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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
No new data were created or analysed in this study. Data availability is not applicable to this article.
Notes
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.
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.
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.
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 \(S\in \mathcal {H}\).
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 \(S\in \mathcal {H}'\)
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.
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 \(S\subseteq N\).
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.
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 \(RM(v)=OF^\psi (v)\).
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 \(\psi \).
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.
References
Aoki R, Nagaoka S (2004) The consortium standard and patent pools. Hitotsubashi Univ Econ Rev 55(4):345–357
Aumann RJ, Maschler M (1964) The bargaining set for cooperative games. In: Dresher M, Shapley LS, Tucker AW (eds) Advances in game theory. Annals of mathematics studies No. 52. Princeton University Press, Princeton
Casajus A (2009) Networks and outside options. Soc Choice Welf 32:1–13
Hafalir IE (2007) Efficiency in coalition games with externalities. Games Econ Behav 61(2):242–258
Kim SH (2004) Vertical structure and patent pools. Rev Ind Organ 25:231–250
Layne-Farrar A, Lerner J (2011) To join or not to join: examining patent pool participation and rent sharing rules. Int J Ind Organ 29(2):294–303
Lerner J, Tirole J (2004) Efficient patent pools. Am Econ Rev 94(3):691–711
Myerson RB (1977) Graphs and cooperation in games. Math Oper Res 2(3):225–229
Myerson RB (1980) Conference structures and fair allocation rules. Int J Game Theory 9:169–182
Shapiro C (2001) Navigating the patent thicket: cross licenses, patent pools, and standard-setting. In: Jaffe A, Lerner J, Stern S (eds) Innovation policy and the economy, vol 1. MIT Press, Cambridge
Shapley LS (1953) A value for n-person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games, vol II. Princeton University Press, Princeton
Tesoriere A (2019) Stable sharing rules and participation in pools of essential patents. Games Econ Behav 117:40–58
Thrall RM (1962) Generalized characteristic functions for n-person games. In: Proceedings of the Princeton university conference of Oct, 1961
Thrall RM, Lucas WF (1963) N-person games in partition function form. Nav Res Logist Q 10(1):281–298
van den Nouweland A, Borm P, Tijs S (1992) Allocation rules for hypergraph communication situations. Int J Game Theory 20:255–268
Acknowledgements
The authors acknowledge the financial support from JSPS: (Abe) No. 22K13362, No. 22H00829, and (Abe and Fukuda) No. 24K04776. We wish to thank René van den Brink, Frank Huettner, Takumi Kongo, and Satoshi Nakada for their comments. We are grateful to two anonymous reviewers and the Associate Editor for their helpful suggestions.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Abe, T., Fukuda, E. & Muto, S. Patent package structures and sharing rules for royalty revenue. Soc Choice Welf 63, 277–297 (2024). https://doi.org/10.1007/s00355-024-01532-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-024-01532-3