24 200902728

1 4 1.1......................... 4 1.2......................... 4 1.3......................... 5 1.4......................... 5 1.5........................... 5 1.6...................... 6 2 7 2.1....................... 7 2.1.1................... 7 2.1.2................... 9 2.1.3................... 9 2.2..................... 10 2.3................. 11 2.3.1........... 14 2.3.2........... 14 2.4......................... 15 2.4.1................ 15 2.4.2................. 16 2.4.3................. 16 2.4.4................ 17 2.5........................... 21 2.5.1................... 21 2.5.2................... 21 1

2 3 22 3.1.................... 23 3.1.1....................... 23 3.1.2..................... 24 3.1.3....................... 26 3.2......................... 31 3.2.1........................ 31 3.2.2................. 32 4 35 4.1......................... 35 4.2....................... 35 4.2.1...................... 35 4.2.2....................... 36 4.2.3....................... 37 5 39 40 43

2.1............. 12 2.2............ 12 2.3.................... 13 2.4.................... 13 2.5 LETS....................... 18 3

1 1.1 [1][2][3] 1.2 4

1 5 [1][2][3] 1.3 1.4 1.5 1

1 6 1.6 2 3 4 5

2 2.1 [4] 2.1.1 [3][4] 7

2 8 [3][4] [3][4] 0 [3][4]

2 9 2.1.2 2.1.3

2 10 2.2 1 3

2 11 2.3 2 1 Edy( ) Suica( ) 1 2.1 2.2

2 12 2.1: 2.2: IC 1 IC 1 IC 2

2 13 [?] 2.3 2.4 2.3: 2.4:

2 14 2.3.1 2.3.2 ( )

2 15 2.4 2.4.1 [5]

2 16 2.4.2 2.4.3 3 [6]

2 17 [6] [6] 2.4.4 2,000 100 LETS LETS 1983 LETS LETS LETS 4 LETS LETS

2 18 LETS 2.5 LETS 2.5: LETS LETS

2 19 LETS LETS LETS LETS LETS LETS

2 20

2 21 2.5 ( ) 2 1 1 [7][8] 2.5.1 2.5.2 2

3 n (N v) N N = n v v N (v 2 N R) v( ) = 0 N S v(s) N [9][10] 22

3 23 3.1 [9] 3.1.1 k : N S T : S : v(s) : S k v(s) = 0 (3.1) k S T \{i} S T i N v(s {i}) v(s) v(t {i}) v(t ) (3.2) S T (S T N) v(s) v(t ) (3.3)

3 24 3 k (3.2) v(n) v(s) (v(n) v(n)\{j})) S k (3.4) j N\S (3.2) (3.4) N\S = {i 1 i n s } v(n) v(n\{i 1 }) = v(n) v(n\{i 1 }) v(n\{i 1 })) v(n\{i 2 }) v(n) v(n\{i 2 }). v(n\{i n s 1 })) v(n\{i n s }) v(n) v(n\{i n s }) k [9] 3.1.2 v (N v) n v(n) > v({i}) (3.5) i=1 (3.5) S T S T v(s T ) v(s) + v(t ) (3.6)

3 25 (3.6) 2 S T v(s T ) v(s) v(t ) (N v) v S T S T v(s) v(t ) (3.7) S(N ) v(n) = v(s) + v(n S) (3.8) [9]

3 26 3.1.3 1 (N v)(n = 1 2 n) x = (x 1 x 2 x n ) R n 2 n x i = v(n) (3.9) i=1 i N x i v({i}) (3.10) (3.9) {x R n i N x i v(n)} (3.10) I I = {x R n n x i = v(n) x i v({i}) i = 1 2 n} (3.11) i=1 (N v) I(N v) I(v) I [9][11][10][12]

3 27 C(N v) = {x I(N v) 0 x i v(n) v(n)\{i} i k}(3.12) k x k = v(n) x k = v(n) j k v((n) v(n{j})) C = {x I y I(y x) y dom x } 1 C x i v(s) S N i S C C C C (N v) 2 x = (x 1 x n ) y = (y 1 y n ) S 2 v(s) i S x i (3.13) (3.14) x i > y i i S (3.15) x S y x dom S y

3 28 (3.14) S v(s) x (3.15) S x y S y 2 x y S x dom S y x y x dom y (N v) X dom S dom X S dom S 2 x y x dom S y y dom S x dom 2 [9][10][11][12] ν(s) (N v) x = (x 1 x 2 x n ) S S e(s x) = v(s) i S x i (3.16) x S 1 [9][10][11][12][13] ϕ(s) (N v) i N ϕ(v) i = 1 ( ) S!(n S 1)! v(s {i}) v(s) (3.17) n! S N\{i}

3 29 ϕ(v) v(c {i}) v(s)) i i i v(s {i}) = v(s) S N\{i} i j v(s {i}) = v(s {j}) S N\{i j} v w v + w (v + w)(s) = v(s) + w(s) S N (N v) 1 ϕ(v) = (ϕ 1 (v) ϕ 2 (v) ϕ n (v)) 4 ϕ i (v) = v(n) (3.18) i N i ϕ i (v) = 0 (3.19) i j ϕ i (v) = ϕ j (v) (3.20) v w ϕ i (v + w) = ϕ i (v) + ϕ i (w) i N(3.21) (3.18) (3.19) (3.20) 2 (3.21) 2

