Heterogeneous Multidimensional Colonel Blotto: Framework and Equilibrium Structure

Classical Colonel Blotto models predict smooth and monotone allocation patterns under a homogeneous-resource benchmark. This paper studies how heterogeneous technologies and partially irreversible deployment reshape equilibrium structure through a unifying reduced-form mechanism, which we call the induced cost geometry. In the compatible linear case developed in the main text, heterogeneous technologies and irreversibility generate battlefield-specific effective marginal costs MCig(μ)=κig+μβig, where μ is the endogenous shadow price of the global budget. We distinguish results that rely on this compatible linear representation from those that extend directly to the more general lower-envelope induced cost object. The induced cost object serves as the central organizing device for the equilibrium analysis and yields three main structural implications. First, under binding budgets, equilibrium effort can be sparse: positive effort is concentrated on battlefields whose effective marginal costs remain sufficiently low relative to their values, generating selective participation even under smooth contest success functions. Second, within a class of local fixed-support equilibrium configurations with binding budgets, an increase in a battlefield’s value can reduce equilibrium effort on that battlefield via the shadow-price channel—a mechanism-identification result for a specific structural regime rather than a general comparative-statics claim. Third, along durability paths, contestability and equilibrium support can exhibit discrete regime changes generated by technology switching within a finite lower-envelope cost structure. We develop a unified reduced-form characterization of equilibrium structure via induced costs and KKT conditions, highlighting how induced cost geometry reshapes both the intensive and extensive margins of strategic allocation within the equilibrium regimes characterized in the paper.