1. The Shapley Value of a Patent Licensing Game: the Asymptotic Equivalence to Non-cooperative Results by Yair Tauman and Naoki Watanabe

2. １. Introduction patent licensing games: non-cooperative mechanisms (policies) upfront fee or royalty by Kamien and Tauman (1984, 1986) Sen (forthcoming in GEB) auction by Katz and Shapiro (1985, 1986) the innovator has full bargaining power i.e., take-it-or-leave-it offers to potential licensees

3. Other Papers optimal licensing policy Cournot and Bertrand Kamien, Oren and Tauman (1992) Bertrand with differentiated goods Muto (1993) optimal combination of licensing policies Sen and Tauman (2002)

4. Why cooperative approach? Macho-Stadler et al. (1996) licensing agreements are basically contract terms signed as negotiation results a role of patent system may be facilitating the resolution of disputes in complicated bargaining procedures over licensing issues analyze licensing agreements from the cooperative point of view

5. a key problem how to define the worth of a coalition of players in the presence of strategic interactions? a new characteristic function appropriate for oligopolistic markets von-Neumann and Morgenstern ’ s minmax … incredible threat!

6. the main proposition (Proposition 4) In increasing the number of firms in the market, the Shapley value of the innovator approximates his payoff in the auction mechanism (even for general demand functions). quite surprising: (1) the innovator does not have full bargaining power in cooperative games and (2) the Shapley value measures a fair contribution of him to the total industry profit

7. 2. The Characteristic Functions

9. the minmax approach

10. Propositions 1 and 2: minmax=maxmin

11. 3. The Shapley Value

12. Proposition 4 : lim Sho(v)=e(a-c)

13. 4. The Emptiness of the Core

14. 5. Remarks Kamien (1992) : if n>2K, then the innovator auctions off K licenses and extract the entire industry profit, which is e(a-c) This equivalence occurs even with general demand functions that are downward sloping and differentiable in price Watanabe and Muto (2004, 2005) Imai and Watanabe (2005, forthcoming in JER)