Games and Random Search

  • Artur PopławskiEmail author
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 277)


We use dynamics of measures, i.e. iteration of the operators from measurable space to space of probabilistic measures on this space, to model and prove properties of random search algorithms. Specifically using this technique in the context of Game Theory we show that stochastic better response dynamics, where players in the potential game perform their moves independently choosing the random strategy improving their outcome, converges in stochastic sense to playing strategies near equilibrium.


Game Theory Random search Measure dynamics 


  1. 1.
    Giry, M.: A categorical approach to probability theory. In: Banaschewski, B. (ed.) Categorical Aspects of Topology and Analysis. LNM, vol. 915, pp. 68–85. Springer, Heidelberg (1982). Scholar
  2. 2.
    Gutjahr, W.J.: Stochastic search in metaheuristics. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics. ISOR, vol. 146, pp. 573–597. Springer, Boston (2010). Scholar
  3. 3.
    MacKenzie, A.B., DaSilva, L.A.: Game Theory for Wireless Engineers. Synthesis Lectures on Communications. Morgan and Claypool Publishers, San Rafael (2006)Google Scholar
  4. 4.
    Ombach, J., Tarłowski, D.: Nonautonomous stochastic search in global optimization. J. Nonlinear Sci. 22(2), 169–185 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Solis, F.J., Wets, R.J.B.: Minimization by random search techniques. Math. Oper. Res. 6(1), 19–30 (1981)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Tarłowski, D.: Nonautonomous dynamical systems in stochastic global optimization. Ph.D. thesis, Department of Mathematics, Jagiellonian University (2014)Google Scholar
  7. 7.
    Young, H.P.: Learning by trial and error. Games Econ. Behav. 65(2), 626–643 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Łojasiewicz, S.: An Introduction to the Theory of Real Functions. Wiley, Hoboken (1988)zbMATHGoogle Scholar

Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2019

Authors and Affiliations

  1. 1.NOKIA Kraków Technology CenterKrakówPoland
  2. 2.Department of TelecommunicationsAGH University of Science and TechnologyKrakówPoland

Personalised recommendations