theory) (Clarke IoT (International Conference on Autonomous Agents and Multiagent Systems (AAMAS)) 1/3 (Distributed problem solving)

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1 Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, Japan (game theory) (mechanism design) (proper scoring rule) (coalitional game). JL 0011/16/ C 2016 SICE 1. IoT 1) 2), 3) (Distributed AI) 4) (Distributed problem solving) (Multiagent systems) (Equilibrium analysis) Wellman (General equilibrium theory) 5) Ephrati (Clarke tax) 6) 7) 8) 9) 12) (International Conference on Autonomous Agents and Multiagent Systems (AAMAS)) 1/ )

2 1 Target1 Target2 Target1 5, 3 1, 1 Target2 5, 5 2, 1 Tambe (Stackelberg competition) 2 Target1 Target2 1 1 Target2 Target1 Target1 1 Target2 1 1 Target2 1 Target1 5 5 ( ) Target1 Target2 1/2 Target ( 5) = ( 3) =1 Target1 p p 29/52 Target1 23/52 Target2 22/52 Target1 30/52 Target Tambe ARMOR Hurwicz 14), 15) 16), 17) 1 A 500 B 400 C 300 A 500 A 401 A 399 A (Social surplus) ( ) (Vickrey

3 2 A B C (a) 3 A B (b) 2 ) A A B,C ( ) (Incentive compatibility) ( ) ) Vickrey-Clarke-Groves (VCG) Vickrey 1 ( ) 2 (a) 1 1 A B 7 C A C A B 7 A A C 4 A C B ) VCG 19) 2(b) A 7 0=7 A 2(a) A C (7 4) + (7 5) = ) Vickrey

4 1 o(θ H,θ W ): H( ), W( ), M( ), B( ), π H,π W : p: (θ H,θ W )=(high,high) (θ H,θ W )=(high,low) (θ H,θ W )=(low,high) (θ H,θ W )=(low,low) VCG o=m, π H = π W =5,000 o=h, π H =200 o=w, π W =200 o=m, π H = π W =100 5,136 o=b o=h o=w o=m 5,248 o=w (p =0.55), o=h o=w o=h (p =0.43), 5,510 B(p =0.45) W(p =0.57) o=m, π W =100 o=h o=w o=m 5,688 VCG 2(b) 2(a) Conitzer (high) 1 (low) high v( ) =11, 000 v( ) =6, 000 v( ) =1, 000 v( ) =0 low v( ) =1, 200 v( ) =1, 100 v( ) =1, 000 v( ) =0 0.2 high 0.8 low H, W θ H, θ W o(θ H,θ W ) π H (θ H,θ W ), π W (θ H,θ W ) (Individual rationality) v H (θ H,o(θ H,θ W )) π H (θ H,θ W ) 0 v W (θ W,o(θ H,θ W )) π W (θ H,θ W ) 0 ˆθ H, ˆθ W v H (θ H,o(θ H,θ W )) π H (θ H,θ W ) v H (θ H,o(ˆθ H,θ W )) π H (ˆθ H,θ W ), v W (θ W,o(θ H,θ W )) π W (θ H,θ W ) v W (θ H,o(θ H, ˆθ W )) π W (θ H, ˆθ W ) max(v H (θ H,o(θ H,θ W )) + v W (θ W,o(θ H,θ W ))) CPLEX ( 1) 4. 3 Vickrey ) T (s x) x s (Strictly proper)

5 x 1 0 p ˆp pˆp +(1 p)(1 ˆp) p >1/2 ˆp =1 p =3/4 ˆp =3/4 5/8 ˆp =1 6/8 T (x ˆp) = 1 (x ˆp) 2 T (x = 1 ˆp) = ln ˆp T (x = 0 ˆp) = ln(1 ˆp) 1 (1 ˆp) 2 1 (0 ˆp) 2 p(1 (1 ˆp) 2 )+(1 p)(1 ˆp 2 ) ˆp = p ln ˆp ln(1 ˆp) p ln ˆp +(1 p)ln(1 ˆp) ˆp = p Robu 22) 1 Robu 23) 5. 24) 25) A,B,C 3,{A},{B},{C},{AB},{AC},{BC},{ABC} [{A},{B},{C}] 2 1 [{AB},{C}], [{AC},{B}], [{BC},{A}] 3 3 [{ABC}] 5 A v(a)=0 A,B v(ab)=5 A,B,C v(abc)=11 8 (Marginal contribution network, MC-net) 26) MC-net {(A B,5), (B,2), (C,4), (B C, 2)} v(ab) v(ab)= =5 MC-net

27) Shoham 3) (S) (24220002, 24 28 ) 2016 9 21 1 (2015) 2 G. Weiss Ed.: Multiagent Systems, MIT Press (1999) 3 Y. Shoham and K.

