A Rough View on Incomplete Information in Games

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10313)

Abstract

In both game theory and in rough sets, the management of missing and contradicting information is regarded as one of the biggest challenges with significant practical relevance. In game theory, a distinction is made between imperfect and incomplete information. Imperfect information is defined when a player cannot identify the decision node it is presently at. Incomplete information refers to a lack of knowledge about the future actions of one’s opponent, e.g., due to missing information about its payoffs. In rough set theory, missing and contradicting information in decision tables has been extensively researched and has led to the definition of lower and upper approximations of sets. Although game theory and rough sets have already addressed missing and contradicting information thoroughly little attention has been given to their relationship. In the paper, we present an example how games with imperfect information can be interpreted in the context of rough sets. In particular, we further detail Peters’ recently proposed mapping of a game with incomplete information on a rough decision table.

Keywords

Missing and contradicting information Incomplete information Game theory Rough set theory 

References

  1. 1.
    Akerlof, G.A.: The market for “lemons”: quality uncertainty and the market mechanism. Q. J. Econ. 84(3), 488–500 (1970)CrossRefGoogle Scholar
  2. 2.
    Apt, K.R., Grädel, E. (eds.): Lectures in Game Theory for Computer Scientists. Cambridge University Press, Cambridge (2011)MATHGoogle Scholar
  3. 3.
    Fudenberg, D., Tirole, J.: Game Theory. MIT Press, Cambridge (1991)MATHGoogle Scholar
  4. 4.
    Grzymala-Busse, J.: Rough set theory with applications to data mining. In: Negoita, M.G., Reusch, B. (eds.) Real World Applications of Computational Intelligence. Studies in Fuzziness and Soft Computing, vol. 179, pp. 221–244. Springer, Heidelberg (2005). doi:10.1007/11364160_7 Google Scholar
  5. 5.
    Halpern, J.Y.: Computer science and game theory: a brief survey (2007). arXiv preprint: arXiv:cs/0703148
  6. 6.
    Hammerstein, P., Selten, R.: Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol. 2, pp. 929–993. Elsevier (1994)Google Scholar
  7. 7.
    Harsanyi, J.C.: Games with incomplete information played by “Bayesian” players, I–III. Manag. Sci. 14, 159–183 (Part I), 320–334 (Part II), 486–502 (Part III) (1967/1968)Google Scholar
  8. 8.
    Herbert, J.P., Yao, J.T.: Game-theoretic risk analysis in decision-theoretic rough sets. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS, vol. 5009, pp. 132–139. Springer, Heidelberg (2008). doi:10.1007/978-3-540-79721-0_22 CrossRefGoogle Scholar
  9. 9.
    Herbert, J.P., Yao, J.T.: Game-theoretic rough sets. Fundam. Inform. 108(3–4), 267–286 (2011)MathSciNetMATHGoogle Scholar
  10. 10.
    Kreps, D.M.: Game Theory and Economic Modelling. Oxford University Press, Oxford (1990)CrossRefGoogle Scholar
  11. 11.
    Morrow, J.D.: Game Theory for Political Scientists. Princeton University Press, Princeton (1994)Google Scholar
  12. 12.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)CrossRefMATHGoogle Scholar
  13. 13.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)CrossRefMATHGoogle Scholar
  14. 14.
    Peters, G.: A rough perspective on information in extensive form games. In: Flores, V., et al. (eds.) IJCRS 2016. LNCS, vol. 9920, pp. 145–154. Springer, Cham (2016). doi:10.1007/978-3-319-47160-0_13 CrossRefGoogle Scholar
  15. 15.
    Tirole, J.: The Theory of Industrial Organization. MIT Press, Cambridge (1988)Google Scholar
  16. 16.
    Wang, B., Li, R., Perrizo, W.: Big Data Analytics in Bioinformatics and Healthcare. IGI Global, Hershey (2014)Google Scholar
  17. 17.
    Wang, J., Miao, D.: Analysis on attribute reduction strategies of rough set. J. Comput. Sci. Technol. 13(2), 189–192 (1998)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Xu, J., Yao, L.: A class of two-person zero-sum matrix games with rough payoffs. Int. J. Math. Math. Sci. 2010, Article ID 404792, 22 p. (2010). doi:10.1155/2010/404792

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer Science and MathematicsMunich University of Applied SciencesMunichGermany
  2. 2.Australian Catholic UniversitySydneyAustralia

Personalised recommendations