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Games with a Continuum of Strategies

In: Two-Person Zero-Sum Games

Author

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  • Alan Washburn

    (Naval Postgraduate School)

Abstract

It is not unusual to encounter games where the number of available pure strategies is infinite. Any game where the two players each select a time for action is an example, or a submarine can dive to any depth up to some maximum limit. Intervals of real numbers can of course be artificially subdivided to make the number of strategies finite, but that is merely an approximation technique. Sometimes it may even be enlightening to approximate a subdivided interval by a continuous one. The radio frequency spectrum, for example, contains only finitely many frequencies as far as modern digital receivers are concerned, but there are so many frequencies that for some purposes one might as well think of the spectrum as being continuous. In this chapter we consider games where the choice of strategy is not limited to a finite set.

Suggested Citation

  • Alan Washburn, 2014. "Games with a Continuum of Strategies," International Series in Operations Research & Management Science, in: Two-Person Zero-Sum Games, edition 4, chapter 0, pages 83-106, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-9050-0_5
    DOI: 10.1007/978-1-4614-9050-0_5
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