6 27) Shoham 3) (S) ( , ) (2015) 2 G. Weiss Ed.: Multiagent Systems, MIT Press (1999) 3 Y. Shoham and K. Leyton-Brown: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge University Press (2009) 4 (1996) 5 M.P. Wellman: A market-oriented programming environment and its application to distributed multicommodity flow problems, Journal of Artificial Intelligence Research, 1, 1/23 (1993) 6 E. Ephrati and J.S. Rosenschein: The clarke tax as a consensus mechanism among automated agents, Proceedings of the Ninth National Conference on Artificial Intelligence (AAAI- 91), 173/178 (1991) 7 J.S. Rosenschein and G. Zlotkin: Designing conventions for automated negotiation, AI Magazine, 15 3, 29/46 (1994) 8 D. Monderer, M. Tennenholtz, and H. Varian: Economics and artificial intelligence, Games and Economic Behavior, 35 1, 1/5 (2001) 9 R.K. Dash, N.R. Jennings, and D.C. Parkes: Computationalmechanism design: a call to arms, IEEE Intelligent Systems, 18 6, 40/47 (2003) 10 N. Nisan, T. Roughgarden, É. Tardos, and V.V. Vazirani Eds.: Algorithmic Game Theory, Cambridge University Press (2007) 11 V. Conitzer: Making decisions based on the preferences of multiple agents, Communications of the ACM, 53 3, 84/94 (2010) 12 D.C. Parkes and M.P. Wellman: Economic reasoning and artificial intelligence, Science, , 267/272 (2015) 13 M. Tambe: Security and Game Theory: Algorithms, Deployed Systems, Lessons Learned, Cambridge University Press (2011) 14 (2008) 15 (2010) 16 N. Nisan: Introduction to mechanism design (for computer scientists), Algorithmic Game Theory (Eds. by N. Nisan, T. Roughgarden, É. Tardos and V.V. Vazirani), Cambridge University Press (2007) 17 3 ( ) 29 4, 15/31 (2012) 18 P. Cramton, Y. Shoham, and R. Steinberg Eds.: Combinatorial Auctions, MIT Press (2005) 19 M. Yokoo, Y. Sakurai, and S. Matsubara: Robust combinatorial auction protocol against false-name bids, Artificial Intelligence Journal, 130 2, 167/181 (2001) 20 V. Conitzer and T. Sandholm: Complexity of mechanism design, Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence, UAI 02, 103/110 (2002) 21 T. Gneiting and A.E. Raftery: Strictly proper scoring rules, prediction, and estimation, Journal of the American Statistical Association, , 359/378 (2007) 22 V. Robu, R. Kota, G. Chalkiadakis, A. Rogers, and N. Jennings: Cooperative virtual power plant formation using scoring rules, Proceedings of the 26th AAAI Conference on Artificial Intelligence (2012) 23 N. Miller, P. Resnick, and R. Zeckhauser: Eliciting informative feedback: The peer-prediction method, Manage. Sci., 51 9, 1359/1373 (2005) 24 W. Saad, Z. Han, M. Debbah, A. Hjørungnes, and T. Başar: Coalitional game theory for communication networks, IEEE Signal Processing Magazine, 26 5, 77/97 (2009) 25 L. Vig and J.A. Adams: Multi-robot coalition formation, IEEE Transactions on Robotics, 22 4, 637/649 (2006) 26 S. Ieong and Y. Shoham: Marginal contribution nets: A compact representation scheme for coalitional games, Proceedings of the 6th ACM Conference on Electronic Commerce, EC 05, 193/202 (2005) 27 H.R. Varian: Economic mechanism design for computerized agents, First Usenix Workshop on Electronic Commerce (1995) NTT 2007 ( )

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