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As the main objective of the study is to evaluate the adoption of third generation technology where there is more the one mobile operator in the market. Therefore keeping that in mind we will take into consideration "strategic" options, characteristically duopolies, where there is possibility of leader followed by a follower. The choice of valuating the introduction of 3G options with respect to a telecommunication industry should be analyzed with the help of real options because first of all telecommunication is considered to be a competitive sector and therefore as a consequence a natural relevance for the models of game theory, secondly it is considered to be a license race market and above all it is subject to R&D due to major revolutionization in the field of technology.
Two of the models that I will illustrate in the research methodology were developed by Paxson and Pinto (2004) where two firms are bearing in mind the option in order to enter a new market. The firm that would be the first to enter the market would be defined as the leader from now onwards and will get hold of a first mover advantages in terms of a higher share of the market as compare to a follower that would be second firm or in other words the competitor to enter the market. The roles of the leader and the follower are characterized endogenously in the opinion obtained from Fudenberg and Tirole (1985) where the two firms are supposed to be symmetrical ex- ante however they tend to be asymmetrical ex-post. Above all the leader will always be having a competitive advantage over the follower in terms of first mover advantages, therefore with respect to the upshot each of the firm will want to acquire the position of the leader, which generates a pre-emption effect.
First mover advantages or the competitive advantages that the leader possesses over the follower are created firstly in the terms of the technological advantages of being the first to enter the market. Secondly the leader has incentives in terms of patents if there is innovation. Furthermore the leader gains the competitive advantage in terms of brand image by being the first mover, and finally leader has a competitive edge with respect to organization and advantage of key location. On the other hand, being first in the market may not be necessarily considered the same as being the best, due to the fact that follower may turn up having an incentive to wait and learn from the mistakes of the leader. One of the key challenges faced by the researchers is to measure the advantages and disadvantages of being the first mover. For instance from the follower's point of view in the circumstances of public marketing in terms of innovations and patent applications, frequent public monitoring seems to be practical. On the other hand, brand loyalty along with differential pricing for the first mover or the leader is not always apparent, or quantifiable. For instance, with respect to mobile operators, only a few companies provide regular information in terms of new accounts and usage, whereas rarely they provide comprehensive information in terms of volume, costs and revenues.
There are several cases in R&D where the advantages of being first can be taken into account. With reference to introduction and adoption of 3G technology which is main subject of focus with respect to my study, the first company in a telecommunication industry (leader) to have introduced 3G might have the pre-emptive advantages of attracting and capturing the high end customers at individual and corporate levels in the market. Also as the leader has the competitive edge in terms of monopoly of providing 3G services they can charge higher fees to their customers for providing 3G services which in turn will generate substantial revenue towards the recovery of R&D expenditure. In particular, once a patent is acquired as a consequence of R&D, the first mover may have an incentive a number of years.
4.1 ASSUMPTIONS UNDERLYING PAXSON AND PINTO (2004) MODELS:
The Paxson and Pinto (2004) models makes the following assumptions. Firstly the models assume a duopoly environment which refers to the fact that there are only two competitors in the existing market that have the opportunity to invest. Secondly it assumes that the market share of the leader does not remain constant upon the entry of the follower in the market. However, at the same time it also considers the fact regarding the permanent first mover advantage which implies that leader retains a higher proportion of market share even after the entry of the follower. Additionally the market share of the follower is determined by subtracting the leader's market share from 1. Moreover it assumes that investment opportunity tends to offer stochastic cash flows in perpetuity. Finally it assumes that net revenues follow a log normal diffusion process which refers to geometric Brownian motion (GBM).
