Symmetric Solutions of Some General n-Person Games

John Von Neumann, Oskar Morgenstern

Expert InsightsPublished 1961

One step in the search for an exhaustive list of the solutions to a particular n-person game (namely, the game where all coalitions of n - 1 players win, but all smaller coalitions lose). The game has a unique solution that is symmetric with respect to all the players. It consists of all the imputations in which the number of players receiving any particular amount above the minimum is even. This paper (based on a 1946 manuscript) examines the class of solutions that are symmetric in just the first n - 1 players. It breaks off after arriving at an interesting property of the payoffs to the nth player in any given solution of this class, to wit: any gap that may exist in the set of nth player payoffs cannot be wider than <>, where a is the upper endpoint of the gap. In particular, the minimum payoff to the nth player is always less than <>. This latter bound is known to be best possible, since solutions coming arbitrarily close to it can be constructed by Gillies' inflation techniques.

Document Details

  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1961
  • Pages: 16
  • Document Number: P-2169

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Von Neumann, John and Oskar Morgenstern, Symmetric Solutions of Some General n-Person Games. Santa Monica, CA: RAND Corporation, 1961. https://www.rand.org/pubs/papers/P2169.html.
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