Skip to main content

Repeated games and multinomial distributions


We consider two person zero-sum games with lack of information on one side given bym matrices of dimensionm×m. We suppose the matrices to have the following “symmetric” structure:a s ij =a ij +cδ s i ,c>0, whereδ s i =1 ifi=s andδ s i =0 otherwise. Under certain additional assumptions we give the explicit solution for finite repetitions of these games. These solutions are expressed in terms of multinomial distributions. We give the probabilisitc arguments which explain the obtained form of solutions. Applying the Central Limit Theorem we get the description of limiting behavior of value closely connected with the recent results of De Meyer [1989], [1993].

This is a preview of subscription content, access via your institution.


  • Aumann RJ, Maschler M (1966) Game theoretic aspects of gradual disarmament. Mathematica 5

  • De Meyer B (1989) Repeated games and multidimensional normal distribution. CORE Discussion Paper 8932

  • De Meyer B (1993) Repeated games and the central limit theorem. CORE Discussion Paper 9303

  • Domansky V, Kreps V (1994) Eventually revealing. Repeated games with incomplete information. IJGT 23:89–99

    Google Scholar 

  • Heuer M (1991) Optimal strategies for uninformed player. IJGT 20:33–51

    Google Scholar 

  • Mertens JF, Sorin S, Zamir S (1990) Repeated games. Chapter 5 Lack of Information on One Side, CORE Prerprint

  • Mertens JF, Zamir S (1976) The normal distribution and repeated games. IJGT 5:187–197

    Google Scholar 

  • Mertens JF, Zamir S (1984) Incomplete information games and the normal distribution. Mimeo

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Cite this article

Domansky, V., Kreps, V. Repeated games and multinomial distributions. ZOR - Methods and Models of Operations Research 42, 275–293 (1995).

Download citation

  • Received:

  • Issue Date:

  • DOI:

Key Words

  • Repeated games
  • incomplete information
  • multinomial distribution