Considering the investment decisions with real options games approach

Renewable and Sustainable Energy Reviews xx (xxxx) xxxx–xxxx

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Considering the investment decisions with real options games approach Abdollah Arasteh Industrial Engineering Department, Babol Noshirvani University of Technology, Shariati Ave., P.O. Box: 484, Babol, Iran

A R T I C L E I N F O

A BS T RAC T

Keywords: Investment analysis Option games Incomplete information Asymmetric information Least Squares Monte Carlo

The mix of games theory with the real options has been a dynamic range of exploration in the most recent decade. The engaging quality of the specialists for displaying aggressive speculation choices by blending ideas from both hypotheses is on account of a venture choice in a focused business sector can be seen, in its substance, as a “game” between firms. In this paper, we expand a model to consider finite horizon real option games under incomplete information with various parameters. In incomplete information games, firms’ actions express significant information about profitability to contestants. The encapsulation of this information proposed original blocks in models with strategic interactions. This is because of circularity where best exercise decisions are based on previous decisions taken, which at a given time are quiet to be mentioned because about the dynamic programming principle. We expand an extended version of the Least Squares Monte Carlo algorithm to confront these results. The model can aid in understanding the relation between strategic optionality and information besides how this influences the best decision policy and its value results. We find the informational feature is of great significance for firms’ best decision policy and optimization of project values.

1. Introduction As of late, a developing number of papers in the real options writing join amusement theoretic ideas. The explanation behind this propensity, it has been contended, is that such approach is frequently alluring as far as real options applications since numerous ventures are portrayed by both vulnerability and key associations. Game theory has been the center of incredible consideration in the scholastic field in the course of the most recent decades and has impacted the advancement of an extensive variety of exploration zones from financial aspects, science and arithmetic to political science. Real options theory, then again, developed in the eighties as a valuation method, particularly suitable for speculations with high instability, and is today instructed in any MBA and Postgraduate courses. A venture choice in aggressive markets can be seen, in its pith, as a “game” among firms, following in their speculation choices firms verifiably check what they think will be the other firms’ responses to their own behavior, and they realize that their rivals think the same way. In strategic settings firms, investment decisions affect competitors’ actions. Thus, firms’ decisions are conditional on the information accessible about competitors. Most models choose firms’ investment decisions under a complete information framework. Looking at the real world it is difficult to consider the basis for stating such a supposition. In competitive R & D markets, research programs are managed privately, and competitors realize little about developing opponents [16,27,4]. How a firm selects to apply its operating decisions expresses

information to market participants, among these its rivals. The real options exercise strategy is a significant information transmission mechanism. This paper mostly follows in the steps of the real options literature and is assigned to the subset of papers underlined on models with competitive interactions and on the information dimension. Game theoretical considerations have been included in several significant papers. Smets [35], Grenadier [12–14], Weeds [39] and Murto [29] to name a few. Grenadier [12] models incomplete information in a real options model by supposing that information is an external signal that is handed to the firm and learning comes in the form of more exact signals. Miltersen and Schwartz [34] consider a model with competitive interactions when there is both market-wide uncertainty about the size of the market and firm-specific uncertainty about the completion time of the R & D project. The competitive nature of Miltersen and Schwartz are similar to this article. Lambrecht and Perraudin [25] and Hsu and Lambrecht [17] consider games of incomplete information. In Lambrecht and Perraudin a symmetric incomplete information case is modeled and the firms update its opinion about its competitor's investment trigger relied on in the way of the underlying state variable [25]. Morellec and Schürhoff analyze corporate investment and financing when corporate members have better information about the firm's growth views [28]. A few papers have considered real options problems using the Least Squares Monte Carlo algorithm of Longstaff and Schwartz [26], among others, Schwartz [34], Miltersen and Schwartz [27] and Grenadier and Malenko [15].

