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Equilibria in Nonantagonistic Positional Games on Graphs and Searching for Them

  • Mathematical Game Theory and Applications
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Abstract

We distinguish some cases of existence of a stationary equilibrium in nonantagonistic games on directed graphs with terminal payoffs along trajectories. The proof of the existence of stationary equilibria implies polynomial search algorithms for them.

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References

  1. Gurvich, V.A., Karzanov, A.V., and Khachivan, L.G., Cyclic Games and an Algorithm to Find Minimax Cycle Means in Directed Graphs, USSR Comput. Math. Math. Phys., 1988, vol. 28, no. 5, pp. 85–91.

    Article  MATH  Google Scholar 

  2. Kuhn, H.W., Extensive Games and the Problem of Information, in Contributions to the Theory of Games, Ann. Math. Studies, 28, Kuhn, H.W. and Tucker, A.W., Eds., Princeton: Princeton Univ. Press, 1953, pp. 193–216.

    Google Scholar 

  3. Boros, E., Elbassioni, K., Gurvich, V., and Makino, K., On Nash Equilibria and Improvement Cycles in Pure Positional Strategies for Chess-like and Backammon-like N-Person Games, Discr. Math., 2012, vol. 312, pp. 772–788.

    Article  MATH  Google Scholar 

  4. Boros, E. and Gurvich, V., On Nash-Solvability in Pure Stationary Strategies of Finite Games with Perfect Information Which May Have Cycles, Math. Social Sci., 2003, vol. 46, pp. 207–224.

    Article  MathSciNet  MATH  Google Scholar 

  5. Kukushkin, N.S., Acyclicity of Improvements in Finite Game Forms, Int. J. Game Theory, 2011, vol. 40, pp. 306–317.

    MathSciNet  MATH  Google Scholar 

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Correspondence to I. A. Bashlaeva.

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Original Russian Text © I.A. Bashlaeva, 2013, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2013, No. 4, pp. 3–13.

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Bashlaeva, I.A. Equilibria in Nonantagonistic Positional Games on Graphs and Searching for Them. Autom Remote Control 79, 360–365 (2018). https://doi.org/10.1134/S0005117918020145

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  • DOI: https://doi.org/10.1134/S0005117918020145

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