This document discusses incomplete information dynamic games. It begins by introducing the topic and defining some key terms. It then provides three examples to illustrate dynamic games with incomplete information: (1) The "Market for Lemons" which describes quality uncertainty in the used car market. (2) An example game with an incomplete information matrix that models players' private information and payoffs. (3) An example signaling game with two players and two types that models the information revealed through players' actions.

1. ήʔϜཧ࿦#4*$ୈճ
த‫ࢢंݹ‬৔ͱϨϞϯ

2. 1. ʮத‫ࢢंݹ‬৔ͱϨϞϯʯͰͷ
‫׬‬શϕΠδΞϯ‫ߧۉ‬Λ֬ೝ
ຊಈըͷ໨త

3. 1. ಈతͳ৘ใෆ‫׬‬උήʔϜͷྫ
(1)த‫ࢢंݹ‬৔ͷϞσϧ
(2)த‫ࢢंݹ‬৔ͷ෼ੳ
໨࣍

4. Example:Dynamic games with Incomplete information
ಈతͳ৘ใෆ‫׬‬උήʔϜͷྫ

5. த‫ࢢंݹ‬৔ͷϞσϧ
৘ใෆ‫׬‬උͷϞσϧΛ༻͍ͯ
ΞΧϩϑʹΑͬͯ෼ੳ͞Εͨ
Akerlof, George A. (1970),
“The Market for ‘Lemons’: Quality Uncertainty and the Market Mechanism.”
Quarterly Journal of Economics, 84(3), pp. 488-500.
ˎLemons͸࣭ͷѱ͍த‫ंݹ‬ͷ͜ͱΛࢦ͢
࣋ͪࠐ·ͳ͍ 065
࣋ͪࠐΉ */
ߴ )
௿ -

6. த‫ࢢंݹ‬৔ͷϞσϧ
ंͷॴ༗ऀ͕ंΛചΔ͜ͱΛߟ͑Δ
σΟʔϥʔ͸࣋ͪࠐ·Εͨंʹର͠
ʮߴ͍Ձ֨Λ͚ͭΔʯ
·ͨ͸ʮ௿͍Ձ֨Λ͚ͭΔʯΛબͿͱ͢Δ
͜͜Ͱंͷॴ༗ऀ͸ं͕ྑ͍ঢ়ଶ
ѱ͍ঢ়ଶͲͪΒͳͷ͔Θ͔Δ΋ͷͱ͠
Ұํ
σΟʔϥʔ͸Θ͔Βͳ͍΋ͷͱ͢Δ
࣋ͪࠐ·ͳ͍ 065
࣋ͪࠐΉ */
ߴ )
௿ -

7. த‫ࢢंݹ‬৔ͷϞσϧ
ల։‫ܗ‬ද‫ݱ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
ྑ͍ंࣗମՁ஋͋Γ
‫͍ྑʹ͍ޓ‬औҾ
ചΓखṶ͚
ଥ౰ͳऔҾ
ѱ͍ं͸Ձ஋ͳ͠
ച٫ͤͣʹ࣋ͪ‫ؼ‬Γ
1
2
1
2
٬‫཰֬؍‬

8. த‫ࢢंݹ‬৔ͷϞσϧ
ల։‫ܗ‬ද‫ݱ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
ྑ͍ंࣗମՁ஋͋Γ
‫͍ྑʹ͍ޓ‬औҾ
ചΓखṶ͚
ଥ౰ͳऔҾ
ѱ͍ं͸Ձ஋ͳ͠
ച٫ͤͣʹ࣋ͪ‫ؼ‬Γ
1
2
1
2
٬‫཰֬؍‬

9. த‫ࢢंݹ‬৔ͷϞσϧ
ల։‫ܗ‬ද‫ݱ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
ྑ͍ंࣗମՁ஋͋Γ
‫͍ྑʹ͍ޓ‬औҾ
ചΓखṶ͚
ଥ౰ͳऔҾ
ѱ͍ं͸Ձ஋ͳ͠
ച٫ͤͣʹ࣋ͪ‫ؼ‬Γ
1
2
1
2
٬‫཰֬؍‬

