Discrete Lanchester attrition models: the case of precautionary surrender

TL;DR

This paper explores a specialized discrete Lanchester attrition model where a fleet surrenders upon falling behind by a few units, providing theoretical and numerical insights into this surrender behavior.

Contribution

It introduces a new variant of Lanchester models incorporating immediate surrender upon being behind, expanding the understanding of attrition dynamics with surrender behavior.

Findings

The model demonstrates how surrender impacts fleet survival.

Numerical simulations illustrate different outcomes based on initial conditions.

Theoretical analysis provides conditions for fleet victory or surrender.

Abstract

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.