Shin Kishimoto, Shigeo Muto (2012) “Fee Versus Royalty Policy in Licensing Through Bargaining: An Application of the Nash Bargaining Solution." Bulletin of Economic Research， Volume 64, Issue 2, pages 293–304. DOI: 10.1111/j.1467-8586.2010.00356.x. 220.127.116.11 [PDF]
==notes by yinung==
這是理論文章，證明 Royalty licensing 比 fixed fee licensing 來得好 for firms and social veiw.
裡頭有 licensing patents 的理論文獻
理論證明 fixed 比 royalty 好 in Kamien and Tauman (1986)
…Despite the fact that a royalty is often observed, theoretical analyses including Kamien and Tauman (1986) showed that a
ﬁxed fee was superior to a royalty for both the patent holder and consumers.
但 Kamien and Tauman (2002) and Wang (1998) 證明 royalty 比 fixed 好
…Kamien and Tauman (2002) extended the model of Wang (1998) to a Cournot oligopoly market, and showed that if the patent holder competed in the product market with a suﬃciently large number of ﬁrms, then a royalty is superior to a ﬁxed fee for
談判方式： “take-it-or-leave-it“ (像 ultimatum game)
…These studies basically assumed a “take-it-or-leave-it” licensing manner; that is, the patent holder ﬁrst announces a level of a ﬁxed fee (or a royalty), and then ﬁrms decide whether or not to buy the patent. Analyses were done in terms of noncooperative game theory.
也有用合作賽局為理論架構來研究 for licensing the patent
…Tauman and Watanabe (2007) applied the Shapley value and showed that the patent holder’s proﬁt in the Shapley value approximated his/her equilibrium proﬁt in the noncooperative model of Kamien and Tauman (1986) as the number of ﬁrms became large. Watanabe and Muto (2008) characterized the upper bound and the lower bound of the patent holder’s proﬁts in the bargaining set.
In this paper, we consider a Cournot duopoly market in which the patent-holding firm negotiates with its rival firm about payments for licensing a cost-reducing innovation. Applying the Nash bargaining solution, we compare two licensing policies, a fixed fee and a royalty. Our results are as follows. Royalty licensing is better than fixed fee licensing for both firms if the innovation is not drastic. So, royalty licensing is always carried out. Moreover, though there exists a case in which consumers prefer fixed fee licensing, royalty licensing is always superior to fixed fee licensing from the social point of view.
Kamien, M.I., Tauman, Y. (1986). Fees Versus Royalties and the Private Value of a Patent. Quarterly Journal of Economics, 101, 471-491.
Kamien, M.I., Tauman, Y. (2002). Patent Licensing: The Inside Story. The Manchester School, 70, 7-15.
 Rubinstein, A. (1982). Perfect Equilibrium in a Bargaining Model. Econometrica, 50, 97-109.
 Sen, D. (2005). Fee Versus Royalty Reconsidered. Games and Economic Behavior, 53, 141-147.
 Sen, D., Tauman, Y. (2007). General Licencing Schemes for a Cost-reducing Innovation. Games and Economic Behavior, 59, 163-186.
 Sempere-Monerris, J.Jos´ e., Vannetelbosch, V.J. (2001). The Relevance of Bargaining for the Licensing of a Cost-reducing Innovation. Bulletin of Economic Research, 53, 101-115.
 Tauman, Y .,Watanabe, N. (2007). The Shapley value of a patent licensing game: the asymptotic equivalence to non-cooperative results. Economic Theory, 30, 135-149.
 Wang, X.H. (1998). Fee Versus Royalty Licensing in a Cournot Duopoly Model. Economics Letters, 60, 55-62.
 Watanabe, N.,Muto, S. (2007). Stable Proﬁt Sharing in Patent Licensing: General Bargaining Outcomes. Int. Journal of Game Theory, forthcoming.