10. த‫ࢢंݹ‬৔ͷϞσϧ
ల։‫ܗ‬ද‫ݱ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
ྑ͍ंࣗମՁ஋͋Γ
‫͍ྑʹ͍ޓ‬औҾ
ചΓखṶ͚
ଥ౰ͳऔҾ
ѱ͍ं͸Ձ஋ͳ͠
ച٫ͤͣʹ࣋ͪ‫ؼ‬Γ
1
2
1
2
٬‫཰֬؍‬

11. த‫ࢢंݹ‬৔ͷϞσϧ
ల։‫ܗ‬ද‫ݱ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
ྑ͍ंࣗମՁ஋͋Γ
‫͍ྑʹ͍ޓ‬औҾ
ചΓखṶ͚
ଥ౰ͳऔҾ
ѱ͍ं͸Ձ஋ͳ͠
ച٫ͤͣʹ࣋ͪ‫ؼ‬Γ
1
2
1
2
٬‫཰֬؍‬

12. த‫ࢢंݹ‬৔ͷϞσϧ
ల։‫ܗ‬ද‫ݱ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
ྑ͍ंࣗମՁ஋͋Γ
‫͍ྑʹ͍ޓ‬औҾ
ചΓखṶ͚
ଥ౰ͳऔҾ
ѱ͍ं͸Ձ஋ͳ͠
ച٫ͤͣʹ࣋ͪ‫ؼ‬Γ
1
2
1
2
٬‫཰֬؍‬

13. த‫ࢢंݹ‬৔ͷ෼ੳ
ϕΠδΞϯήʔϜ
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
̍ʘ )JHI -PX
065065
065*/
*/065
*/*/

14. த‫ࢢंݹ‬৔ͷ෼ੳ
ϕΠδΞϯήʔϜ
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
̍ʘ )JHI -PX
065065
065*/
*/065
*/*/

15. த‫ࢢंݹ‬৔ͷ෼ੳ
ϕΠδΞϯήʔϜ
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
̍ʘ )JHI -PX
065065
065*/
*/065
*/*/

16. த‫ࢢंݹ‬৔ͷ෼ੳ
‫׬‬શϕΠδΞϯ‫ߧۉ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
ϓϨΠϠʔͷ ্ͷ৴೦Λ
u2
1 (r,1 − r)
r
1 − r
u2
1
u1
1
u1
2

17. த‫ࢢंݹ‬৔ͷ෼ੳ
‫׬‬શϕΠδΞϯ‫ߧۉ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
r
1 − r
u2
1
ϓϨΠϠʔͷ ্ͷ৴೦Λ
͜ͷ৴೦ͷ΋ͱஞ࣍߹ཧతͳߦಈ͸
u2
1 (r,1 − r)
H2
(r, b1
, b2
)
= r{2b2
+ 0(1 − b2
)} + (1 − r){(−1)b2
+ 2(1 − b2
)}
= (5r − 3)b2
+ 2(1 − r)
b2
r
1
1
0
3
5
ͷ஋ʹΑΓ࠷దͳߦಈ ͕มԽ
r b2
u1
1
u1
2
b2
1 − b2

18. த‫ࢢंݹ‬৔ͷ෼ੳ
‫׬‬શϕΠδΞϯ‫ߧۉ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
r
1 − r
u2
1
ϓϨΠϠʔͷ ্ͷ
ஞ࣍߹ཧతͳߦಈ͸
u1
1
H1
(r, b1
, b2
)
= b1
1{3b2
+ 1(1 − b2
)} + 2(1 − b1
1)
= (2b2
− 1)b1
1 + 2
b1
1
b2
1
1
0
1
2
u1
1
u1
2
b2
1 − b2
1 − b1
1
b1
1 ͷ஋ʹΑΓ࠷దͳߦಈ ͕มԽ
b2
b1
1

