Chapter 4 Analysis of User’s Best Response Using Game Theory
4.2 Developing Payoff Matrixes
4.2.2 Payoff Values If Service Provider Provide MNP in Near Future
When service provider really supports MNP service as a fulfillment of current demands, service provider is providing better service to user and their image will be better for fulfillment of demands and understanding to support the requirement. The benefits and payoff values when service provider supports MNP are as follow:
Figure 4.3 The benefits of players if service provider support MNP
Each benefit will be counted as 1 and payoff value will be sum of benefits for related action. If both players make a move as MNP, their payoffs will be 3 for each.
Benefits of user for MNP = Easy to move & easily contact + Cost effective + Better services = 1 + 1+ 1
= 3
Benefits of service provider for MNP = More User + More profit + Better image = 1+ 1+ 1
= 3
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If both players choose to play No MNP, their payoffs will be 0 because service provider's preference is playing MNP in this condition. This means that both players will not receive any benefit for both playing No MNP.
Benefit of user for No MNP = No benefit = 0
Benefit of service provider for No MNP = No benefit = 0
If one player plays MNP and another player’s choice is No MNP, the player who plays No MNP will get payoff value 0 as the condition is SP providing MNPservice. The player who chooses MNP will get payoff value (-1) because for service provider, he has investment cost to provide MNP service but user's choice is No MNP and for user, he has many sim numbers which cause higher cost because he chooses No MNP service provider.
Payoff matrix when service provider support MNP service will be present with these payoff values of both players.
Figure 4.4 Payoffs Matrix If Service Provider provide MNP in near future
Where SP means service provider, User means mobile user, C = cooperate (playing MNP service) and D = defect (playing No MNP).
C D
C
D
SP
User
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4.3 Analysis of two conditions in extensive form
To analyze these conditions, we will add "Nature" as a participant to make a move to help the user because user is unaware of service provider's preference whether he will support MNP service or not. To play "Nature", we will set the probabilities of service provider being nice and selfish. If service provider is nice, he will provide MNP service and if service provider is selfish, he will not support MNP service. To know whether service provider is nice or selfish, we will analyze in two extensive forms: one is with higher probability of service provider being nice and another one is higher probability of service provider being selfish.
4.3.1 Case study 1: SP with a higher probability of being nice
Probability of service provider being nice is1⁄2, so we set 2⁄3 as higher probability of being nice and 1⁄3as lower probability of being nice (probability of being selfish). In this extensive form, Nature will help to know service provider's preferences of being nice and selfish. Service provider will decide to choose cooperative or defect by playing C or D and user will also make a move as cooperative or defect, playing C or D, with the prediction of service provider's preference by using Nature's help The payoff vales of user and service provider are showing in the boxes and they will represent as the action of user and service provider in extensive form.
Where SP means service provider, User means mobile user, C= cooperate (MNP), D= defect (No MNP).
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Figure 4.5 Extensive form with higher probability being nice 4.3.2 Case study 2: SP with a higher probability of being selfish
Probability of service provider being selfish is 1⁄2 , so we set 2⁄3 as higher probability of being selfish and 1⁄3as lower probability of being selfish (probability of being nice).
SP SP
User User
User User
Nature
C D C D C D D
SP: 2 SP: 0 SP: 1 SP: 1 SP: 3 SP:-1 SP: 0 SP: 0
C
C D D
U : 2 U : 1 U : 0 U : 1 U : 3 U : 0 U :-1 U : 0
1/3, Selfish P 1/3 2/3, Nice P 2/3
C
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Figure 4.6 Extensive form with higher probability being selfish
Where SP means service provider, User means mobile user, C= cooperate (MNP), D= defect (No MNP).
4.3.3 Analysis of case 1 and 2
Service provider knows his type, and plays his preferred strategyD if he is selfish and plays C if he is nice. Based on the probability of service providerbeing nice or selfish, user’s choice will depend on his expectation from service provider. Suppose user will attach probability (p) to service providerplaying C, and so (1-p) is the probability that service provider is playing D.
Therefore,
SP SP
User User
User User
Nature
C D C D C D D
SP: 2 SP: 0 SP: 1 SP: 1 SP: 3 SP:-1 SP: 0 SP: 0
C
C D D
U : 2 U : 1 U : 0 U : 1 U : 3 U : 0 U :-1 U : 0
2/3, Selfish P 2/3 1/3, Nice P 1/3
C
29 User's expected payoff from SP with no MNP = 2p+1(1-p) User's expected payoff from SP providing MNP = 3p+0(1-p)
User's expected payoff from SP with no MNP = Use's expected payoff from SP providing MNP 2p+1(1-p)= 3p+0(1-p)
P= 1⁄2
According to the result, user’s best response is to play C (MNP) if p>1⁄2, and to playD (No MNP) if p<1⁄ .2 Therefore, User will play MNP for case study 1 where service provider with higher probability of being nice, MNP probability, p=2⁄3. User will play No MNP for case study 2 where service provider with lower probability of being nice, No MNP probability, p=1⁄3.
Based on the user's best response for the case of service provider with higher probability of supporting MNP, there are not only the highest value of the benefits of user and also the highest value of the benefits of service provider. Therefore, this result of user's preference gives the best choice for both players.
According to payoffs, the benefits of user and subscribers for choosing MNP service are twice of the benefits of user and subscriber for choosing No MNP service. So, estimated number of subscribers for MNP service will be twice of normal increased numbers of subscribers. We estimate the average percentage of increased number of subscribers for operators in Myanmar.
Increased number = New number – Original number
Increased Percent (%) = (Increased number/ Original number) * 100
Average Percentage = Total Increased Percent for all operators/ No: of Operators
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Figure 4.7: Normal increased numbers of subscribers in million with No MNP service
In figure 4.7, we represented the normal increased numbers of subscribers in million with No MNP service and estimated number of subscriber with No MNP service between 2016 and 2017.
Figure 4.8: Estimated number of subscribers in million with MNP service
Figure 4.8 describes the estimated number of subscribers in million with MNP service. In the situation of providing MNP service, we estimated that the average value of the numbers of subscribers will increase 25% than normal increased amount of subscribers for No MNP serviceby analyzing the historical data.