The Proof That a Game May Not Have a Solution

W. F. Lucas

ResearchPublished 1968

A solution concept for [n]-person games in characteristic function form was introduced in 1944 by von Neumann and Morgenstern. RM-5518-PR, November 1967, described a ten-person game having no solution, as a counterexample to the conjecture that every game has at least one solution. The present study reviews the definition of an [n]-person game, describes the counterexample again, and presents a detailed proof that this particular game has no solution.

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Lucas, W. F., The Proof That a Game May Not Have a Solution. Santa Monica, CA: RAND Corporation, 1968. https://www.rand.org/pubs/research_memoranda/RM5543.html.
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