Relative Allocation, Protection, and Excess Investment

This paper develops a structural theory of investment under dual incentive structures. Investment affects economic outcomes through two distinct channels. First, it increases aggregate protection against external threats and enlarges total feasible surplus through an increasing defense technology. Second, it improves relative standing within an allocation rule that redistributes the resulting surplus across agents. When investment operates through both channels, private and social incentives need not coincide. In a symmetric environment with monotone relative allocation, I show that equilibrium investment exceeds the social optimum whenever comparative screening intensity exceeds the critical ratio of marginal aggregate protection to average protected surplus. Overinvestment therefore does not arise because protection lacks social value; it arises because relative evaluation adds a positional component to private returns without increasing aggregate surplus. The paper further shows that transparency acts as an amplification parameter, while public standards mitigate escalation by reducing the granularity with which investment is translated into relative ranking. The analysis unifies ideas from contests, status competition, public information, and incentive design, and identifies a general mechanism of protection-compatible escalation.