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Social Choice and Welfare
Published in:

20-06-2024 | Original Paper

Patent package structures and sharing rules for royalty revenue

Authors: Takaaki Abe, Emiko Fukuda, Shigeo Muto

Published in: Social Choice and Welfare | Issue 2/2024

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Abstract

The role of patent pools—one-stop systems that gather patents from multiple patent holders and offer them to users as a package—is gaining research attention. To bolster the scarce stream of the literature that has addressed how a patent pool agent distributes royalty revenues among patent holders, we conduct an axiomatic analysis of sharing rules for royalty revenue derived from patents managed by a patent pool agent. In our framework, the patent pool agent organizes the patents into some packages, which we call a package structure. By using the hypergraph formulation developed by van den Nouweland et al. (Int J Game Theory 20:255–268, 1992), we analyze sharing rules that consider the package structure. In our study, we propose a sharing rule and show that it is the unique rule that satisfies efficiency, fairness, and independence requirements. In addition, we analyze sharing rules that enable a patent pool agent to organize a revenue-maximizing and objection-free profile.
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Footnotes
1
See Subsection 4.2 of Kim (2004) for the details. In the conclusion (Kim 2004), the author also mentioned the importance of exogenously specified sharing rules.
 
2
The Myerson value is an extension of the Shapley value (Shapley 1953). Myerson (1980) extended the Myerson value (for games with network structures) to the class of NTU-games with hypergraph structures. van den Nouweland et al. (1992) generalized the Myerson value to the class of TU-games with hypergraph structures.
 
3
A sharing rule assigns a share to each patent and a patent holder who contributes some patents to the agent receives the sum of the shares assigned to the patents. Moreover, an international agent usually calculates royalty revenue by country. Therefore, in this study, we focus on revenue sharing within one country.
 
4
Specifically, van den Nouweland et al. (1992) used component efficiency: for communication situations. The component efficiency requires an allocation to be efficient for every component (see van den Nouweland et al. (1992) for details). Moreover, the Shapley value (Shapley 1953) is defined as follows. For every \(i\in N\), \({\text {Sh}}_i(v)=\sum _{S:i\in S\subseteq N} \frac{(|S|-1)!(|N|-|S|)!}{|N|!}\left( v(S)-v(S{\setminus } \{i\})\right) \). For every S with \(i\in S\subseteq N\), \(v(S)-v(S{\setminus } \{i\})\) represents the marginal contribution of i to S. Therefore, the Shapley value can be seen as the expected value of the marginal contributions of i.
 
5
The original form of this concept was introduced by Thrall (1962) and Thrall and Lucas (1963) to describe externalities among coalitions and later called an embedded coalition in the class of partition function form games. We extend this concept to our framework.
 
6
This framework can be generated from the demand side for patent packages à la the Shapiro–Cournot model (Shapiro (2001)). Let \(\mathcal {H}=\{S_1,\ldots ,S_m\}\) be a package structure. For every \(S\in \mathcal {H}\), consider the demand \(D_S^\mathcal {H}(r_{S_1},\ldots ,r_{S_m})\) for package S, where \(r=(r_S)_{S\in \mathcal {H}}\) represents a profile of the license fees \(r_S\) for packages \(S\in \mathcal {H}\). Assuming the patent pool agent maximizes the total revenue obtained from \(\mathcal {H}\), let \(r^*=(r^*_S)_{S\in \mathcal {H}}=\arg \max _{r}\sum _{S\in \mathcal {H}}r_S D^\mathcal {H}_S(r)\) subject to \(0\le r_S\le \bar{r}_S\) for every \(S\in \mathcal {H}\). We set \(v(S,\mathcal {H})=r^*_S D^\mathcal {H}_S(r^*)\) for every \(S\in \mathcal {H}\).
 
7
No problem arises by assigning an arbitrary value to \(v(S,\mathcal {H}')\) for every \(\mathcal {H}'\subseteq 2^N{\setminus } \{\emptyset \}\) with \(\mathcal {H}'\not \in \{\mathcal {H}_1, \mathcal {H}_2, \mathcal {H}_3\}\) and every \(S\in \mathcal {H}'\)
 
8
As demonstrated in Table 2, the package-wise equal sharing rule does not straightforwardly obey F and PI in the presence of substitutability. This is because substitutability allows S to change its worth depending on \(\mathcal {H}\) and, hence, the requirements of F and PI become very demanding. Nevertheless, in the next section, we will propose another sharing rule that satisfies the generalized fairness requirement even in the presence of substitutability.
 
