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These results underline the necessity of evaluating a contract format under various forms of system-parameter uncertainties — often at the expense of analytical tractability.
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We first present, for the deterministic-system-parameter situation, contract-designing procedures under two contract formats; namely, a "regular" version of [VD] (hereafter "[RVD]") and a "continuous" version of [VD] (hereafter "[CVD]").
In contrast, we show that [CVD] leads to perfect channel coordination — a significant result since most contract formats have been shown in the literature to be unable to coordinate a (p,e -channel.
The team proposed converting the seven contract formats into one single plain-language contract.
Our results highlight the need to study purchase contract formats designed specifically for dominant-retailer newsvendor-product channels.
The first-group consists of procedures for Reta to compute optimal parameters for each of these contract formats.
Reta may implement any one of four contract formats: price-only; franchise fee; two-part tariffs; and menu of contracts ([MC]).
For this increasingly prevalent but inadequately studied scenario, we propose plausible adaptations of several contract formats that have been widely studied in the dominant-manufacturer context.
Can the manufacturer induce the retailer to share her superior knowledge by informing the retailer that he will be using sophisticated channel-coordinating contract formats?
Our results then reveal that the performance of these contract formats under our scenario differs considerably from what one would surmise from the well-known results published for closely related scenarios.
These first-group results are then used to study: (i) the conditions under which Manu is interested in sharing his m-information and thus improving Reta's ˜m-perception; and (ii) how such information sharing conditions are affected by the contract formats.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com