Optimal strategies in a game of economic survival

The 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 insurance.