Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, Japan E-mail: matsubara@i.kyoto-u.ac.jp (game theory) (mechanism design) (proper scoring rule) (coalitional game). JL 0011/16/5511 0948 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)) 1/3 2. 13) 948 55 11 2016 11
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 Target1 0.5 5+0.5 ( 5) = 0 0.5 ( 3) + 0.5 5=1 Target1 p p 29/52 Target1 23/52 Target2 22/52 Target1 30/52 Target2 0.433 0.294 Tambe ARMOR 3. 2 3 4 Hurwicz 14), 15) 16), 17) 1 A 500 B 400 C 300 A 500 A 401 A 399 A (Social surplus) ( ) (Vickrey 55 11 2016 11 949
2 A 5 0 5 B 0 0 7 C 0 4 4 (a) 3 A 5 4 9 B 0 0 7 (b) 2 ) A 2 400 A B,C ( ) (Incentive compatibility) ( ) 2 3.1 18) Vickrey-Clarke-Groves (VCG) Vickrey 1 ( ) 2 (a) 1 1 A 5 0 5 B 7 C 0 4 4 A C A B 7 A A C 4 A 7 4 3 C 7 5 2 B 9 7 18) VCG 19) 2(b) A 7 0=7 A 2(a) A C (7 4) + (7 5) = 5 7 5 3.2 20) Vickrey 950 55 11 2016 11
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 4 1. 2. 3. 4. 2 1 (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 0.6 0.3 0.1 21) T (s x) x s (Strictly proper) 55 11 2016 11 951
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} 8 1 1 3 [{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) 1 2 4 v(ab)= 5 + 2 2=5 MC-net 6. 952 55 11 2016 11
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