19. த‫ࢢंݹ‬৔ͷ෼ੳ
‫׬‬શϕΠδΞϯ‫ߧۉ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
r
1 − r
u2
1
ϓϨΠϠʔͷ ্ͷ
ஞ࣍߹ཧతͳߦಈ͸
ͷ஋ʹؔΘΒͣ
u1
2
H1
(r, b1
, b2
)
= b1
2{3b2
+ 1(1 − b2
)} + 0(1 − b1
2)
= (2b2
+ 1)b1
2
b2
b1
2 = 1
u1
1
u1
2
b2
1 − b2
1 − b1
1
b1
1
1 − b1
2
b1
2

20. த‫ࢢंݹ‬৔ͷ෼ੳ
‫׬‬શϕΠδΞϯ‫ߧۉ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
r
1 − r
u2
1
ϓϨΠϠʔͷ ্ͷ
ஞ࣍߹ཧతͳߦಈ͸
ͷ஋ʹؔΘΒͣ
u1
2
H1
(r, b1
, b2
)
= b1
2{3b2
+ 1(1 − b2
)} + 0(1 − b1
2)
= (2b2
+ 1)b1
2
b2
b1
2 = 1
u1
1
u1
2
b2
1 − b2
1 − b1
1
b1
1
0
1

21. த‫ࢢंݹ‬৔ͷ෼ੳ
‫׬‬શϕΠδΞϯ‫ߧۉ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
r
1 − r
u2
1
ϓϨΠϠʔͷ ্ͷ
੔߹తͳ৴೦͸
u2
1
r* =
1
2
b1
1
1
2
b1
1 +
1
2
1
=
b1
1
b1
1 + 1
u1
1
u1
2
b2
1 − b2
1 − b1
1
b1
1
0
1

22. த‫ࢢंݹ‬৔ͷ෼ੳ
‫׬‬શϕΠδΞϯ‫ߧۉ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
u2
1
u1
1
u1
2
b2
1 − b2
1 − b1
1
b1
1
0
1
r* =
b1
1
b1
1 + 1
b2
r
1
1
0
3
5
b1
1
b2
1
1
0
1
2
1
2
r* =
b1
1
b1
1 + 1
≤
1
2
͕࠷ద൓ԠͷϖΞ
b1
1 = 0, b2
= 0

23. த‫ࢢंݹ‬৔ͷ෼ੳ
‫׬‬શϕΠδΞϯ‫ߧۉ‬
࣋ͪࠐ·ͳ͍ 065
N
࣋ͪࠐΉ */
ߴ )
௿ -
1
1
2
2
*/
065
ࣗવ
ྑ͍ (PPE
ѱ͍ #BE
(2, 0)
(3, 2)
(1, 0)
(3, − 1)
(1, 2)
(0, 0)
ߴ )
௿ -
1
2
1
2
u2
1
u1
1
u1
2
0
1
1
0
0
1
r* = 0 b2
r
1
1
0
3
5
b1
1
b2
1
1
0
1
2
1
2
r* =
b1
1
b1
1 + 1
≤
1
2
͕࠷ద൓ԠͷϖΞ
b1
1 = 0, b2
= 0
0
1
1

24. த‫ࢢंݹ‬৔ͷ෼ੳ
৘ใෆ‫׬‬උͷϞσϧΛ༻͍ͯ
ΞΧϩϑʹΑͬͯ෼ੳ͞Εͨ
Akerlof, George A. (1970),
“The Market for ‘Lemons’: Quality Uncertainty and the Market Mechanism.”
Quarterly Journal of Economics, 84(3), pp. 488-500.
த‫ࢢंݹ‬৔ʹ͸࣭ͷѱ͍ঢ়ଶͷं͔͠ࢢ৔ʹग़ճΒͳ͍͜ͱʹͳΔ͜ͷ‫ݱ‬৅Λ‫ٯ‬બൈͱ‫Ϳݺ‬
࣋ͪࠐ·ͳ͍ 065
࣋ͪࠐΉ */
ߴ )
௿ -

25. ήʔϜཧ࿦#4*$ୈճ
த‫ࢢंݹ‬৔ͱϨϞϯ
‫׬‬
ήʔϜཧ࿦#4*$ୈճʹͭͮ͘
See you next timeʂ