§3.2, p. 13 — low-type incentive condition iff θH/θL ≥ ΔL
ProvedCustomerVoice.ALearn.icl_iff_thresholdcheap-talkincentive-compatibilityp2o-batch-pfp2ap2o-gran-per-chapterp2o-plan-paperp2o-v1threshold
Under the A-Learning model's standing assumptions, the low-type buyer weakly prefers truthful communication to overstating its preference if and only if
The buyer payoff allows the low type to decline a product priced above its valuation.
This gives the low-type component of the threshold in Proposition 1.
Formalization Note The weak inequality is the statement on p. 13 and in Proposition 1. The max with zero in the payoff is essential for the low type's deviation; the pricing stage enters through equation (5).
Preamble
import Mathlib import Definitions.Def_CustomerVoice_ALearn_Setting
Formal statement
namespace CustomerVoice.ALearn
/-- §3.2, p. 13: the low-type IC condition is the threshold condition. -/
theorem icl_iff_threshold (M : Model) (hM : M.Standing) :
M.ICL ↔ M.θH / M.θL ≥ M.DeltaL := by sorry
end CustomerVoice.ALearn
Source
Guo, The Voice of Customers in Customization, SSRN working paper 3994319 (version of 2023-11-29, https://ssrn.com/abstract=3994319), p. 13, §3.2, low-type threshold sentence following Proposition 1
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.