t Prs r - PowerPoint PPT Presentation

◗✉❛❧✐t② Pr♦✈✐s✐♦♥ ✐♥ ❛ ❙❡❛r❝❤ ❊♥❣✐♥❡ ❊♥✈✐r♦♥♠❡♥t ●❡♦r❣✐♦s P❡tr♦♣♦✉❧♦s ✭❇r✉❡❣❡❧✮ ❛♥❞ ▼❛r✐❛ ❚❤❡❛♥♦ ❚❛❣❛r❛❦✐ ✭❊q✉❛❧ ❙♦❝✐❡t②✮ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❊✲❝♦♠♠❡r❝❡✱ ❉✐❣✐t❛❧ ❊❝♦♥♦♠② ❛♥❞ ❉❡❧✐✈❡r② ❙❡r✈✐❝❡s ❚♦✉❧♦✉s❡✱ ▼❛r❝❤ ✸✶✱ ✷✵✶✻ ✶ ✴ ✶✹

■♥tr♦❞✉❝t✐♦♥ ❙❡❛r❝❤ ❡♥❣✐♥❡ ♦r❣❛♥✐❝ r❡s✉❧ts ❛r❡ t❤❡ ♠❛✐♥ s♦✉r❝❡s ❢♦r tr❛✣❝ ✐♥ ✇❡❜s✐t❡s ✭❏❡r❛t❤✱ ▼❛ ❛♥❞ P❛r❦✱ ✷✵✶✸ ❛♥❞ ❇❛②❡✱ ❙❛♥t♦s ❛♥❞ ❲✐❧❞❡♥❜❡❡st✱ ✷✵✶✹✮ ❊✈❡r② ♣r♦♠✐♥❡♥t r❛♥❦ ♣♦s✐t✐♦♥ ✐♥ t❤❡ s❡❛r❝❤ ❡♥❣✐♥❡ r❡s✉❧ts ✐♥ ❛ ❤✐❣❤❡r ❝❧✐❝❦t❤r♦✉❣❤ r❛t❡ ✭●❧✐❝❦✱ ❘✐❝❤❛r❞s✱ ❙❛♣♦③❤♥✐❦♦✈ ❛♥❞ ❙❡❛❜r✐❣❤t✱ ✷✵✶✹✮ ❚❤❡ r❛♥❦✐♥❣ ♦❢ t❤❡ ✜r♠s ✐♥ t❤❡ s❡❛r❝❤ ❡♥❣✐♥❡ ✐s ❞❡t❡r♠✐♥❡❞ ❜② ❛♥ ❛❧❣♦r✐t❤♠ ✇❤✐❝❤ ✐s ♠✉❧t✐❞✐♠❡♥s✐♦♥❛❧✱ ✐♥❝❧✉❞✐♥❣ ❙❡❛r❝❤ ❊♥❣✐♥❡ ❖♣t✐♠✐③❛t✐♦♥ ✭❙❊❖✮ ❛♥❞ ♣r♦❞✉❝t q✉❛❧✐t②✮ ■♥ ❝♦♥tr❛st t♦ t❤❡ ❛✉❝t✐♦♥ ❛♣♣r♦❛❝❤ ♦❢ t❤❡ ♣❛✐❞ ♣❧❛❝❡♠❡♥t✱ ✜r♠s ✇❤✐❝❤ ✇✐s❤ t♦ ❣❛✐♥ ♣r♦♠✐♥❡♥❝❡ ✐♥ ♦r❣❛♥✐❝ r❡s✉❧ts s❤♦✉❧❞ ❝♦♠♣❧② ✇✐t❤ t❤❡ r❡q✉✐r❡♠❡♥ts ♦❢ t❤❡ ❛❧❣♦r✐t❤♠ ✷ ✴ ✶✹

