摘要：命题5要证明的是：存在一个出版商成本分担比例 ϕ的范围，使得在这个范围内，出版商和平台都愿意接受“成本分担契约”并投资区块链，从而实现供应链协调（即双方利润均不低于传统模式，且供应链总利润提高）。

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今天小编为大家带来“精读期刊《数字出版供应链下区块链投资与版权保护策略》命题5的证明”。

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Today, the editor brings the "Proof for Proposition 5 in the Journal Article ‘Blockchain Investment and Copyright Protection Strategies within the Digital Publishing Supply Chain’ ".

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一.思维导图（Mind Mapping)

二.精读内容（Intensive reading content）

命题5要证明的是：存在一个出版商成本分担比例 ϕ的范围，使得在这个范围内，出版商和平台都愿意接受“成本分担契约”并投资区块链，从而实现供应链协调（即双方利润均不低于传统模式，且供应链总利润提高）。

Proposition 5 seeks to demonstrate that there exists a range of publisher cost-sharing ratios ϕ within which both publishers and platforms are willing to accept the ‘cost-sharing agreement’ and invest in blockchain technology, thereby achieving supply chain coordination (i.e., ensuring that neither party's profits fall below those of the traditional model while increasing overall supply chain profitability).

具体条件分为两种情况：

The specific conditions are divided into two scenarios:

证明的核心是确保契约对双方都有利，即满足以下两个参与约束：出版商在契约下的利润不低于在传统版权保护模式下的利润；平台的参与约束：平台在契约下的利润不低于在传统版权保护模式下的利润。其中，在区块链模式（无论是否协调）下，均衡价格 pN∗=1/2pN∗=1/2，需求 D=1−pN∗=1/2D=1−pN∗=1/2。

The core of the proof lies in ensuring the contract benefits both parties, satisfying the following two participation constraints: the publisher's profit under the contract is no less than that under the traditional copyright protection model; the platform's participation constraint: the platform's profit under the contract is no less than that under the traditional copyright protection model. Under the blockchain model (whether coordinated or not), the equilibrium price pN∗=1/2pN∗=1/2 and demand D=1−pN∗=1/2D=1−pN∗=1/2.

情况1：k

Scenario 1: When k

ΔΠS1代表出版商从区块链投资中获得的毛利润增量（未扣除分担的成本）。 ΔΠP1代表平台从区块链投资中获得的毛利润增量（未考虑分担的成本）。

ΔΠS1 represents the incremental gross profit gained by the publisher from blockchain investment (before deducting shared costs). ΔΠP1 represents the incremental gross profit gained by the platform from blockchain investment (without considering shared costs).

我们要找到那个使契约刚好可行的临界点，即当F=FSP1时，ϕ的上下限重合。我们将F=FSP1代入ϕ的上下限表达式求解ϕ1。

We must identify the critical point at which the contract becomes viable, namely when F = FSP1, and the upper and lower bounds of ϕ coincide. Substituting F = FSP1 into the expressions for the upper and lower bounds of ϕ yields:ϕ1.

情况2：k>k1时，将函数代入参与约束不等式。

Scenario 2: When k > k1, substitute the function into the constraint inequality.

ΔΠS2代表出版商从区块链投资中获得的毛利润增量（未扣除分担的成本）。ΔΠP2代表平台从区块链投资中获得的毛利润增量（未考虑分担的成本）。

ΔΠS2 represents the incremental gross profit gained by the publisher from blockchain investments (before deducting shared costs).ΔΠP2 represents the incremental gross profit gained by the platform from blockchain investments (without considering shared costs).

我们要找到那个使契约刚好可行的临界点，即当F=FSP2时，ϕ的上下限重合。我们将F=FSP2代入ϕ的上下限表达式求解ϕ2。

We must identify the critical point where the contract becomes viable, namely when F equals FSP2, causing the upper and lower bounds of ϕ to coincide. We shall substitute F=FSP2 into the expression for the upper and lower bounds of ϕ to solve for ϕ2.

用“成本分担契约”可以解决市场失灵，实现双赢。当平台因投资成本高而犹豫时，出版商可以主动分担一部分成本。只要出版商分担的比例不超过一个上限，就能同时实现：

A “cost-sharing agreement” can resolve market failures and achieve mutual benefit. When platforms hesitate due to high investment costs, publishers can proactively share a portion of these expenses. Provided the publisher's contribution does not exceed a predetermined threshold, the following outcomes are simultaneously realised:

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本文由LearningYard新学苑原创，如有侵权，请联系删除。

参考资料：百度百科，Deepseek

参考文献：甄烨,田佳乐,王文利.数字出版供应链下区块链投资与版权保护策略[J].系统管理学报,2024,33(3):589-600.

翻译：DeepL

编辑：熙

排版：熙

审核：qin

来源：LearningYard学苑