小平 裕１２３‐１３９／１２３‐１３９
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6 v 0 r r Cournot r (2.3 1!F (r (2.7 max(r!v 0 1!F ( (r r r (r r!1!f v 0 f (r (Vck- aucto counteroffer k k
7 rey (1961 (1962 Rley and Samuelson (1981 Myerson (1981 Myerson Rley and Samuelson Myerson Rley and Samuelson Myerson Rley and Samuelson Myerson!N v f (Myerson (1981 Bulow and Roberts (1989 Dasgupta, Hammond, and Maskn (1979
8 1"!" v v((v v n $V v X (v X (v(1 X (v(0 X (v P (v X : V#%0"1&n #% P : V#Rn (X"P v &''$N (3.1 U 0 (X"P ((V v 0 1!'$N X (s P (s $f (sds ds(ds 1"""ds n (X"P! "f! (3.2 U (X"P"v v ((V! X (v!p "s! (v "s! (s! ds! ds!(ds 1"""ds n (X"P X!1 ds '1"""ds Maskn and Rley (1984
9 (3.3 X (v#0 %$N %v$v #$N X (v"1 %v$v (3.4 U (X"P"v #0 %$N %v $[v "v ] v t (3.5 $V!! "f! v X (t "s!!p (t "s! (t '(s 1"!"s "s!!1"t "s &1"!"s (s! ds! n Bayesan Nash (X"P (3.6 U (X"P"v #$V!! "f! v X (t "s!!p (t "s! (s! ds! %$N"%v "t $[v "v ] (3.6 (X"P (3.6 (3.3 - (3.4
10 X P (3.3 - (3.4(3.6 n v%(v 1"v 2"!"v n #V X (v P (v (X"P (3.3 - (3.4(3.6 #N X (t "v!!j%$ f (v j dv! (4.1 x (t %"v!#v! P (t "v!!j%$ f (v j dv! (4.2 p (t %"v!#v! (4.3 v #arg max v x (t!p (t t #[v "v ] (4.3 dx (4.4 v!dp %0 dv dv v (4.4 v p "0
11 (4.5 p #&v v s dx (s ds"p ds x (! p (! p x (! p (! (4.5 v x (sds v (4.6 v x!p #&v n E[p ] (4.6 %#1 E[p ]#&v!# "$f (v v p f dv (4.7 #&v v v x!&v v x (sds dv v #&v v x f dv!&v v v x (sf dsdv &v (4.8 #&v &v v &v v x (sf dsdv #&v v v &v v &v v x (sf dv ds (4.7 x (sf dsdv (4.7 (4.9 Burguet (2000
12 (4.9 #+v E[p ]#+v %' v %' v x f!+v v # v!1 f +v $x v (v #+v v!1!f f &(dv v x f (sds &(x v f (sds (v f (v dv f dv (v (4.10! "v!1!f f v (Myerson (1981! v! v Cournot (2.7! r v (4.2 (4.9 - (4.10 v! x f dv n #1 E [p n+v ]##1 v n (4.11!(v n+v ##1 X f (v j dv (v*j#1! "*j#1 v n!(v #+v X (v #1 n f (v j dv (4.10 1!F hazard rate f! F (v#1!f (v lnf F F "2 Laplace Bagnol and Bergstrom (1989 Bulow and Roberts (1989
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13 !(!! v((v 1#"#v n " $V (4.12 A (v($n'! #0 $ % A (v # (4.13 A"(v($N'! #!(v j #j$a (v (4.14 X (v(1 A (v(%& $A"(v n #(1 X (v(0 A (v(& (4.11 (4.14 $ % (4.15 p(mn v $[v #v ]'! #0 p v p Bayesan
14 p v v $A"(v!(!! #0 (4.15 p p (4.14 v x (v, %1#2#"#n
15 v 0$v $p!!n F (p%0 p p p v 0 (4.15 p p (4.10! v 0"0 "1#"#n v [0#1] Bulow and Roberts (1989
16 Rley and Samuelson (1981 v # F 'v p 1 2 Cournot! r%[0!1] F (r'r n 1 r" r"(n'n R R (n' n&1 n r"(n 1!F (r"(n"'r"(n n&1 r"(n R (n n Cournot r"(1'1 2 R (1'1 4 n#$n'1 Cournot r"(1 Bagnol, M., and T. Bergstrom (1989 Log-concave probablty and ts applcatons, Unversty of Mchgan. Bulow, Jeremy, and John Roberts (1989 The smple economcs of optmal auctons, Journal of
17 Poltcal Economy, 95(5: Burguet, Roberto, (2000 Aucton theory: a guded tour, Investgacones Economcas, 34(1: Dasgupta, P., Peter Hammond, and Erc S. Maskn (1979 The mplementaton of socal choce rules, Revew of Economc Studes, 46: Maskn, Erc, and John Rley (1984 Optmal auctons wth rsk averse buyers, Econometrca, 52(6: Myerson, Roger B., (1981 Optmal aucton desgn, Mathematcs of Operatons Research, 6: Rley, John G., and Wllam F. Samuelson (1981 Optmal auctons, Amercan Economc Revew, 71: Trager, James, (1979 The People s Chronology: A Year-by-Year Record of Human Events from Prehstory to the Present, Holt, Rnehart and Wnston 1985 Vckrey, Wllam, (1961 Counterspeculaton, auctons, and sealed tenders, Journal of Fnance, 16: Vckrey, Wllam, (1962 Auctons and bddng games, n O. Morgenstern and A. Tucker eds., Recent Advances n Game Theory, Prnceton Unversty Press.
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