❖❜❥❡❝t✐✈❡s ❊✈❛❧✉❛t❡ t❤❡ ✐♠♣❛❝t ♦❢ t❤❡ s❡❛r❝❤ ❡♥❣✐♥❡ ❛❧❣♦r✐t❤♠ ❢♦r ♣r♦♠✐♥❡♥❝❡ ♦♥ ✜r♠s✬ ♦♣t✐♠❛❧ ❛❧❧♦❝❛t✐♦♥ ♦❢ ✐♥✈❡st♠❡♥ts ❜❡t✇❡❡♥ ❙❡❛r❝❤ ❊♥❣✐♥❡ ❖♣t✐♠✐③❛t✐♦♥ ✭❙❊❖✮ ❛♥❞ q✉❛❧✐t② ❙❊❖ ✭✇❤✐t❡✲❤❛t✮ ✈❛r✐❡s ❢r♦♠ ❞❡✈❡❧♦♣✐♥❣ s✐t❡ ❞❡s✐❣♥ ❛♥❞ ❝♦♥t❡♥t q✉❛❧✐t② ❛s ✇❡❧❧ ❛s ❜r❛♥❞ ❛✇❛r❡♥❡ss ❛♥❞ r❡♣r❡s❡♥t❛t✐♦♥ ❲❡ ✐♥✈❡st✐❣❛t❡ ✇❤❡t❤❡r ❛♥❞ ✉♥❞❡r ✇❤❛t ❝♦♥❞✐t✐♦♥s t❤❡ ❙❊❖ ✐♥✈❡st♠❡♥t ❧❡❛❞s t♦ ❛ ❞✐st♦rt✐♦♥ ✐♥ t❤❡ ❧❡✈❡❧ ♦❢ q✉❛❧✐t② ❛♥❞ ✐❢ ②❡st✱ ✐ts ✐♠♣❛❝t ♦♥ ❝♦♥s✉♠❡r s✉r♣❧✉s ❛♥❞ t♦t❛❧ ✇❡❧❢❛r❡ ✸ ✴ ✶✹

▼♦❞❡❧✿ P❧❛②❡rs ❈♦♥s✉♠❡rs ♦❢ ♠❛ss ✶ t②♣❡ ❛ q✉❡r② ✐♥ ❛ s❡❛r❝❤ ❡♥❣✐♥❡✳ Pr❡❢❡r❡♥❝❡s✿ � ✐❢ ❝♦♥s✉♠❡r ♠❛t❝❤❡s ❛♥❞ ♣✉r❝❤❛s❡s v − p ✭✶✮ U = 0 ♦t❤❡r✇✐s❡ ❈♦♥s✉♠❡r ❧❡❛r♥s ❤✐s ✈❛❧✉❛t✐♦♥ ✇❤❡♥ ❤❡ ❛❝t✉❛❧❧② ❜✉②s t❤❡ ❣♦♦❞✿ v ∈ [ v, v ] ✱ 0 ≤ v < v ✱ G ( v ) ❛♥❞ g ( v ) > 0 ❚✇♦ ✜r♠s t❤❛t ❝♦♠♣❡t❡ ❢♦r ♣r♦♠✐♥❡♥❝❡ ✐♥ ❛ s❡❛r❝❤ ❡♥❣✐♥❡ ❜② ❝❤♦♦s✐♥❣ t❤❡✐r ❧❡✈❡❧ ♦❢ ❙❊❖ ❛♥❞ ♣r♦❞✉❝t q✉❛❧✐t② ❆ s❡❛r❝❤ ❡♥❣✐♥❡ r❛♥❦s t❤❡ t✇♦ ✜r♠s ❜❛s❡❞ ♦♥ ✐ts ❛❧❣♦r✐t❤♠ t❤❛t t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t ✜r♠s✬ ❝❤❛r❛❝t❡r✐st✐❝s s✉❝❤ ❛s t❤❡ ✐♥✈❡st♠❡♥ts ♦♥ q✉❛❧✐t② ❛♥❞ ❙❊❖ ✹ ✴ ✶✹

