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1 2 ver 1.0 ( ) (Neumann and Morgenstern 1953=2009:136). 1 S 2. S , ( hamada/ ) 1

2 ,

3 2, 1 0, 0 0, 0 1, 2 1:

4 2.2 1 ( ) (, ) 最初の状態 青葉が変更 花京院が変更 1: 1 0 4

5 2 0 (, ) (, ) 5

6 最初の状態 青葉が変更 花京院が変更 2: (, ) (, ) (, ), (, ) 6

7 : : (, ), (, ) (, ) (, ) (). N = {1, 2,, n} n i S i S i i {a, b, c} = S i i a, b, c 3 7

8 N = {1, 2}, S 1 = {a, b}, S 2 = {c, d} S 1 S 2 = {(a, c), (a, d), (b, c), (b, d)} 3 (a, c) 1 a 2 c 3 ( ). i u i u i : S 1 S 2 R u i i R 3 8

9 2 N = {1, 2}, S 1 S 2 = {(a, c), (a, d), (b, c), (b, d)} u 1 ((a, c)) = 3, u 2 ((a, c)) = 5 (a, c) OK N = {, } S S = {(, ), (, ), (, ), (, )} u ((, )) = 2, u ((, )) = 0, u ((, )) = 0, u ((, )) = 1 u ((, )) = 1, u ((, )) =, 0u ((, )) =, 0u ((, )) = 2 () 2 2 9

10 4 (). N = {1, 2,, n} i S i S = S 1 S 2 S n, s S s i s i s i = (s 1, s 2,..., s i 1, s i+1,..., s n ) s s i s i s i s = (s i, s i ) s S i N ( t i S i u i (s i, s i ) u i (t i, s i )) ν() 2.4 t i S i t i S i i N 10

11 i N N i 1 n i N u i (x) = 10 i n u i (x) = 10. u 1 (x) = u 2 (x) = = u n (x) = 10 t i S i S i t i t i 1 S i t i S i S i t i S i u i (s i, s i ) u i (t i, s i ) S i t i u i (s i, s i ) u i (t i, s i ). i s i S i i t i S i i S i = {a, b, c} t i S i a, b, c t i S i f(t i ) > 10 f(a) > 10 f(b) > 10 f(c) > 10 11

12 2.5 (, ) (, ) 2 (, ) (, ) 2 : (, ) (, ) : (0, 0) (2, 1) 1 (, ) (, ) : (, ) (, ) : (0, 0) (1, 2) 12

13 動物園 水族館 動物園 (2, 1) (0, 0) パレート改善 水族館 (0, 0) パレート改善 (1, 2) 3: (, ) (, ), (, ) (, ) 1 1 (2, 1) (2, 2)

14 5 ( ). s S i N u i (t) > u i (s) t S

15 References Gibbons, R., 1992, Game Theory for Applied Economists, Princeton University Press 1995,, [1996] 2011,. Osborne, Martin J., and Ariel, Rubinstein, 1994, A Course in Game Theory, MIT Press. 15

( ) ver.2015_01 2

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