Competitive Automation Overshoot: Demand-Side and Capital-Composition Channels, with Market Concentration as a Moderator

Firms adopting AI to substitute for labor face a coordination problem that recurs across two theoretically incompatible traditions: demand-side models, where aggregate demand depends on the same wage income that firms are cutting, and Marxian value-theoretic models, where the rate of profit depends on a capital-composition ratio that competitive automation drives in a self-undermining direction. We define a latent labor-intensity variable and channel-specific mappings into each tradition's own state variable, rather than assuming the two traditions share a state variable, and ask a narrower, computationally checkable question: under what conditions does decentralized, competitive automation converge on a labor intensity below the level that maximizes each channel's own aggregate outcome, a condition we call automation overshoot. Computed independently across a shared parameter space, the two channels show substantial but incomplete agreement (95% and 84% of the swept region show overshoot in the demand and Marxian channels respectively, 83% show it in both), a result that survives a fifteen-specification robustness check across alternative functional forms and internalization strengths (intersection fraction range 0.57-0.94, mean 0.82). Market concentration moves both channels toward less overshoot under fully independent native-parameter sampling that removes any shared coordinate system, a directional claim that survives four targeted falsification tests, one of which an earlier version of this model failed: a mechanical scale artifact in the demand channel, where more competing firms mechanically implied more aggregate automation activity regardless of any internalization behavior, is identified, derived away analytically, and corrected, with every result in this draft reported post-correction. A follow-up generalization addresses a further concern directly: firm count is not the same thing as market concentration. Removing the symmetric-firm assumption and re-deriving the demand channel's internalization term for heterogeneous market shares shows the correction scales as s_i^2 for each firm's own share s_i, so that aggregate internalization is governed by the Herfindahl-Hirschman Index, HHI = sum over i of s_i^2, with the earlier N-based results recovered as the symmetric-share special case. Holding firm count fixed at N=10 while redistributing shares from equal to one dominant firm moves demand-channel overshoot by a factor of 37; plotting demand-channel overshoot against HHI directly across firm counts from 5 to 50 collapses the resulting curves onto one relationship to within 5%, indicating HHI, not N, explains the concentration dependence in this channel substantially better than firm count alone, within the heterogeneous-share configurations tested and the isolating-benchmark design described in Section 4a. Separately, an analysis of the demand and Marxian channels' concentration relationships under independent sampling shows the two channels do not differ in "magnitude" on a single shared scale so much as in shape: the demand channel exhibits a sharp threshold effect concentrated at low firm counts, while the Marxian channel exhibits a shallow, gradual effect spread across the full sampled range of market structures. We extend the model with a hysteretic labor-effort function motivated by, but formalized independently of, Byung-Chul Han's account of the achievement subject: workers sustain effort under a belief that individual strategy can secure their position, a belief that collapses abruptly once a recognition threshold is crossed and recovers only past a lower threshold than the one that triggered the collapse. Wired into a simulated output trajectory, this produces a counterfactual output shortfall that persists after visible layoffs have already subsided; it is reported as an extension, not as co-equal with the core overshoot and concentration results.