❚✐♠✐♥❣ ✶ ❋✐r♠s ❝♦♠♣❡t❡ ❛♥❞ ♠❛①✐♠✐③❡ t❤❡✐r ♣❛②♦✛ ❢✉♥❝t✐♦♥s ✇✐t❤ r❡s♣❡❝t t♦ q✉❛❧✐t② ❛♥❞ ✐♥✈❡st♠❡♥ts ♦♥ ❙❊❖ ✷ ❋✐r♠s ❝❤♦♦s❡ t❤❡✐r ♣r✐❝✐♥❣ ❜❡❤❛✈✐♦r ✭♠♦♥♦♣♦❧✐st✐❝ ❝♦♠♣❡t✐t✐♦♥✮ ✸ ❚❤❡ s❡❛r❝❤ ❡♥❣✐♥❡ r❛♥❦s t❤❡ ✜r♠s ✹ ❈♦♥s✉♠❡rs ♦❜s❡r✈❡ t❤❡ r❛♥❦✐♥❣ ❛♥❞ t❤❡♥ t❤❡② ❞❡❝✐❞❡ ✇❤✐❝❤ ✜r♠ t♦ ✈✐s✐t ❛♥❞ ✇❤❡t❤❡r t❤❡② ✇✐❧❧ ♣✉r❝❤❛s❡ ♦r ♥♦t ✺ ✴ ✶✹

❊q✉✐❧✐❜r✐✉♠ ❙tr❛t❡❣✐❡s ❈♦♥s✉♠❡rs ✇✐❧❧ ❝❤♦♦s❡ t♦ ❣♦ ✜rst❧② ♦♥ t❤❡ ✜r♠ t❤❛t ✐s r❛♥❦❡❞ ✜rst✳ ■❢ t❤❡② ♠❛t❝❤ t❤❡② ♣✉r❝❤❛s❡ ❛♥❞ t❤❡ ❣❛♠❡ st♦♣s✳ ❖t❤❡r✇✐s❡✱ t❤❡② ✈✐s✐t t❤❡ s❡❝♦♥❞ ✜r♠ ❜② ✐♥❝✉rr✐♥❣ ❛ r❡❧❛t✐✈❡❧② ❧♦✇ s❡❛r❝❤ ❝♦st µ ✳ ■❢ t❤❡② ♠❛t❝❤ t❤❡② ♣✉r❝❤❛s❡✳ ❖t❤❡r✇✐s❡✱ t❤❡② ❡①✐t t❤❡ ♠❛r❦❡t✳ ❇❛s❡❞ ♦♥ t❤❡ ✐♠♣❧❡♠❡♥t❡❞ ❛❧❣♦r✐t❤♠✱ t❤❡ s❡❛r❝❤ ❡♥❣✐♥❡ r❛♥❦s t❤❡ ✜r♠s ❜❛s❡❞ ♦♥ ❜♦t❤ t❤❡ ❙❊❖ ❛♥❞ q✉❛❧✐t② ✐♥✈❡st♠❡♥t ♦✉t❝♦♠❡ ❋✐r♠s ✐♥ ❡q✉✐❧✐❜r✐✉♠ ❝❤❛r❣❡ t❤❡ ♠♦♥♦♣♦❧② ♣r✐❝❡ ❛♥❞ ❡❛r♥✿ Π ∗ = [1 − G ( p )] 2 p ∗ = 1 − G ( p ) , ✭✷✮ g ( p ) g ( p ) ✻ ✴ ✶✹

P❛②♦✛ ❋✉♥❝t✐♦♥s Π i = Π ∗ (Φ i ( x i , x − i , S i , S − i ) x − i x i + (1 − x − i ) x i ) − C ( x i ) − K i ( S i ) ✭✸✮ ✇❤❡r❡ i = A, B ❛♥❞ Φ i ( x i , x − 1 , S i , S − i ) ✿ ✜r♠ ✐✬s ♣r♦❜❛❜✐❧✐t② ♦❢ ❜❡✐♥❣ r❛♥❦❡❞ ✜rst x i ✿ ♠❛t❝❤✐♥❣ ♣r♦❜❛❜✐❧✐t② ♦❢ ✜r♠ ✐ ✇✐t❤ ❛ r❛♥❞♦♠❧② ❝❤♦s❡♥ ❝♦♥s✉♠❡r S i ✿ ✜r♠ ✐✬s ✐♥✈❡st♠❡♥t ♦♥ ❙❊❖ C ( · ) ✱ K i ( · ) ✿ ❆ss♦❝✐❛t❡❞ ❝♦sts ✼ ✴ ✶✹

