AbstractThe games of economic survival introduced by Shubik and Thompson seem tailor‐made for the analysis of some problems in insurance and have found many applications in this industry. The optimal strategy in such games may be a so‐called “band strategy.” This result seems counter‐intuitive and has caused some puzzlement. This paper gives sufficient conditions so that the optimal strategy will be of a simpler form, and it is argued that these conditions are satisfied in most applications to