E-mail address: [email protected]. http://dx.doi.org/10.1016/j.rser.2016.10.043 Received 30 December 2013; Received in revised form 25 August 2016; Accepted 25 October 2016 Available online xxxx 1364-0321/ © 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: Arasteh, A., Renewable and Sustainable Energy Reviews (2016), http://dx.doi.org/10.1016/j.rser.2016.10.043

Renewable and Sustainable Energy Reviews xx (xxxx) xxxx–xxxx

A. Arasteh

opportunity), the systems are the decisions “invest”/”defer” and the settlements are the organizations’ quality capacities. Moreover, to be completely described, a diversion still should be determined as far as what kind of learning (complete/incomplete) and data (perfect/imperfect, symmetric/asymmetric) the players have at every point in time (node of the game-tree) and with respect to the historical backdrop of the diversion; what sort of amusement is being played (a “one-shot” game, a “zero-sum” game, a cooperative/noncooperative game, a sequential/simultaneous game); and whether blended methodologies are permitted. Besides, firms can just enhance their benefits by decreasing the benefits of its rival (zero-sum game) and are thought to be ex-risk symmetric and symmetric/asymmetric after the venture. Moreover, the way the firm’ speculation limits are characterized, in the association's technique space, relies on upon the quantity of fundamental variables utilized. In any case, paying little heed to the quantity of basic variables utilized as a part of the genuine choices show, the rule fundamental the utilization of the speculation threshold(s), inferred through the genuine alternatives valuation procedure, continues as before: “a firm ought to contribute when its venture edge is crossed the first run through”. By “non-standard” real options game models we mean models which, because of one or a few of their attributes, don’t fit into the definition expressed previously. Despite the fact that, at a first look, the versatility of diversion hypothesis ideas to real options models appears glaringly evident and direct, there are a few contrasts between a “standard” ROG and a “standard” game like those which represent fundamental game theory course readings. Beginning from the contrasts between a “standard” diversion in both speculations, one distinction that is quickly perceived respects the way the player's settlements are given: in “standard” games utilized as a part of a large portion of the game theory course books, for occasion, “the prisoners’ dilemma”, the “grab-the-dollar”, or the “burning the bridge” recreations, the player's adjustments are deterministic while in “standard” ROGs they are given by, once in a while, complex numerical capacities that rely on upon one, or more, stochastic hidden variables. These progressions fundamentally the tenets under which the diversion harmony is resolved. Likewise, other potential formal issues may likewise emerge when we consolidate real options and game theories. Case in point, the danger nonpartisan presumption ordinarily made in the real option literature, in light of which firms' adjustments and their separate venture edges are determined, won’t be intelligent with the world under which the guideline of Nash equilibrium works. The primary guideline fundamental game theory is that those included in key choices are influenced by their own particular decisions as well as by the choices of others. Game theory began with the work of John von Neumann in the 1920s, which finished in his book with Oskar Morgenstern distributed in 1944. With the development of game theory, a formal investigation of focused associations got to be conceivable in financial aspects and business technique. Game theory gives an approach to consider social associations of people, by uniting them and looking at the balance of the diversion in which these methodologies interface, on the supposition that each individual (financial operator) has his own particular points and procedures. It describes a diversion in four fundamental measurements: the players, the activities accessible to them, the planning of these activities and the resulting structure of every conceivable result. The players are thought to be judicious and their soundness is acknowledged as a typical learning. Game-theoretic models can be isolated into diversions with or without "perfect information" and with or without complete information. “Perfect information” implies that the players know every single past choice of the considerable number of players in every choice hub; “complete information” implies that the complete structure of the game, including every one of the activities of the players and the conceivable results, is basic knowledge. All things considered, the

