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Competitive Pricing for Spectrum Sharing in Cognitive Radio Networks: Dynamic Game, Inefficiency of Nash Equilibrium, and Collusion. D Niyato, E Hossain - IEEE Journal on Selected Areas in Communications, 2008 - ieeexplore.ieee.org. 指導教授 : 郭文興 學生 :    林庭陽. ABSTRACT.

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3804030

Competitive Pricing for Spectrum Sharing inCognitive Radio Networks: Dynamic Game,Inefficiency of Nash Equilibrium, and Collusion

D Niyato, E Hossain - IEEE Journal on Selected Areas in Communications, 2008 - ieeexplore.ieee.org

指導教授: 郭文興

學生:   林庭陽


Abstract

ABSTRACT

  • 我們討論智慧型射頻網路的頻譜定價問題,其中主要用戶彼此競爭提供次級用戶存取頻譜的機會

  • 主要用戶的目標是在限制的服務質量(QoS)下最大化他的盈利

  • 主要用戶QoS的下降量提供給次級用戶的頻譜之成本

  • 對於次級用戶,我們採用效能函數來獲得其頻譜的需求函數

  • 我們將其視為一個寡頭市場,並使用Bertrand game mode來分析此寡頭市場的賽局


Outline 1

OUTLINE(1)

  • I. INTRODUCTION

  • II. RELATED WORK

  • III. SYSTEM MODEL AND ASSUMPTIONS

    • A. Primary and Secondary Services

    • B. Wireless Transmission Model

    • C. Oligopoly Price Competition and Bertrand Game

  • IV. SPECTRUM PRICING COMPETITION AND SOLUTION

    • A. Utility of Secondary Service

    • B. Revenue and Cost Functions for Primary Service

    • C. Bertrand Game Model

    • D. Dynamic Bertrand Game

    • E. Stability Analysis of the Dynamic Game

    • F. Optimal Pricing to Maximize Total Profit of Primary Services

    • G. Collusion and Repeated Game


Outline 2

OUTLINE(2)

  • V. PERFORMANCE EVALUATION

    • A. Parameter Setting

    • B. Numerical Results

  • VI. CONCLUSION


I introduction 1

I. INTRODUCTION(1)

  • 開發智慧型射頻的目的:增加無線頻譜的適應性和靈活性

  • 可以根據智慧型射頻技術來開發下一代無線網路

  • 本文中,我們討論智慧型射頻中主要用戶的競爭賽局,並使用Bertrand game mode來做分析

  • 我們分析一些系統參數(如頻譜替代性、通道品質)對奈許平衡的影響

  • 我們提出分散式演算法來獲得這個動態賽局的解收斂至奈許平衡


I introduction 2

I. INTRODUCTION(2)

  • 奈許平衡對主要用戶來說並無法最大化其盈利討論其最佳解(主要用戶彼此共謀)

  • 因為主要用戶可能會脫離合作關係採取處罰機制避免之


Ii related work 1

II. RELATED WORK(1)

  • [2]:介紹智慧型射頻技術,並討論智慧型射頻的突現行為

  • [3]:智慧型射頻的概論,包含開放式分享、階級式存取…等

  • Related work 1:

    • [4]: 智慧型射頻rate control的賽局理論技術

    • [5] [6] [7]: 智慧型射頻power control的賽局理論技術

    • [9]: 提出適合的智慧型射頻網路通道分配方法

    • [10]: 研究不同智慧型射頻賽局的收斂動力學

    • [11]: 將頻譜分享問題視為一個潛在賽局,並獲得其奈許平衡

    • 以上研究皆忽略定價問題


Ii related work 2

II. RELATED WORK(2)

  • Related work 2(考慮定價問題):

    • [12]: 提出ad hoc網路的一個根據價格的傳輸速率分配法來達到最高的資源利用

    • [13]: 研究無線網路的效能最大化問題

    • [14]: 介紹WLAN環境語音服務的定價策略(考慮QoS效能和用戶願意付的價格)

    • 雖考慮到定價問題,卻無法解決動態頻譜存取環境的定價問題

  • Related work 3(可解決動態頻譜存取環境的定價問題):

