Studia Logica

, Volume 75, Issue 1, pp 31–62

The Russian Cards Problem

  • Hans van Ditmarsch

DOI: 10.1023/A:1026168632319

Cite this article as:
van Ditmarsch, H. Studia Logica (2003) 75: 31. doi:10.1023/A:1026168632319


Suppose we have a stack of cards that is divided over some players. For certain distributions of cards it is possible to communicate your hand of cards to another player by public announcements, without yet another player learning any of your cards. A solution to this problem consists of some sequence of announcements and is called an exchange. It is called a direct exchange if it consists of (the minimum of) two announcements only. The announcements in an exchange have a special form: they are safe communications, an interesting new form of update. Certain unsafe communications turn out to be unsuccessful updates. A communication is a public announcement that is known to be true. Each communication may be about a set of alternative card deals only, and even about a set of alternatives to the communicating player's own hand only. We list the direct exchanges for a deal of seven cards where the two players holding three cards communicate their hands to each other. Our work may be applicable to the design of cryptographic protocols.

modal logiccryptographic protocolcard gameupdate logicepistemic logicmultiagent system

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Hans van Ditmarsch
    • 1
  1. 1.Department of Computer ScienceUniversity of OtagoDunedinNew Zealand