1. Nanjing University of Aeronautics and Astronautics
Grey Option Prioritization in Graph Model for Conflict Resolution and Application on Price Conflict Model
ZHAO Shinan
Nanjing University of Aeronautics and Astronautics

2. Outline
Introduction of GMCR
Application: Price Conflict Model
Grey Option Prioritization
Conclusion

3. 1. Introduction of GMCR
(1) What is GMCR
The Graph Model for Conflict Resolution （GMCR）is a methodology to deal with conflicts.
The graph model methodology mainly consists of three stages: conflict modeling, stability analysis, and other extended analysis including sensitivity analysis and status quo analysis.
a. Military Conflict
b. Family Conflict
c. Environmental Conflict

4. 1. Introduction of GMCR (2)Game Theory and GMCR Game Theory
Qualitative Method
Quantitative Method
Howard（1971）
Metagame Analysis
Normal
Extension
Cooperation
GMCR is a branch of game theory.
Conflict Analysis
Fraser and Hipel
(1987)
Graph Model for Conflict Resolution

5. 2. Application: Price Conflict Model
2.1 Background
The price conflict in this paper refers to the price dilemma of dual-channel supply chain between a retailer and a manufacturer who owns Internet Direct Marketing Channel (IDMC) and provides products for the retailer. And both of them sell the same products. The manufacturer tends to decrease product price because it has less costs with IDMC than the retailer who is burdened with rents, advertising costs and human resource cost. Therefore, the manufacturer chooses to low-cost competitive strategy to increase more market shares.

6. 2. Application: Price Conflict Model
2.1 Background
Figure2.1 Price conflict model in dual-channel supply chain

7. 2. Application: Price Conflict Model
2.2 Basic price conflict model
2.2.1 DMs and Options
Table 2.1 Feasible states of price conflict
DMs
Options s1 s2 s3 s4 s5 s6 s7 s8 s9
DM1
1. Low price N Y -
2. Differentiation
3. Abandon
DM2
4. Low price
5. Differentiation
6. Reduce orders
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

8. 2. Application: Price Conflict Model
2.2.2 State transition graph model
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.
Figure 3.2 State transition graph model

9. 2. Application: Price Conflict Model
2.2.3 Preference and Option prioritization
Table 2.2 Option statements of DM1
DMs
Statements
Explanation
Manufacturer
(DM1) -3
DM1 does not want to abandon its IDMC 1
DM1 wants to low price -6
DM1 does not want DM2 to reduce orders -4
DM1 does not wants DM2 to low price 5
DM1 wants DM2 to choose differentiation 2
DM1 wants to choose differentiation
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

10. 2. Application: Price Conflict Model
2.2.3 Preference and Option prioritization
Table 2.3 Option statements of DM2
DMs
Statements
Explanation
Retailer
(DM2) 3
DM2 wants DM1 to abandon its IDMC 4
DM2 wants to low price -1
DM2 does not wants DM1 to low price
6 IFF 1
DM2 will reduce orders if and only if DM1 wants to low price 2
DM2 wants DM1 to choose differentiation 5
DM2 wants to choose differentiation price
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

11. 2. Application: Price Conflict Model
Table 2.4 Crisp true values of option statements of DMs
DMs
Statements s1 s2 s3 s4 s5 s6 s7 s8 s9
DM1 -3 1 25 24 -6 23 -4 22 5 21 2 20
Score 47 39 41 33 62 54 56 48 12
DM2 3 4 -1
6 IFF 1 15 11 30 26 16 44
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

12. 2. Application: Price Conflict Model
Preference information
DM1
DM2
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

13. 2. Application: Price Conflict Model
2.2.4 Stability analysis
Table 2.5 Stability results of price conflict model
States
Nash
GMR
SMR
SEQ
DM1
DM2 E S1 S2 S3 √ S4 S5 S6 S7 S8 * S9
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

14. 3. Grey Option Prioritization
3.1 Option statements with interval grey true values
However, the true values of option statements of DMs at some states may be not restricted to just “true” or “false”, which means that the true values can be numbers between 0 and 1. In this conflict, the true value of DM1’s option statement “1” is “true” at s5 according to crisp true values of option prioritization. But DM1 may not prefer to choose the option of “low price” with 100% truth (a truth degree of 1) because s5 means that DM2 chooses the strategy of differentiation.
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

15. 3. Grey Option Prioritization
3.1 Option statements with interval grey true values
DMs
Statements s1 s2 s3 s4 s5 s6 s7 s8 s9
DM1 -3 1 25 24 -6 23 -4 22 5 21 2 20
Score 47 39 41 33 62 54 56 48 12
DM2 3 4 -1
6 IFF 1 15 11 30 26 16 44
[0.4,0.6]
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

16. 3. Grey Option Prioritization
3.1 Option statements with interval grey true values
DMs
Statements s1 s2 s3 s4 s5 s6 s7 s8 s9
DM1 -3 1
[0.7,0.8]
[0.4,0.6]
[0.8,0.9] -6 -4 5 2
DM2 3
[0.6,0.8] 4 -1
6 IFF 1
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

17. 3. Grey Option Prioritization
(1)The incremental score of state s:
(1)
(2)The total score at state s:
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.
(2)

18. 3. Grey Option Prioritization
Preference with interval grey true values
DM1
DM1’
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.
DM2
DM2’

19. 3. Grey Option Prioritization
3.3 Stability analysis
Table 3.1 Stability results of price conflict model
States
Nash
GMR
SMR
SEQ
DM1
DM2 E S1 √ * S2 S3 S4 S5 S6 S7 S8 S9
Low price. Internet Direct Marketing Channel greatly reduces the product costs of the manufacturer, making cost saving be an advantage of it.
Differentiation. The manufacturer can choose differentiation strategy by providing customers with different production combinations to affect consumers 'price perception.
Abandon. If the retailer threatens the manufacturer by reducing orders, the manufacturer may abandon its IDMC to maintain good relationship with the retailer.
Reduce orders. The retailer may reduce orders from the manufacturer or cooperate with other manufacturers to show its dissatisfaction over the manufacturer’s IDMC.

20. 4. Conclusion (1) Contribution and Findings Contribution:
Interval grey true values of option statements and grey option prioritization
Price conflict model based on GMCR.
Findings:
We can conveniently adjust the preference information by means of interval grey true values of option statements.
The stability results based on grey option prioritization are more reasonable and satisfactory.

21. 4. Conclusion (2) Future work
Comparisons of different methods to deal with interval grey true values will be carried out in the future work.

22. Thank you