Abstract
Contrary to what appears to have become an accepted part of the folklore of game theory, a finite two-person zero-sum game with non-Archimedean utilities may have no equilibrium-point solution, and either one or both players may have no “minimax” strategy. Even when both players have “minimax” strategies, such a game may lack an equilibrium point.
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Fishburn, P.C. On the foundations of game theory: The case of non-Archimedean utilities. Int J Game Theory 1, 65–71 (1971). https://doi.org/10.1007/BF01753434
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DOI: https://doi.org/10.1007/BF01753434