ベンチャーと戦略ゲーム

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1 ( ) M&A IPO (John von Neumann) (John F. Nash, Jr.) (Oskar Morgenstern) Theory of games and economic behavior 1) strategic-form game extensive-form game normal-form game non-cooperative cooperative 1

2 10) Nash equivalence 1994 (Reinhard Selten) (John Charles Harsanyi) 5) (John Forbes Nash, Jr.) J. The Agencies Method and Cooperative Games ( ) 9) fixed point theorem two-person game 2 maximin minimax n 2

3 saddle point (Lloyd Stowell Shapley) , 3) - - Nash equilibrium 2 hare( ) 1 stag( ) 2 stag 2 cooperate 1 stag 0 hare-hare payoff matrix - Stag hare stag 2, 2 0, 1 hare 1, 0 1, 1 defect 2 defect Pareto efficiency Cooperate Defect Cooperate 2, 2 0, 3 Defect 3, 0 1, 1 3

4 folklore defect D cooperative C p D Σan = a1/(1-r) D d p 1 p^2 1 p^3 1+ d p/(1 p) C C c p^1c p^2c p^3c c/(1 p) C D p (D C)/(D 1) Q.E.D. p C D ( ) ! cooperative games coalition BPR ( ) 4

5 common knowledge principal agent Strategic complements - maximin - stagstag minimax risk dominant - hare-hare SME correlated strategy zero-sum 2 equilibriumir = ( ) 12) ( Beautiful Mind) NSA 5

6 ( ) YouTube 11) Adam Smith said "the best result comes from everyone in the group doing for himself," Right? Incomplete, incomplete, Okay? ( ) Because the best result will come from everyone in the group doing what's best for himself, right? ( ) The Best for the Group comes when everyone in the group does what's best for himself AND the group (Louis Nirenberg) Theory of nonlinear partial differential equations and its applications to geometric analysis 2014 (2015 ) ( 77 ) )

7 4. networked innovation ecosystem heterogeneous cooperation coalition "The fruits of your research are proportional to the number of your conversations with others. ( ) " seeds SME intellectual property visibility 8) ) 17,000 / ,400 7

8 10,000 60% % 2012 VC 265,24 41% M&A IPO ( ) AIST NIMS10 KEK % ICT ICT ICT TX ( ) ( ) IT 12 8

9 14) " " 5. STEM Science, Technology, Engineering, Mathematics Stem EV3 15)

10 16) "Young man, in mathematics, you don't understand things. You just got used to them." ( ) References: 1) Theory of Games and Economic Behavior, by John von. Neumann, and Oskar Morgenstern, Princeton University Press, reprint in ) Musical Chair: Modeling Noisy Evolution, Kenneth G. Binmore, University College London, Larry Samuelson University of Wisconsin, Richard Vaughan University of College London, ) Strategic merger waves: A theory of musical chairs, Flavio Toxvaerda,b,c, Faculty of Economics, University of Cambridge, UK. Department of Economics and Center for the Study of Rationality. Hebrew University of Jerusalem, Israel ccepr, UK. Received 12 January 2006; final version received 24 May 2007 Available online 27 June ) ) Credit from Lindau Nobel Laureat Meetngs /2006-the-agencies-method-and-cooperative-games/meeting-2006-eco 6) Credit from The Abel Prize, 7) 8) ; ) The Agencies Method for Coalition Formation in Experimental Games, John F.Nash Jr. Rosemarie Nagel, Axel Ockenfels, and Reinhard Selten texts_and_graphics/main.content/vz.class.pac.507/stonybbrooktalknagel.ppt ) Home Page of John F, Nash Jr. 11) Nash Equilibrium from "Beautiful Mind" 12) web.econ.keio.ac.jp/staff/hattori/sep_prbk.pdf 13) 14) Chris Anderson,'s home page 14) Math Obsession, home page of imetrics Academies 15) Photo via google images John von Neumann collection May 23, 2015, Written by S. Kusafusa 10

1. 2. 3. 2 (90, 90) (86, 92) (92, 86) (88, 88) Figure 1 Exam or presentation? a (players) k N = (1, 2,..., k) 2 k = 2 b (strategies) i S i, i = 1, 2 1

1. 2. 3. 2 (90, 90) (86, 92) (92, 86) (88, 88) Figure 1 Exam or presentation? a (players) k N = (1, 2,..., k) 2 k = 2 b (strategies) i S i, i = 1, 2 1 2014 11 in progress 1 1 2 2 2.1................................... 2 2.2........................................ 4 3 Nash Equilibrium 6 3.1........................................ 6 3.2..........................................