    • [15]: 提出結合價格(price)、分配(allocation)和帳單(billing)的智慧型射頻系統,在此系統,經紀人和用戶之間的價格談判被定制成一個多單位密封投標拍賣

    • [16]: 分析編碼劃分多工存取(CDMA)系統的最佳投標、價格和服務差別機制

    • [17] [18]: 將頻譜擁有者之間的競爭模型化成一個賽局

    • 以上研究的頻譜需求函數沒有考慮到次級用戶的頻譜可替代性問題、沒有研究策略適應的穩定性且沒有考慮主要用戶之間的共謀問題


Iii system model and assumptions a primary and secondary services

III. SYSTEM MODEL AND ASSUMPTIONS-A. Primary and Secondary Services

  • N個主要用戶在不同的頻譜

    Fi上運作

  • 次級用戶欲存取這些頻譜

  • 主要用戶i每單位頻譜欲以價

    格pi出售


Iii system model and assumptions b wireless transmission model

III. SYSTEM MODEL AND ASSUMPTIONS-B. Wireless Transmission Model

  • 次級用戶使用適合的調變來傳輸,其傳輸速率會根據通道品質來做調整

  • 次級用戶的頻譜傳輸效能k可以由[19]獲得

γ:訊雜比(SNR,即通道品質)

BER :目標位元錯誤率(bit-error-rate,BER)

tar


Iii system model and assumptions c oligopoly price competition and bertrand game

III. SYSTEM MODEL AND ASSUMPTIONS-C. Oligopoly Price Competition and Bertrand Game

  • 我們將動態頻譜共享的問題模型化成一個寡頭市場:

    • 少數賣家操縱一個特定的市場

    • 賣家之間彼此競爭(控制提供物品的數量或價格)以達到他們自己的目的(即最大化盈利)

    • 每個賣家的決定會受到其他賣家行為的影響

    • 一個賣家的行為可能受到其他賣家的觀察

  • 伯特蘭賽局模型(Bertrand game model)的價格競爭可以適用於分析和獲得多主要用戶的智慧型射頻之平衡價格

    • 次級用戶的頻譜需求取決於分享頻譜的效能和需支付的價格

    • 主要用戶的頻譜成本:根據主要用戶QoS的下降量來估算

    • 主要用戶調整頻譜的價格來使盈利最大化


Iv spectrum pricing competition and solution a utility of secondary service

IV. SPECTRUM PRICING COMPETITION AND SOLUTION- A. Utility of Secondary Service

  • 在本文,我們採用常用的二次效能函數[21]:

  • 求極值:

b = {b1, . . . , bi, . . . , bN}

bi:主要用戶i分享的頻譜大小

pi:主要用戶i的定價

ki :次級用戶使用主要用戶I

的頻譜Fi時的頻譜效能

ν:頻譜替代性參數(考慮頻譜

的可替代性)

(s)

V

V

D i(p):頻譜需求


Iv spectrum pricing competition and solution b revenue and cost functions for primary service

IV. SPECTRUM PRICING COMPETITION AND SOLUTION-B. Revenue and Cost Functions for Primary Service

  • 主要用戶把頻譜分享給次級用戶主要用戶的QoS會下降將QoS下降量視為此頻譜的成本

  • 主要用戶的收益函數Ri和成本函數Ci:

c1:收益函數的一個常量

c2:成本函數的一個常量

B :主要連結的頻寬需求

Wi:主要用戶i的頻譜大小

Mi:主要連結的數量

ki :主要用戶i的頻譜效能

req

i

(p)


Iv spectrum pricing competition and solution c bertrand game model 1

IV. SPECTRUM PRICING COMPETITION AND SOLUTION- C. Bertrand Game Model(1)

  • 定義Bertrand game:

    • 參與者 : 主要用戶

    • 參與者的策略 : 每單位頻譜的價格(pi)

    • 盈利 : 出售頻譜給次級用戶的利潤

  • 主要用戶的利潤可表示成:

    P i(p) = bipi + R i − C i(bi)

  • 定義p-i: p = p−i ∪ {pi}

p : 所有參與者價格的集合(即p = {p1, . . . , pi, . . . , pN})


