Source clarification: Lemma 5 applies its stated
policy-reward continuity to the finite endpoint families in its
compactness argument, including their boundary representatives.
Source clarification: its near-optimal
response-shape condition is used on the policies in that reward band.
The checked endpoint form makes the zero-length comparisons explicit
when an interval collapses.
Theorem 4 policy continuity — Source clarification.
The paper’s assumed continuity covers the acceptance-set domain used in
the formalization, for either state in each feasible open two-state
context.
Theorem 3 proof route
Lemma 9’s “for each non-surge policy, there exists a feasible price
ratio” → a direct Theorem 3 proof fixing one structured price before
comparing every policy (Appendix D.4). This avoids reversing the
quantifiers. If C<R1/R2<1, with target earning rates
R1,R2 and source feasibility threshold C, the
comparison gives acceptance of every trip in both states. The general
clause gives a finite or infinite upper cutoff in the non-surge state
and acceptance of every surge trip.