4.2 RIVALRY UNDER PRICE AND QUANTITY UNCERTAINITY
The first model that I am referring to with respect to introduction and adoption of 3G technology by mobile operators takes into consideration the fact that both number of units (quantity) and profit per unit (price) follow different but perhaps correlated geometric Brownian motion processes. While demonstrating the model let correspond to profit per unit sold whereas refers to the quantity that has been sold by the follower in a market. Assuming that both the variables follow a geometric Brownian motion, they can be illustrated in the following manner:
Where and refers to the expected multiplicative trends of and, whereas and represent the volatilities and and corresponds to increments of a wiener process. Furthermore the two variables and may appear to be correlated with the correlation coefficient denoted by.
Taking two firms into consideration that are contemplating to enter a new market with identical investment cost denoted by K, the firm that is first to enter the market which is referred to a leader will be able to obtain first mover advantages. Therefore as a consequence, the leader is expected to obtain a higher share of the market. Keeping that in mind, the differential equation for an idle follower can be illustrated in the following manner:
The equation (3) illustrated above explains that the movements with respect to the value function of an idle follower are usually subject to two boundaries conditions. The first boundary condition refers to the value matching condition which provides the value of (P, Q) at which the follower should make investment. The second boundary condition refers to the smooth pasting condition that makes sure that the derivatives of the two functions which refer to before and after the entry of follower in the market are equivalent at the investment point.
Supposing that X = PQ that corresponds to the total profit for the follower, which implies that. Therefore after the appropriate substitutions, the equation (3) can be demonstrated as following:
In addition the equation (4) mentioned above engages the following characteristic quadratic function shown below:
Furthermore Equation (5) has two roots, whereby the positive root is shown as:
The solution for the equation (4) is:
As we are aware of the fact that as X tend to increase, the value function of the follower has to increase as well and for that reason the equation (7) has to be finite, therefore B equals zero. Apart from that equation (7) is subject to the value-matching condition which is illustrated below:
Where refers to the trigger value of the follower which in other words is the value of X at which it is appropriate for the follower to enter the market, and moreover it is also subject to the smooth-pasting condition which is shown below:
Additionally equations (7), (8) and (9) imply that:
Thus as a result the value function of the follower denoted by P (F) is given by:
The equation (11) demonstrated above explains the follower's value function before and after the trigger is hit. Before the trigger is hit, we are aware of the fact that the follower has not yet made its entry into the market and additionally its value function corresponds to a monopolist perpetual American option with respect to being second to make a investment in a new market. At the trigger, the follower makes investments and followed by that its value function is the perpetuity. Furthermore consider m* to be an absolute value that is larger than one which is when multiplied by Q results in the number of units that are sold by the leader at the time when its alone in the market. Apart from that consider m to be a value larger than one, however smaller than m*, which is when multiplied by Q results in the number of units that are sold by the leader after the entry of follower in the market. Moreover Q (m-1) corresponds to the first-mover advantage, with respect to number of units, after the follower makes its entry in the market.
The value function of the leader which is denoted by P (L) is given by:
The trigger value of the leader denoted by can be obtained by solving the following non-linear equation where is unknown:
It should be also noted that is a closed form solution for the trigger value of the leader, when and when the follower's trigger = 1, based on the quadratic equation solution.
It is a known fact that the value function of the leader is most of the time larger than the value function of the follower, except the time when the number of units is exceptionally low. At this particular point the follower has not yet made its entry in the market, and if the leader has already entered the market it would have been better off being a follower. Furthermore it is important to be noted that when the follower enters the market the two functions tends to get closer. Apart from that the value function of the leader seems to be more complicated than that of the follower due to the fact that it is concave until the time the follower makes its entry, and at that particular moment its slope turn to be discontinuous. This behaviour occurs because although the number of units is increasing, but at the same time they are also approaching towards the trigger value of the follower, which corresponds to the fact that the negative effect of the entry of the follower tends to increase. Finally it should be taken into consideration that there is a point where the two functions meet. Therefore as a consequence, before this point which refers to the intersection of the two functions, a firm would be better off being a follower and after that a firm would be better off being a leader.
