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A family of games on 1,∞)2 with payoff a function of y/x

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  • G. A. Heuer

Abstract

A two‐parameter class of games on 1,∞)2 is studied. The games may be regarded as analogs of Silverman games, having continuous payoff function in place of a step function of y/x. This change is motivated by a desire to move toward a model for competitive situations where the penalty for overspending increases with the amount of overspending. There are some similarities to games with bell‐shaped kernel. For most of the region considered in the plane of the two parameters there are solutions of finite type, which are obtained explicitly. There are, however, pockets in this plane where no optimal strategies have been found and possibly where none of finite type exist.

Suggested Citation

  • G. A. Heuer, 1984. "A family of games on 1,∞)2 with payoff a function of y/x," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(2), pages 229-249, June.
    • Handle: RePEc:wly:navlog:v:31:y:1984:i:2:p:229-249
    DOI: 10.1002/nav.3800310206
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    Cited by:

    1. Gerald A. Heuer & Ulrike Leopold‐Wildburger, 1995. "The advantage of deeper pockets in Silverman's game on intervals," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 123-140, February.

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