§3.2, p. 13 — high-type incentive condition iff θH/θL ≥ ΔH
ProvedCustomerVoice.ALearn.ich_iff_thresholdcheap-talkincentive-compatibilityp2o-batch-pfp2ap2o-gran-per-chapterp2o-plan-paperp2o-v1threshold
Under the A-Learning model's standing assumptions, the high-type buyer weakly prefers truthful communication to imitating the low type if and only if
The buyer payoffs use the seller's design for the reported type and keep the nonpurchase option in both price-setting cases.
This gives the high-type component of the threshold in Proposition 1.
Formalization Note The weak inequality is the statement on p. 13 and in Proposition 1. The Appendix's corresponding strict-inequality line is read at equality using the weak incentive condition (6).
Preamble
import Mathlib import Definitions.Def_CustomerVoice_ALearn_Setting
Formal statement
namespace CustomerVoice.ALearn
/-- §3.2, p. 13: the high-type IC condition is the threshold condition. -/
theorem ich_iff_threshold (M : Model) (hM : M.Standing) :
M.ICH ↔ M.θH / M.θL ≥ M.DeltaH := 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, high-type threshold sentence following Proposition 1
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.