Discrete Lanchester attrition models: the case of precautionary surrender

Discrete Lanchester-type attrition models describe many types of antagonistic situations; the preferred interpretation is two fleets of battleships, each trying to sink the other. Such models may be characterised by a bivariate recurrence relation. Here I consider a restricted case in which a fleet that finds itself two or three units behind its opponent immediately surrenders. I present some theoretical and numerical results and suggest lines for further work.