The story of our model is as follows. Two firms are engaging in an R & D game. Both firms are in an R & D period, investing in a product that is to be sold in the same part of the market. At a limited horizon, the R & D period ends and both firms start their product in the marketplace at the same time. The firms’ market portions rely on their product quality compared with competitors. A higher product quality is presented as a sustainable competitive benefit giving a higher market share. That is, a higher market share is got by getting a higher product quality than the competitors. The game has an asymmetric informational framework in that one firm has complete information about the growth of both products. Therefore, the firm can notice the product quality level of both competing firms. The asymmetric information framework of the model can be arrested for one firm (i) having higher competitor consideration capabilities, (ii) having formerly started a similar product and its competitor on this ground realizes what it is competing against, (iii) having engaged a standard technology in expanding the product, whereas the competitor is using an unproven and more uncertain technology and/or the other firm (iv) being a PLC and adjusted to reveal information [2,30]. If the market visions become gloomy, because of the proportional power of the competitor, there is a strategic option to cut losses and abandon the R & D project. In the standard complete information case, the best abandonment strategy will rely on equating the instant benefits of exercise with the borderline value of continuing. In the asymmetric information case, the firms will also consider the benefits of waiting for other firms to show information through their (in)actions. This impact is expressed in equilibrium [24]. We suppose the expected technological growth of the two competitors’ R & D projects is symmetric. Our model can easily manage with asymmetries about this feature. The value of the product development projects and the best abandonment strategies are getting from implementing an extended recursive version of the Least Square Monte Carlo Algorithm (RLSM) by Longstaff and Schwartz [26]. This algorithm permits us to solve our complex problem given the number of state variables in our model and the incomplete information game setting. 2. Literature review The primary paper in real options literature to consider collaborations between firms was Smets [35]. Since Smets’ work another branch of real options models, checking the communications between firms, emerged, being Grenadier [12], Smit and Trigeorgis [36], Huisman [18], Murto and Keppo [29], Weeds [39], Lambrecht and Perraudin [25], Huisman and Kort [19,20], Smit and Trigeorgies [37], Paxson and Pinto [32], Pawlina and Kort [31] and Kong and Kwok [23] and Azevedo and Paxson [3] great case of this kind of models. In the real options literature, a “standard” real options game (ROG) model can be depicted as a model where the estimation of the venture is dealt with as a state variable that takes after a known procedure; time is viewed as vast and consistent; the speculation expense is sunk, unbreakable and settled; firms are accepted to have enough inward assets to attempt ventures when it is ideal to do as such; the venture diversion is played on a solitary venture; the quantity of firms holding the choice to contribute is typically two (duopoly); and the center of the examination is the determination of the organizations’ worth capacities and their individual venture edge under the suspicion that either firms are danger unbiased or the stochastic development of the variable(s) hidden the speculation quality is spread over by the current prompt comes back from an arrangement of securities that can be exchanged constantly without exchange costs in a consummately aggressive capital business sector. As indicated by game theory, the three most essential components that describe a game are the players and their strategies and payoffs. Making an interpretation of these to a ROG we have that the players are the organizations that hold the choice to contribute (speculation 2

Azevedo and Paxon [3] Baker et al. [48]

Bouis et al. [49]

Cabral and Dezső [50] Carlson [51]

4

5

6

7

3

Game information

* *

*

23 Lee [64]

*

*

21 Kellog [63] 22 Kong and Kwok [23]

*

*

*

*

*

*

* *

*

*

*

*

*

* *

*

*

*

*

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* *

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*

*

*

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*

*

13 Dixit and Pindyck [56] 14 Ernst et al. [57] * 15 Feil and * Musshoff [58] 16 Foster et al.[59] *

*

*

*

*

*

*

*

*

*

*

*

*

17 Grullon et al. [60] 18 Huisman and Kurt [20] 19 Karatzas and Shreve [61] 20 Kauffman and Li [62]

Game type

*

*

*

*

* *

*

*

*

*

*

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>2

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*

New tech adoptions Textbook

Patent value Investment decisions New plants generation Stock markets

Company evaluation Preemption and war of attrition games, incomplete info Textbook

Textbook

renewable energy facilities Non-storable Commodities Projects Private and public sectors of markets New tech adoptions Investment decisions Standard investment project Technology adoption Industry equilibrium nanotechnology

Application

Optimal investment timing Oil industry Standard investment project technology investments (continued on next page)

endogenous Exogenous

Firms# Leadership

Discrete Continuous complete Incomplete symmetric Asymmetric simultaneous sequential One- large Winner Zero- cooperative Non 2 shot takes all sum cooperative

Time

12 Décamp and Mariotti [55]

Casparri and Fronti [52] 10 Chevalier and Trigeorgis [53] 11 Culík [54]

9

8

Amador and Weill [47]

Adkins and Paxson [45] Aguerrevere[46]

3

2

1

Papers

Table 1 Game theory aspects underlying the most relevant literature on real options games.

A. Arasteh

Renewable and Sustainable Energy Reviews xx (xxxx) xxxx–xxxx

Game information

4

*

*

*

*

*

43 Wu and Tseng [82]

44 Wu [83]

45 Wu et al. [84]

46 Zhu [85]

*

*

*

*

*

*

* *

*

*

*

*

* *

* *

35 Siddiqui [75] 36 Smit and * Trigeorgis [37] 37 Sneed and Jognson [76] 38 Suh [77] 39 Suttinon et al. [78] 40 Tallau et al. [79] *

