Information Games: Strategic Crowding and Firm Repositioning in Language-Model Space

Abstract

Firms follow changing economic opportunities, but rivalry changes their response. We develop ESCAPE, a rational-share game of distribution-valued positioning with heterogeneous capability costs, establish a unique equilibrium, and derive an exact reallocation restriction separating opportunity and crowding contributions. Competition need not push firms apart: rational firms can enter increasingly crowded regions, because the full reallocation gain can be positive even when its crowding component is negative. Rivalry instead changes how differently firms respond to the same opportunity shift. In the benchmark many-firm economy, the relative-response component accounts for 90.5% of the weighted squared composition-response contrast between strategic and independent firms; it is numerically zero under identical capabilities. The contrast remains distinguishable under corpus-scale measurement. Corporate news distributions document persistent but changing peer structure: optimized peer reconstructions retain 86.5% of their aggregate validation advantage one year later even as absolute distance to both frozen reconstructions increases. Peer structure is persistent without being a fixed destination, so current similarity can remain informative without fixing firms' future relative positions.