Iv spectrum pricing competition and solution c bertrand game model 2

IV. SPECTRUM PRICING COMPETITION AND SOLUTION-C. Bertrand Game Model(2)

  • 在給定其他用戶之定價後,用戶i的best response函數定義為:

  • p = {p1, . . . , pN}表示奈許平衡:

  • 將bi替換成Di(p),則主要用戶的利潤函數可以表示成:


Iv spectrum pricing competition and solution c bertrand game model 3

IV. SPECTRUM PRICING COMPETITION AND SOLUTION-C. Bertrand Game Model(3)

  • (4)式可以寫成: D i(p) = D1(p−i)−D2pi

  • 利用 ,可以得到:(可解得best response(pi))

  • 式子(9),兩個主要用戶(i=1,j=2)的special case,可以表示成(10)和(11)


Iv spectrum pricing competition and solution c bertrand game model 4

IV. SPECTRUM PRICING COMPETITION AND SOLUTION-C. Bertrand Game Model(4)


Iv spectrum pricing competition and solution d dynamic bertrand game 1

IV. SPECTRUM PRICING COMPETITION AND SOLUTION- D. Dynamic Bertrand Game(1)

  • 實際的智慧型射頻中,主要用戶無法看到其他主要用戶的利潤觀察其他主要用戶以前的行為需要一個分散式調整演算法

  • 定義:pi[t] : 主要用戶i在時間t定的價格

  • Case I(用戶可以觀察到先前其他主要用戶的策略):

    • 給定其他參與者在t時所提的策略(即p–i [t])

    • 可以得到主要用戶i在下回合的策略:


Iv spectrum pricing competition and solution d dynamic bertrand game 2

IV. SPECTRUM PRICING COMPETITION AND SOLUTION-D. Dynamic Bertrand Game(2)

  • Case II(用戶只能觀察到先前一部份主要用戶的策略):

    • 得到的資訊不夠求出的best response較不可靠根據現在的價格做調整(避險)

    • 策略之間的關係可以表示成:

  • 要估算邊界利潤,可以觀察在一個很小的價格變動ε,其頻譜需求的變化量,如(14)(15)

αi :調整速率


Iv spectrum pricing competition and solution d dynamic bertrand game 3

IV. SPECTRUM PRICING COMPETITION AND SOLUTION-D. Dynamic Bertrand Game(3)


Iv spectrum pricing competition and solution e stability analysis of the dynamic game 1

IV. SPECTRUM PRICING COMPETITION AND SOLUTION-E. Stability Analysis of the Dynamic Game(1)

  • 我們使用Jacobian matrix分析動態演算法的穩定性,在這個案例,定義Jacobian matrix為:

  • 定義jx,y:矩陣第x列第y行的元素


Iv spectrum pricing competition and solution e stability analysis of the dynamic game 2

IV. SPECTRUM PRICING COMPETITION AND SOLUTION-E. Stability Analysis of the Dynamic Game(2)

  • For Case I:

    • 其mapping function沒有控制參數使其價格適應穩定

    • 在只有兩個主要用戶的special case,其Jacobian matrix為:

    • 穩定


Iv spectrum pricing competition and solution e stability analysis of the dynamic game 3

IV. SPECTRUM PRICING COMPETITION AND SOLUTION-E. Stability Analysis of the Dynamic Game(3)

  • For Case II:

    • 價格適應和學習速率是相依的

    • 在只有兩個主要用戶的special case,其Jacobian matrix為:

    • 其eigenvalues

    • 可能穩定也可能不穩定(與αi、Mi、ν有關)


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IV. SPECTRUM PRICING COMPETITION AND SOLUTION-F. Optimal Pricing to Maximize Total Profit of Primary Services(1)

  • 所有主要用戶的利潤總和為

  • 所有主要用戶的最佳出價可以由以下式子獲得:

  • 在只有兩個主要用戶的case(i=1 j=2),我們可以得到式子(19)(20)

  • 使整體效能最大化的pi值≠奈許平衡的pi值主要用戶可能會合作來獲取最高的利潤


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IV. SPECTRUM PRICING COMPETITION AND SOLUTION-F. Optimal Pricing to Maximize Total Profit of Primary Services(2)