*

*

34 Shibata [74]

*

*

*

*

*

*

*

*

* *

*

* *

*

*

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*

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*

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*

*

31 Pimentel et al. [71] 32 Rogova and Yarygin [72] 33 Savva and Scholtes [73]

*

*

*

*

*

*

*

*

*

*

*

30 Paxon and Pinto [70]

*

*

*

*

27 Odening et al. [68] 28 Park and Kang [69] 29 Pawlina and Kort [31]

*

*

*

41 Thijssen et al. [80] 42 Weyant and Yao [81]

Game type

*

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endogenous Exogenous

Firms# Leadership

Discrete Continuous complete Incomplete symmetric Asymmetric simultaneous sequential One- large Winner Zero- cooperative Non 2 shot takes all sum cooperative

Time

26 Moon and Yao [67]

24 Lombardi et al. [65] 25 Mason and Weeds [66]

Papers

Table 1 (continued)

Patent value, R &D Patent value Water infrastructure Information security Investment analysis R & D Market & technical uncertainty Production capacity expansion patent value using option models Technology investment Nuclear energy

Partnershi p deals biotech industries Investment analysis R&D Textbook

Mobile industry

Technology choice Standard investment project Standard investment project railway

structural capital Standard investment project Negotiation under Incomplete Information Agriculture

Application

A. Arasteh

Renewable and Sustainable Energy Reviews xx (xxxx) xxxx–xxxx

Renewable and Sustainable Energy Reviews xx (xxxx) xxxx–xxxx

A. Arasteh

greater part of the times, it might be hazy to every firm where its opponent is at every point in time thus the suspicion of complete information may not be reasonable. Likewise, games can likewise be characterized by participation among players is permitted or not. In the previous case, the diversion is known as a “cooperative game”, in the later, it is known as a non- cooperative diversion. In noncooperative games, it is accepted that players can't make an authoritative understanding. That is, every helpful result must be supported by Nash balance procedures. Then again, in agreeable recreations, firms must choose the option to coordinate. Numerous real life investment situations display both cooperative and non-cooperative features. In our survey we select a broad number of papers, distributed or are in advancement, displaying speculation choices considering uncertainty and competition, created throughout the most recent 30 years. As a supplement, we utilize commitments from other real optionsrelated areas. We will likely incorporate every one of the commitments to the writing on real options game models, abridge their outcomes, relate these outcomes to the known exact proof, assuming any, and propose new boulevards for future exploration. We focus our discussions and analysis, chiefly, on the game theory part hidden the real options model. In Table 1, we exhibit a synopsis of our outcomes. The real options game models inspected address present day questions in venture investigation and give new answers for speculation issues, contributing, along these lines, to a superior comprehension of the mind-boggling nature of firms' speculation conduct in business sectors where instability and rivalry hold. We gave specific accentuation to the game theory viewpoints fundamental every speculation model checked on, for four principle reasons: to begin with, on the grounds that, these days couple of monopolistic divisions remain thus rivalry got to be a standout amongst an essential perspective driving association's venture conduct; second, on the grounds that the stochastic detailing of real options game models is, in its substance, like that utilized as a part of genuine choices models produced for monopolistic markets, henceforth it has been widely talked about in the course of the most recent 30 years; third, in light of the fact that regardless of all advances made in real options game models in the course of the most recent two decades, there is an implicit agreement among specialists that the venture models accessible, albeit more practical as far as presumptions when contrasted with those inferred for monopolistic settings, are still an excessive amount of deterministic and, to some degree, unsophisticated in the way the “competition factor” is fused in the model; fourth, in light of the fact that there is the instinct or regular except among scientists, that it is conceivable to enhance current real options game models by uniting real options and game theory. This paper examines the information feature in option games. We expand a method that lets us consider the suggestions of incomplete information with optimal decision policy and the relative project valuations in complicated environments. We appeal the dynamic programming principle to specify the optimal decision policy dependent on future strategic optionality. This paper concerns about the circularity result of the backwardforward problem, to value projects with strategic flexibility under incomplete information. This result is general in the sense that it will be a major part of any dynamically limited horizon real options model if there is asymmetric information between the different firms. Our method can so be appealed to consider the effect of information on many aspects, when the problem mentioned is of such a complexity that no closed-form solutions are available. In other words, the paper contributes to the literature by showing a way for solving dynamic games with incomplete information where the state space is driven by various processes. This is done through an expanded Least Squares Monte Carlo algorithm. Therefore, this paper adds to the arsenal of simulation methods to solve option problems. Our method can aid whenever there is a need for absorbing complex

