The Market's Conditioning Representation: Equilibrium, Crowding, and Convention Multiplicity

Abstract: Asset-pricing models typically condition on a fixed information set. This paper endogenises the market's conditioning architecture by allowing portfolios to choose representations whose induced exposures affect prices. Capital allocated across representations determines aggregate positions and the clearing premium, while price feedback changes representation value and, through causal certification, admissible representations. A representation equilibrium is the fixed point of this configuration--price--certification loop. The framework separates position crowding through market impact from representation crowding generated by driver-space overlap and priced through a basis-invariant information-capacity cost. Under compactness, resolvent regularity and continuous certification, equilibrium exists at every switching cost; within a stable certification cell, informational congestion yields a concave population game and local uniqueness under a small-gain condition. At a settled configuration, a spectral statistic combining cross-impact, covariance and deployed capacity determines three position-path regimes: below one half the fundamental solution is unique; at the boundary only innovation-free deviations remain; above it, destabilising directions support a continuum of self-confirming conventions. Monotone impact lies inside the uniqueness region, while indefinite impact alone is not sufficient for multiplicity. Intermediary hedging can generate an indefinite response while round trips remain costly. Endogenous risk capacity bounds convention amplitudes, and least-squares learning makes the dominant convention neutral rather than attracting. The threshold is not estimated in data; instead, the empirical exercise documents an out-of-sample, driver-specific signature consistent with representation crowding and states the conditions required for direct measurement.