3 30 2 v w v + w 4 [9][10][11][12][13]

3 31 3.2 (N v) N v* v*(s) = v(n) v(n\s) S N (3.22) x v S N x(s) v(s) v*(n\s) x(n\s) (3.23) [13] 3.2.1 (N, v L ) { v L (S) = v L (N) (1 S) i S v L({i}) (1 S) ν v L i { v L (N) 1 2 ν v L i = v BB ν v BB { v BB (N) 1 2 ν v BB i = j N\{1} v L({j}) (i = 1) 1 2 v L({i}) (i 1) j N\{1} m j (i = 1) 1 2 m i (i 1) m i = v BB (N) v BB (N\{i}) i N\{1}

3 32 3.2.2 v L v L (S) i S v L({i}) S N v L { v L (N) (1 S) v L (S) = i S v L({i}) (1 S) i 1 S 1 S = v L (S {i}) v L (S) = 0 1 S = v L (S {i}) v L (S) = v L ({i}) i 1 ϕ(v L ) i = 1 ( ) S!(n S 1)! v L (S {i}) v L (S) n! S N\{i} = 1 S!(n S 1)!v L ({i}) n! S N\{i,1} ( ) = 1 n 2 n 2 S!(n S 1)!v L ({i}) n! S = 1 n! = = n 2 S =0 S =0 n 2 S =0 (n 2)! S!(n 2 S )! S!(n S 1)!v L({i})) n S 1 n(n 1) v L({i}) 1 ( ) (n 1) + (n 2) + + 2 + 1 v L ({i}) n(n 1) = 1 2 v L({i}) ϕ(v L ) 1 = v L (N) i N\{1} ϕ(v L ) i = v L (N) 1 2 i N\{1} v L ({i})

3 33 ν(v L ) i ϕ(v L ) = ν(v L ) C(v) ˆν C(v) ˆν ν ϕ(v BB ) = ν(v BB ) v L (S) < i S v L({i}) S N\{S} ϕ(v L ) i = 1 n! S N\{1} ( ) S!(n S 1)! v L (S {i}) v L (S) > 1 ( S!(n S 1)! v L (N) v L ({i})) n! S N\{1} i S = v L (N) S!(n S 1)! v L ({i}) n! = v L (N) = v L (N) = v L (N) = v L (N) 1 2 S N\{1} i S ( i N\{1} S =1 i N\{1} S =1 i N\{1} i N\{1} n 2 S 1 ) v L ({i}) S n(n 1) v L({i}) 1 + 2 + + (n 1) v L ({i}) n(n 1) v L ({i}) S!(n S 1)! n! ν(v L ) i ϕ(v L ) 1 = ν(v L ) 1 ϕ(v L ) = ν(v L ) ϕ(v L ) = ν(v L ) v L (S) = { v L (N) (1 S) i S v L({i}) (1 S) v L v L ({i}) 0 i N

3 34 ( v) v. v BB ν(v BB ) = ϕ(v BB ) ν(v L ) = ϕ(b L ) 1 { vp 1 B(S) C > 0 (1 S) (S) = 0 (1 S) v L ν(v L ) = ϕ(v L ) ν(v BB ) = ϕ(v BB ) ν(v 1 P ) i = ϕ(v 1 P ) i = { 1 2 B i + 1 2B(N) C (i = k) 1 2 B i (i k) [9]

4 4.1 4.2 4.2.1 1 35

4 36 4.2.2 k: B(S) S B i D v(s) v(s) = { B(S) D > 0 (S k) 0 (S k) C(N v) = {x I(N v) 0 x i v(n) v(n)\{i} i k} ν(s) ϕ(s) { 1 ν(s) = ϕ(s) 2 B i + 1 2B(N) D (i = k) 1 2 B i (i k)

4 37 4.2.3 k a,b,c,d k:a:b:c:d=100:10:12:20:16 70 7 v(s) v(s) = B(S) D = (100 + 10 + 12 + 20 + 16) 70 = 158 70 = 88 C(N v) = {x I(N v) 0 x i v(n) v(n)\{i} i k} :{k:a:b:c:d=43:9:10:15:11} ν(s) ϕ(s) k ν(s) = ϕ(s) = 1 2 B i + 1 2 B(N) D 59

4 38 a b c d ν(s) = ϕ(s) = 1 2 B i 5 6 10 8

5 39

2013 2 40

[1] K.Hiritsugu T.Yoshiaki K.Naoya M.Tetsuya S.Kazuhiro A Local Currency System Reflecting Variety of Values, Proc.IEEE/EPSJ SAINT2011, pp. 562 567, July2011 [2], vol. 112 no. 343 SITE2012-43 pp. 1 6 2012 12 [3] - - 1998 [4] 7 pp.103-107 2007 3 [5] 60 pp.57-68 2008 3 [6] SNS,, vol. 108, no. 331, SITE2008-37, pp. 7 12, 2008 12 41

42 [7] 60 pp.69-76 2008 3 [8] - - 2001 [9] 2012 [10] [ ] 2011 [11] 2004 [12] 2001 [13] 2012

Q1: ( ) A1: Q2: ( ) A2: 43