information frameworks in option game models. We propose the method for including incomplete information into option games model in a special setting for two reasons. First, it clarifies the opinions of the method and second, it allows us to assume economic understandings from the method. 3. Model We start structuring our model. All over our consideration, we will suppose that capital markets are frictionless and that agents are competent to borrow and lend directly at a given constant interest rate i > 0 . Time is continuous and labeled by t ≥ 0 . Uncertainty is modeled by a filtered probability space (S , f , π ). This risk-neutral probability measure of the economy is labeled by r and the relating probability space is therefore given by (S , f , r ). 3.1. Setup Our model has an asymmetric structure. Firm one is provided with an informational benefit as it has complete information over the operating state variables. Firm two is the less-informed firm and cannot see developing firm one's R & D project. In the literature, this setup is labeled shortage of information on one side. To expand their projects both firms must spend an investment cost each period. We will propose the market size, C, for the products the firms are growing is deterministic. We can think of C as the present value of all future cash flows that can be got in the market from T to ∞. In this section, we start defining the underlying state variables. 3.1.1. Product quality It is the R & D innovation projects the quality of the resulting products is uncertain. At the time firms capture in R & D projects they are unconfident about the precise features of the product they end up creating the market. The dynamics of the product quality determinants of firm i is given by the stochastic differential equation

dyti = di yti dt + σi dBti

(1)

where σi is the immediate volatility and di is the immediate drift. Besides, σi is a precisely positive constant solution of the stochastic differential equations above exist. Bi shows standard Brownian motions which are uncorrelated. 3.1.2. Market share When the R & D period is completed and if neither firm has abandoned the market, the market share relies on the distinction in the quality of their products. The market share is so the driver of future cash flows. The market share firm i will achieve in the marketing period is given by qi . Remark 1. The market share of firm i (given firm j has not abandoned) is at time T given by:

qi = min [{0.5 + α ( yTi − yTj )}+ , 1]

(2)

whereas firm j's (given firm i has not abandoned) market share is given by:

qj = 1 − qi

(3)

α is a constant competition parameter specifying the degree of market share the firms get by getting a higher level of product quality. 3.2. Strategic options Firms do to a large area have the flexibility to maneuver their strategic plan. This managerial flexibility is examined in the following. In our model, we concentrate on the optionality which has the highest 5

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A. Arasteh

degree of significance in R & D settings – the option to abandon the investment.

4.1. Monopoly situation In the monopoly condition, the competitor was abandoning the market before time T. That is to say, the value of the firm's project is relying on supposing being the monopolist in the market at time T. The decision on whether to keep investing or abandon the market before time T is insignificant as there is no stochasticity. To solve that problem we first need to realize the value of the project at time t. That is, we have the following remark for firm i = {1, 2} given firm j = 3 − i , has abandoned.

3.2.1. Abandonment option When firms absorb in R & D projects, they are not needed to invest all over the whole development period. Firms have the option to abandon their projects if the viewpoint of the resulting market becomes gloomy. In the incomplete information case, the option to abandon also contains the optionality of waiting for rivals to disclose information through their (in) actions. It is an essential strategic decision to continually decide whether to continue investing or exit the R & D project. The decision relies on the profit potential in the market and is so completely influenced by the rivals' exercise strategy. The best exercise strategy for the contending firms has to be solved concurrently. This is further complicated by the incomplete information framework [11,33]. Dutta and Rustichini highlight that in a multi-firm setting the firm's optimal decision cannot be untangled using the optimization methods applied in the standard real options analysis [8]. Alternatively, the optimal control problem has to be explained since a stopping time game, which is formally a stochastic game, i.e. a game where the firms' pure strategies are stopping times selections.

Remark 3. The value of firm i's project at any given date t ∈ [0, T ), if firm j has abandoned its project, is given as:

ωiN (t ) = max {Ce−i (T − t ) −

∫t

T

vi e−i (s − t ) ds, 0}

(6)

The first term in Eq. (6) is the present value of the entire flow of cash flows that can be got by firm i as a monopolist in the market during [T , ∞) given that it does not abandon its project before time T. The second term in Eq. (6) is the discounted flow of costs caused by firm i in the remaining growth period. We will suppose that ∀ t ∈ [0, T ]: ωiN (t ) > 0 . 4.2. Duopoly situation

3.3. Filtrations When both firms are investing in their R & D projects, the decision on whether to preserve investing or whether to abandon the project is especially depending on the expected product quality of both firms. The valuation problem in the duopoly condition is solved by going backward in time in the normal dynamic programming method. The best stopping time logic cannot be applied in this condition because of the competitive interactions [4,44]. We so have to resort to getting the objective function as a solution to a dynamic programming problem. At date t we solve for the value relying on that we have already solved the problem for any later date. ω1D ( yt1, yt2 , t )chooses the total value to firm one at date t given that future strategic decisions at any later date s > t are exact Bayesian equilibria. The values at date t when both firms are investing in their R & D projects can be delegated by the following remarks.

