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Quantile criteria for the selection of strategies in game theory

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Abstract

The use of quantile criteria in two-person matrix games is explored: maximizing the confidence of a fixed payoff level or maximizing the payoff level for a given confidence level.

We define a series of payoff levels, and indicate lower and upper bounds on their confidences, as a generalization of the maximum security level.

Also the existence of a finite spectrum (to be calculated with L.P.) of optimal quantile strategies is demonstrated. Such a spectrum allows a direct trade-off between payoff and risk and therefore eliminates the impractical need of a utility function.

Only a preference ranking of outcomes is required for the analysis.

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References

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Authors and Affiliations

  1. Koninklijke/Shell-Laboratorium, Shell Research B.V., Amsterdam

    H. de Vries

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  1. H. de Vries
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de Vries, H. Quantile criteria for the selection of strategies in game theory. Int J Game Theory 3, 105–114 (1974). https://doi.org/10.1007/BF01766396

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  • DOI: https://doi.org/10.1007/BF01766396

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