Iv spectrum pricing competition and solution g collusion and repeated game 1

IV. SPECTRUM PRICING COMPETITION AND SOLUTION- G. Collusion and Repeated Game(1)

  • 若賽局只執行一回合參與者會選擇奈許平衡的pi值來最大化自己的利潤

  • 賽局執行很多回合(重複賽局)選擇讓自己長期下來的利潤最高可適用處罰機制迫使用戶合作

  • 我們考慮我們的重覆賽局 :

    • 如果其他用戶同意的話,主要用戶將保持共謀

    • 如果其中一個主要用戶脫離共謀,則所有其他用戶將永久的進行處罰行為

    • 主要用戶考慮的是長期的利潤

    • 當前stage的利潤比未來的重要(這個stage的利潤為Pi,則下個stage的利潤為δiPi,0 ≤ δi ≤ 1)


Iv spectrum pricing competition and solution g collusion and repeated game 2

IV. SPECTRUM PRICING COMPETITION AND SOLUTION- G. Collusion and Repeated Game(2)

  • 定義:

    • Pi: optimal price

    • Pi: the price at the Nash equilibrium

    • Pi: the price due to deviation

o

n

d


Iv spectrum pricing competition and solution g collusion and repeated game 3

IV. SPECTRUM PRICING COMPETITION AND SOLUTION- G. Collusion and Repeated Game(3)

  • 若共謀永久保持,則主要用戶i的長期利潤可以表示成:

  • 如果主要用戶i脫離合作,則其長期利潤可以表示成:

  • 若要迫使主要用戶永久保持共謀,需要符合以下條件:

  • 因此可以獲得δi的下界


V performance evaluation a parameter setting

V. PERFORMANCE EVALUATION- A. Parameter Setting

  • 參數設定:

    • 主要用戶:

      • 可用的頻譜總數為20MHz(即Wi= 20)

      • 區域連結M1 = M2 = 10

      • 每個連結的頻寬需求為2 Mbps(即B = 2)

      • c1 = c2 = 2

      • 價格初始值p1[0] = p2[0] = 1

    • 次級用戶:

      • BER = 10

      • 通道品質γ: 9dB ~ 22dB

      • ν: 0.1 ~ 0.6

  • Note:視模擬的情況參數可能會有所變動

req

tar

−4


V performance evaluation b numerical results 1

V. PERFORMANCE EVALUATION- B. Numerical Results(1)


V performance evaluation b numerical results 2

V. PERFORMANCE EVALUATION-B. Numerical Results(2)


V performance evaluation b numerical results 3

V. PERFORMANCE EVALUATION-B. Numerical Results(3)

  • 設M1 = 10 ; M2 = 14


V performance evaluation b numerical results 4

V. PERFORMANCE EVALUATION-B. Numerical Results(4)


V performance evaluation b numerical results 5

V. PERFORMANCE EVALUATION-B. Numerical Results(5)


V performance evaluation b numerical results 6

V. PERFORMANCE EVALUATION-B. Numerical Results(6)

  • 固定α2為0.3


V performance evaluation b numerical results 7

V. PERFORMANCE EVALUATION-B. Numerical Results(7)

  • 總頻譜大小為60 MHz、所有主要用戶的主要連結總數為24:

    • N=2Wi = 30 MHz Mi= 12

    • N=3Wi = 20 MHz Mi= 8

    • N=4Wi = 15 MHz Mi= 6


V performance evaluation b numerical results 8

V. PERFORMANCE EVALUATION-B. Numerical Results(8)


V performance evaluation b numerical results 9

V. PERFORMANCE EVALUATION-B. Numerical Results(9)


V performance evaluation b numerical results 10

V. PERFORMANCE EVALUATION-B. Numerical Results(10)

  • δi太小用戶短視近利用戶不合作δi 要夠大用戶才會戶相合作


Vi conclusion

VI. CONCLUSION

  • 我們考慮多個主要用戶彼此競爭分享頻譜給次級用戶的機會,並將其視為一個寡頭市場

  • 我們使用效能函數來獲得次級用戶的頻譜需求函數,且此效能函數有考慮通道品質與頻譜的可替代性

  • 我們分析Bertrand game的奈許平衡與最佳解,並使用處罰機制來迫使主要用戶合作

  • 我們研究演算法的穩定條件


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