❇❡♥❝❤♠❛r❦✿ ❙❡❛r❝❤ ❡♥❣✐♥❡ ❞♦❡s ♥♦t ❡①✐st Pr♦♣♦s✐t✐♦♥ ❲❤❡♥ ❛ s❡❛r❝❤ ❡♥❣✐♥❡ ❛❞♠✐ts t❤❡ r❛♥❦✐♥❣ r❛♥❞♦♠❧② ❛♥❞ ✜r♠s ❛r❡ s②♠♠❡tr✐❝ ✭ Φ = 1 2 ✮✱ t❤❡r❡ ❡①✐sts ❛ s②♠♠❡tr✐❝ ◆❛s❤ ❡q✉✐❧✐❜r✐❛ ✐♥ ♣✉r❡ str❛t❡❣✐❡s ✇❤❡r❡ t❤❡ ✐♥✈❡st♠❡♥t ♦♥ ❙❊❖ ✐s ③❡r♦ ✇❤✐❧❡ t❤❡ q✉❛❧✐t② ✐s ❣✐✈❡♥ ❜②✿ � 2 Π ∗ − C x ✐❢ 0 < Π ∗ − C x < 1 x r = Π ∗ Π ∗ 2 ✭✹✮ 1 ♦t❤❡r✇✐s❡ ✽ ✴ ✶✹

◗✉❛❧✐t② ❛♥❞ ❙❊❖ ✐♥ t❤❡ s❤♦rt✲r✉♥ ◗✉❛❧✐t✐❡s ❛r❡ ✜①❡❞ ❋✐r♠s ♦♣t✐♠✐③❡ ✇✐t❤ r❡s♣❡❝t t♦ ❙❊❖✿ ❙②♠♠❡tr✐❝ ◆❛s❤ ❡q✉✐❧✐❜r✐✉♠ ❍♦✇ ❞♦❡s s❡❛r❝❤ ❡♥❣✐♥❡✬s ❛❧❣♦r✐t❤♠ ♣❡r❝❡✐✈❡s ❙❊❖ ❛♥❞ q✉❛❧✐t②❄ ∂ 2 Φ i ∂ 2 Φ i ■♥❞❡♣❡♥❞❡♥t✿ ∂S i ∂x i = 0 ❛♥❞ ∂S i ∂x − i = 0 ✶ ∂ 2 Φ i ∂ 2 Φ i ❈♦♠♣❧❡♠❡♥ts✿ ∂S i ∂x i > 0 ❛♥❞ ∂S i ∂x − i < 0 ✷ ∂ 2 Φ i ∂ 2 Φ i ❙✉❜st✐t✉t❡s✿ ∂S i ∂x i < 0 ❛♥❞ ∂S i ∂x − i > 0 ✸ ✾ ✴ ✶✹

◗✉❛❧✐t② ❛♥❞ ❙❊❖ ✐♥ t❤❡ s❤♦rt✲r✉♥ ✭✷✮ ■♥❞❡♣❡♥❞❡♥t✿ ❡✈❡♥ ✐❢ t❤❡r❡ ✐s ❛s②♠♠❡tr② ✐♥ ♦✛❡r❡❞ q✉❛❧✐t✐❡s✱ ✜r♠s s❡❧❡❝t t❤❡ s❛♠❡ ❙❊❖ ✐♥ ❡q✉✐❧✐❜r✐✉♠ ❈♦♠♣❧❡♠❡♥ts✿ ❚❤❡ ✜r♠ t❤❛t ♦✛❡rs ❤✐❣❤❡r q✉❛❧✐t②✱ ❛❧s♦ s❡ts ❣r❡❛t❡r ❙❊❖ ❙✉❜st✐t✉t❡s✿ ❚❤❡ ✜r♠ t❤❛t ♦✛❡rs ❤✐❣❤❡r q✉❛❧✐t②✱ s❡ts ❧♦✇❡r ❙❊❖ ✶✵ ✴ ✶✹