Unconditional logarithmic rent conjecture

Let $T$ denote the time horizon, and let $\mathrm{Rent}_t$ be the rent at time $t$. Suppose the cumulative-rent bound of Theorem~ is

$$\sum_{t\le T}\mathrm{Rent}_t=\tilde O(\log T).$$

Unconditional logarithmic rent conjecture. The bound continues to hold when (L2)--(L4) are dropped: when the excitation is endogenous to the designer's policy, agents learn from their own (possibly off-path) data, and agents' learning is mutually entangled, with each tracking the others' evolving models, so that the policy, the estimators, and the obedience constraints co-evolve as an informational arms race.

Removing (L2)--(L4) removes the controls on these three couplings and leaves an open problem: whether logarithmic cumulative rent persists when endogenous excitation, self-perturbed estimation data, and mutually entangled learning are all present.