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Advances in Dynamic Games pp 95–109Cite as

Notes on Risk-Sensitive Nash Equilibria

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Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 7))

Abstract

We discuss the risk-sensitive Nash equilibrium concept in static non-cooperative games and two-stage stochastic games of resource extraction. Two equilibrium theorems are established for the latter class of games. Provided examples explain the meaning of risk-sensitive equilibria in games with random moves.

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References

  1. Balbus, L. and Nowak, A.S. Construction of Nash equilibria in symmetric stochastic games of capital accumulation. Math. Methods of Oper. Res. 60 No.1 (2004).

    Google Scholar 

  2. Başar, T. Nash equilibria of risk-sensitive nonlinear stochastic differential games. J. Optim. Theory Appl. 100 (1999), 479–498.

    Article  MathSciNet  MATH  Google Scholar 

  3. Bielecki, T.R. Risk-sensitive dynamic asset management. Appl. Math. Optim. 39 (1999), 337–360.

    Article  MATH  MathSciNet  Google Scholar 

  4. Cavazos-Cadena, R. Solution to the risk-sensitive average cost optimality equation in a class of Markov decision processes with finite state space. Math. Methods of Oper. Res. 57 (2003), 263–285.

    Article  MATH  MathSciNet  Google Scholar 

  5. Fishburn, P.C. Utility Theory for Decision Making. Wiley, New York, 1970.

    MATH  Google Scholar 

  6. Glicksberg, I.E. A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points. Proc. Amer. Math. Soc. 3 (1952), 170–174.

    Article  MATH  MathSciNet  Google Scholar 

  7. Howard, R.A. and Matheson, J.E. Risk-sensitive Markov decision processes. Management Sci. 18 (1972), 356–369.

    Article  MathSciNet  MATH  Google Scholar 

  8. Jacobson, D.H. Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games. IEEE Trans. Automatic Control 18 (1973), 124–131.

    Article  MATH  MathSciNet  Google Scholar 

  9. Klompstra, M.B. Nash equilibria in risk-sensitive dynamic games. IEEE Trans. Automatic Control 45 (2000), 1397–1401.

    Article  MATH  MathSciNet  Google Scholar 

  10. Markowitz, H. Portfolio selection. J. of Finance 7 (1952), 77–91.

    Article  Google Scholar 

  11. Monahan, G.E. and Sobel, M.J. Risk-sensitive dynamic market share attraction games. Games and Econ. Behavior 20 (1997), 149–160.

    Article  MATH  MathSciNet  Google Scholar 

  12. Nash, J.F. Equilibrium points in n-person games. Proc. Natl. Acad. Sci.U.S.A. 36 (1950), 48–49.

    Article  MATH  MathSciNet  Google Scholar 

  13. Nowak, A.S. On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points. Int. J. of Game Theory 32 (2003), 121–132.

    Article  MATH  Google Scholar 

  14. Nowak, A.S. Risk-sensitive equilibria in stochastic games of resource extraction. (2004), preprint.

    Google Scholar 

  15. Nowak, A.S. and Szajowski, P. On Nash equilibria in stochastic games of capital accumulation. Game Theory and Appl. 9 (2003), 118–129.

    MathSciNet  Google Scholar 

  16. Pratt, J.W. Risk aversion in the small and in the large. Econometrica 32 (1964), 122–136.

    Article  MATH  Google Scholar 

  17. Whittle, P. Risk-Sensitive Optimal Control. Wiley, New York, 1990.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, 65-246, Zielona Góra, Poland

    Andrzej S. Nowak

Authors
  1. Andrzej S. Nowak
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wypiańskiego 27, 50-370, Wrocław, Poland

    Andrzej S. Nowak  & Krzysztof Szajowski  & 

  2. Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Podgórna 50, 65-246, Zielona Góra, Poland

    Andrzej S. Nowak

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© 2005 Birkhäuser Boston

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Nowak, A.S. (2005). Notes on Risk-Sensitive Nash Equilibria. In: Nowak, A.S., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 7. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4429-6_5

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