Costly force relocation in the Colonel Blotto game

This paper examines a new extensive-form variation of the Colonel Blotto game with two distinct features: (i) in the first stage each player inherits an initial allocation of force across battlefields, which is publicly observable, and (ii) in the second stage it is costly to relocate forces across battlefields. A first-stage pair of allocations of force is said to be stable if there exists an equilibrium of the two-stage game in which neither player relocates any forces from one battlefield to another. We examine the set of stable initial allocations as a function of the implicit and explicit costs of relocating forces.