The private value of a patent: A cooperative approach
We consider a game in coalitional form played by the firms of a Cournot industry and an outside patent holder of a cost-reducing innovation. The worth of a coalition of players is the total Cournot profit of the active firms within this coalition. The number of firms that a coalition activates is determined by the Nash equilibrium of the game played by the coalition and its complement, where the strategy of each is the number of firms to be activated. Only firms in a coalition containing the patent holder are allowed to use the new technology. We prove that when the industry size increases indefinitely, the Shapley value of the patent holder approximates the payoff he obtains in a standard non-cooperative setup where he has the entire bargaining power. We also examine a partition game which considers for every coalition all structures of its complement, namely all partitions of the complement into sub-coalitions. The coalition and every sub-coalition of the complement simultaneously decide how many of their firms to be activated. We prove a similar equivalence result for an extension of the Shapley value from coalitional games to partition games.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Morton I. Kamien & Yair Tauman, 1986.
"Fees Versus Royalties and the Private Value of a Patent,"
The Quarterly Journal of Economics,
Oxford University Press, vol. 101(3), pages 471-491.
- Morton I. Kamien & Yair Tauman, 1984. "Fees Versus Royalties and the Private Value of a Patent," Discussion Papers 583, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Michael L. Katz & Carl Shapiro, 1986. "How to License Intangible Property," The Quarterly Journal of Economics, Oxford University Press, vol. 101(3), pages 567-589.
- Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 37-44.
- Sen, Debapriya & Tauman, Yair, 2007. "General licensing schemes for a cost-reducing innovation," Games and Economic Behavior, Elsevier, vol. 59(1), pages 163-186, April.
- Debapriya Sen & Yair Tauman, 2002. "General licensing schemes for a cost-reducing innovation," Department of Economics Working Papers 02-03, Stony Brook University, Department of Economics.
- Kenneth Arrow, 1962. "Economic Welfare and the Allocation of Resources for Invention," NBER Chapters,in: The Rate and Direction of Inventive Activity: Economic and Social Factors, pages 609-626 National Bureau of Economic Research, Inc.
- Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
- Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions and Externalities in the Value," Working Papers 2005-11, Brown University, Department of Economics.
- Serrano, Roberto & Clippel, Geoffroy de, 2005. "Marginal contributions and externalities in the value," UC3M Working papers. Economics we057339, Universidad Carlos III de Madrid. Departamento de Economía.
- Geoffroy de Clippel & Roberto Serrano, 2007. "Marginal contributions and externalities in the value," Working Papers 2007-04, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
- Kamien, Morton I., 1992. "Patent licensing," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 11, pages 331-354 Elsevier.
- Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
- Kamien, Morton I. & Tauman, Yair & Zamir, Shmuel, 1990. "On the value of information in a strategic conflict," Games and Economic Behavior, Elsevier, vol. 2(2), pages 129-153, June.
- Can Erutku & Yves Richelle, 2007. "Optimal Licensing Contracts and the Value of a Patent," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 16(2), pages 407-436, 06.
- Yair Tauman & Naoki Watanabe, 2007. "The Shapley Value of a Patent Licensing Game: the Asymptotic Equivalence to Non-cooperative Results," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 135-149, January.
- Navarro, Noemi, 2007. "Fair allocation in networks with externalities," Games and Economic Behavior, Elsevier, vol. 58(2), pages 354-364, February. Full references (including those not matched with items on IDEAS)