4.3 RIVALRY UNDER REVENUE AND INVESTMENT COST UNCERTAINITY:
The second model that I am referring to with respect to introduction and adoption of 3G technology by mobile operators takes into consideration the fact that both total annualized profits which is termed as "return" and denoted by R, along with investment cost which is represented by K follows a log normal diffusion process which in other words corresponds to geometric Brownian motion. The fact that both the variables R and K follow a geometric Brownian motion is demonstrated by the help of equations shown below:
Where and are considered to be expected gain with respect to R and K or in other words the drift of the Brownian motion. Furthermore in equation (15) and in equation (16) correspond to volatilities, whereas refers to the coefficient of correlation. Furthermore similar to the previous model, also this model assumes that two companies are considering entering a new market where the leader which refers to first firm to enter the market has an incentive to pre-emption in the terms of obtaining a competitive advantage m which corresponds to dominant market share.
Therefore as a result, the differential equation of the value function of an idle follower turns out to be following:
The equation (17) illustrated above is subjected to the two usual boundary conditions. The first boundary condition refers to the value matching condition and its it important to notice that at this point the option value is equivalent to the present value of the total returns which is denoted by R minus the investment cost which is represented by K. Therefore at this point, the investment is made and as a consequence all the uncertainty which is related to the cost of investment tends to disappear.
Thereby now we will substitute which implies that
Therefore after all the substitutions shown above, equation (17) can be demonstrated in the following manner:
Furthermore the characteristic quadratic function of equation (18) can be illustrated in the following manner:
Whereby with one solution the positive root is:
The trigger value of the follower is demonstrated as:
And the value function of the follower is demonstrated as:
As a matter of fact it is assumed that the leader which refers to the first-mover firm in the market will always tend to have an advantage over the follower. Until the time when follower which refers to the second competitor, makes its entry in the market, the leader tends to receive, whereby m* corresponds to a factor that is when multiplied by the return gives the total return of a monopoly. After the time when follower makes its entry in the market, the leader will still tend to have a permanent pre-emptive advantage, m, which refers to a multiplicative factor, larger than one, that can be characterized as either larger market share than the follower or higher prices. The value function of the leader is demonstrated as following:
The trigger value of the leader can be obtained numerically by equating the first line of equation (24) which refers to the value function of the leader with the first line of equation (23) which represents the value function of the follower, furthermore by substituting for and for R. Additionally it is appropriate to convert V which corresponds to the present value of the future cash flows into R where, especially under the circumstances where cash flows appear to be irregular. Finally, under certain restricted circumstances by means of expressing the triggers multiplied by K so that the follower's trigger might be equivalent to 1, there is a closed-form solution for the trigger value of leader, if .
The models formulated by Paxson and Pinto (2004) best suits the circumstance of a duopoly environment where the first firm to enter the market is considered as a leader and the second firm or the competitor is considered to be a follower. Furthermore Paxson and Pinto (2004) formulated analytical solutions with respect to the leader and follower options to invest in the market along with quantitative explanation for the optimal investment timing of the leader. Additionally they computed the partial derivatives of the leader and follower value option in order to determine their respective proportions in the market share in order to their profitability and effectiveness in the market. This model proposed by Paxson and Pinto (2004) belongs to the class of pre-emption models. However, like sequential models they take the strategic consequences on the worth of an investment opportunity into consideration that tends to result from the competitor's behaviour. When analyzing this model critically, it can be derived that the value function of the follower is less sensitive in comparison to leader's value function in terms of market share or entrance/exit of the customer till the time when the expected revenue exceeds the investment level of the follower's trigger. Additionally it is important to note that the follower's trigger tends to increase along with the market share and the volatility of the revenue, where as the value function of the leader is extremely sensitive and downward sloping as the revenue approaches the follower's trigger. Summing up, the Paxson and Pinto (2004) models seems to be more appropriate than models demonstrated by other authors with respect to my study on introduction and adoption of 3g technology and are perhaps more realistic than other models that in relation to advantages of being first mover due to the proposition of permanent first mover advantage.