Chapter 4: The structure for basic model
4.6 Results for basic model
4.6.1 Conflicts between Chorus and CFH
In our model, there are two sorts of conflicts between Chorus and CFH. A) The conflict of construction timing, in which Chorus and CFH may have different opinions about choosing when to construct the fibre network (parties disagree on whether construction is optimal in the next period). B) The conflict of construction sequence, in which the two parties may have different ideas about choosing the construction order among different cities (they consider construction in the next period is optimal but disagree about which city should go next). We would like to apply our numerical example to demonstrate these two conflicts. All values of parameters for our numerical example can be found at table 4.1. Any modification will be notified.
We provide the most interesting information about the optimal construction policies for both Chorus and CFH at table 4.2 and table 4.3 respectively. We only report the information about the first six periods due to the limited space (there are twelve periods in total).
Specifically, these tables describe the optimal policies once city HL has been finished. Both parties are deciding when, and what, to build next. Every cell at table 4.2 or table 4.3 represents the adopted construction behaviour of the underlying party corresponding to the
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node ( ). For example, the first entry at table 4.2 is * +, which means that Chorus would like to wait at node ( ).
Table 4.2: Chorus’s optimal policy at state (1, 0, 0, 0)
Table 4.3: CFH’s optimal policy at state (1, 0, 0, 0)
A) The conflict of construction timing
The conflicts of construction timing could be identified from comparing table 4.2 and table 4.3, which are highlighted by yellow boxes. For example, if CFH and Chorus are in state (1, 0, 0, 0) during date 0 to date 2, there is a timing conflict between two parties if the current state is not too bad. (That is, not all the past moves are down moves) At date 3, the timing conflict only disappears if at least 2 down moves have occurred in the past. However, at date 4, the threshold for the timing conflict to be able to disappear has extended to at least 3 down moves having occurred in the past. At date 5, the timing conflict does not show up when
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there have been 5 up moves or there have been at least 3 down moves. At date 6, the timing conflict vanishes when there have been 5 up moves or there have been at least 4 down moves. B) The conflict of construction sequence
In contrast, we highlight the sequencing conflicts by red boxes. As we may find in table 4.2 and table 4.3, the sequencing conflict only exists when the current level of demand is high.42 For example, at date 5 and date 6, the sequencing conflict only shows up when there have been more than four up moves.
4.6.2 The consequences of conflict
If CFH works in the best interests of society as a whole, its optimal policy will maximise social welfare. Therefore, any policy which deviates from CFH‟s optimal policy may bring a potential social welfare loss (the present value of conflict), where these welfare losses may be raised either from an undersupply in the UFB network during certain periods43 or an incorrect priority policy among different cities.44 And it will be useful to measure the potential social welfare losses from the adopted suboptimal policies. In our numerical example, we apply equation 11 and equation 12 to calculate the present value of social welfare loss and the proportion of conflict respectively.
( * +) ( * +)( ) ( * +)
( * +) ( )
Where ( * +) is the present value of the UFB contract for CFH at state * +
under CFH‟s optimal policy (therefore in the view of society, it is the maximised present value of social welfare raised from the UFB project), and ( * +) is the present value of the UFB contract for CFH at state * + under Chorus‟s optimal policy. (Therefore in the view of society, it is only one of the social welfare present values rather than the maximum.)This present value may be equal to or smaller than the maximum depending on whether Chorus‟s optimal policy is the same as CFH‟s. If state * + is
42 It does not mean high demand always bring sequencing conflicts. For example, at date 5, when there have been five up moves, a timing conflict rather than a sequencing conflict shows up since the demand is high enough to induce CFH to build up both city HH and city LL once.
43 The firm may work too slowly to provide enough supply to meet the social demand.
44 For saving the cost, the firm may give priority to the low cost city instead of the high cost city, even though the high cost city has a higher total surplus than that of the low cost city.
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equal to * +, we have Table 4.4 for ( * +) and Table 4.5 for ( * +)
respectively.
Table 4.4: Present value of UFB for CFH under Chorus policy at state (0, 0, 0, 0)
Table 4.5: Present value of UFB for Chorus under Chorus policy at state (0, 0, 0, 0)
The present values of social welfare under two different policies have been highlighted by yellow boxes. With equation 11 and 12, we find the present value of welfare loss and proportion of conflict equal 29 and 0.274 respectively.
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