9
This example is also generated from the demand side with the following setups. For every \(\mathcal {H}=\mathcal {H}_2,\ldots ,\mathcal {H}_8\) and \(S\in \mathcal {H}\), let \(D_S^\mathcal {H}(r)=a^\mathcal {H}_S-b^\mathcal {H}_S \cdot (\sum _{S'\in \mathcal {H}}\theta _{SS'}r_{S'})\), where \(|\theta _{SS'}|\) represents the degree of substitutability between S and \(S'\): specifically, \(\theta _{SS'}=\theta _{S'S}\) for every \(S,S'\subseteq N\); \(\theta _{SS'}=1\) if \(S=S'\); and \(\theta _{SS'}\le 0\) if \(S\ne S'\). Note that \(\theta _{SS'}= 0\) states that there is no substitutability between the two packages. The numerical example Table 3 is obtained from, for example, the following parameters: \((\theta _{\{1\}\{1\}},\theta _{\{1\}\{2\}},\theta _{\{1\}\{1,2\}})=(1,0,-1)\), \((\theta _{\{2\}\{1\}},\theta _{\{2\}\{2\}},\theta _{\{2\}\{1,2\}})=(0,1,-1)\), and \((\theta _{\{1,2\}\{1\}},\theta _{\{1,2\}\{2\}},\theta _{\{1,2\}\{1,2\}})=(-1,-1,1)\); \(a^{\mathcal {H}_2}_{\{1\}}=a^{\mathcal {H}_3}_{\{2\}}=2\sqrt{2}\), \(a^{\mathcal {H}_4}_{\{1,2\}}=4\sqrt{2}\), \((a^{\mathcal {H}_5}_{\{1\}},a^{\mathcal {H}_5}_{\{2\}})=(2\sqrt{2},2\sqrt{2})\), \((a^{\mathcal {H}_6}_{\{1\}},a^{\mathcal {H}_6}_{\{1,2\}})=(a^{\mathcal {H}_7}_{\{2\}},a^{\mathcal {H}_7}_{\{1,2\}})=(2\sqrt{2},\sqrt{2})\), \((a^{\mathcal {H}_8}_{\{1\}},a^{\mathcal {H}_8}_{\{2\}},a^{\mathcal {H}_8}_{\{1,2\}})=(\sqrt{2},\sqrt{2},\sqrt{2} /2)\); \(b^\mathcal {H}_S=1/2\) for \((S,\mathcal {H})=(\{1,2\},\mathcal {H}_8)\) and 1 otherwise; and \(\bar{r}_{S}=\sqrt{2}\) for every \(S\subseteq N\).
 
10
In the absence of substitutability, the sharing rule readily achieves this requirement because the full profile \(\mathcal {H}= 2^N {\setminus } \{\emptyset \}\) maximizes \(\sum _{T\in \mathcal {H}}v(T)\), and no one has an incentive to withdraw its patents.
 
11
If condition (a) requires “weak inequalities \(\ge \) for all \(j\in S\) and strict one > for some \(i\in S\),” then the combination of PM and PE implies \(RM(v)=OF^\psi (v)\).
 
12
Note that for \(\mathcal {H}_0=\emptyset \), we have \(\psi _i(v,\mathcal {H}_0)=\psi '_i(v,\mathcal {H}_0)\) for every \(i\in N\) by PE and the non-negativity of \(\psi \).
 
13
For the details of components of a hypergraph, see van den Nouweland et al. (1992). The collection of the components of \(\mathcal {H}\), i.e., \(\mathcal {C}(\mathcal {H})\), partitions N, and every pair of the components has an empty intersection.
 
Literature
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Hafalir IE (2007) Efficiency in coalition games with externalities. Games Econ Behav 61(2):242–258CrossRef
Kim SH (2004) Vertical structure and patent pools. Rev Ind Organ 25:231–250CrossRef
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Metadata
Title
Patent package structures and sharing rules for royalty revenue
Authors
Takaaki Abe
Emiko Fukuda
Shigeo Muto
Publication date
20-06-2024
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 2/2024
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-024-01532-3

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