. 34, no. 10, pp. 1337-1345.

    Google Scholar 

  12. Smol'yakov, E.R., Heuristic Procedures of the Search for Equilibria in Noncooperative and Two-Person Zero-Sum Games, Avtom. Telemekh., 1996, no. 9, pp. 18-28.

  13. Smol'yakov, E.R., On Some Generalized Theorems of Existence of Saddle Points in Differential Games, Differ. Uravnen., 1995, vol. 31, no. 11, pp. 1881-1886.

    Google Scholar 

  14. Smol'yakov, E.R., Theorems on Existence of the Equilibrium in Noncooperative Games, Dokl. Ross. Akad. Nauk, 1998, vol. 361, no. 1, pp. 28-30.

    Google Scholar 

  15. Luce, R.D. and Raiffe, H., Games and Decisions, New York: Wiley, 1957.

    Google Scholar 

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Smol'yakov, E.R. An Extended Basic System of Equilibria and the Technique of the Solution of Noncooperative Games. Automation and Remote Control 62, 1890–1897 (2001). https://doi.org/10.1023/A:1012750509533

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