Relied on the information framework and the strategic decision variables we can condense the filtrations access to both firms, which is an about important problem in an incomplete information modeling framework. The incomplete information framework creates novel conceptual barriers. A contribution of this paper is defining a way for how to include the incomplete information framework in a Monte Carlo procedure to hold several state variables. The following remark condenses the filtrations. Remark 2. The information accessible to the separate firms can be condensed in the filtrations. The filtration accessible to the informationally advantaged firm one f1, (complete information) is given by:

ft1 = σ {( ys1, ys2)|s ∈ [0, t ]}

Remark 4. Valuating firm one's R & D project by firm one at date t ∈ [0, T ) if firm two has not abandoned is given by:

(4)

∼ D ( y1, y 2 , t ) = E r [e−idt {−v dt + ω D ( y1 + dy1, y 2 + dy 2 , t + dt )}|f 1 ] ω i 1 1 t t t t t t t

whereas the sub-filtration accessible to firm two f2, (incomplete information) is given by:

ft2

=

σ {( ys2 ,

Ns )|s ∈ [0, t ]}

(7) whereas the estimate of firm one's project value if firm two has not abandoned is given by:

(5)

where ft1 = ft2 ∨ σ {( ys1)|s ∈ [0, t ]}. Precisely containing the information from the investment signal of the knowledgeable firm into this signing process becomes of the core in our implementation.

∼ D* ( y 2 , U , t ) = E r [e−idt {−v dt + ω D* ( y 2 + dy 2 , U + dU , t + dt )}|f 2 ] ω t i t t 1 1 t t t t

4. Valuation

ω1D ( yT1 , yT2 , T ) = qT1 C

(8) with the border state given by the value of the project when it is completed:

In combining with evaluating the firm's R & D projects we need to get the best decision strategies. As highlighted, the decision on whether to exercise the options is extremely conditional on the value of the competitor's project. So, we have to evaluate the value of both projects concurrently during the R & D period. The project value has to be found in both the situation where only one firm is left in the R & D period with the situation where both firms are still investing in the R & D period. When the firm has an evaluation of the project value as a monopolist and duopolist, it is able to determine an optimal stopping time gave the available filtration. We begin evaluating the two separate R & D projects in the monopoly case.

(9)

where qT1 is the market share as stated in Remark 1. The border state is * similar for ω1D and ω1D as all information is revealed at time T. The free border states are given by:

ω1D ( yt1, yt2 , t ) ≥ 0

(10)

and *

ω1D ( yt2 , Ut , t ) ≥ 0

(11)

The difference between the firms’ valuation functions is the 6

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information accessible in their filtrations. In the same dynamic programming method, we get the following remark.

two's ideas about its competitor's product [38]. The naive method is clearly performed as we apply the standard LSM algorithm. As the problem essentially becomes Markov we can apply the standard dynamic programming opinion as the result of way dependence is assumed everywhere. In the following section, we will examine the revised LSM algorithm which is applied to get a more precise approximation of the value of the two distinct firms’ projects by involving speculations about the competitor firm.

Remark 5. Valuating the naive firm two's R & D project if firm one has not abandoned is given by:

∼ D* ( y 2 , U , t ) = E r [e−idt {−v dt + ω D* ( y 2 + dy 2 , U + dU + dt )}|f 2 ] ω t i t t 2 2 t t t t (12) whereas evaluating firm two's project by the informed firm one if firm one has not abandoned is given by:

5.3. Sophisticated naive firm

∼ D* ( y1, y 2 , t ) = E r [e−idt {−v dt + ω D* ( y1 + dy1, y 2 + dy 2 , t + dt )}|f 1] ω i 2 2 t t t t t t t

Refining the naive firm two's beliefs must be encapsulated in our model to allow firm two to update its beliefs about the informed firm one's product quality/project price once it notes the investment selections of firm one. Firm one has complete information about the game. Therefore, it learns nothing further about firm two mainly based on its investment choices. The complication is with relevance the naive firm two. There are two sorts of learning outcomes for the naive firm two. The primary form of learning is wherever firm two's logical thinking of firm one's product quality, mainly based on its actions, has no significance of the result of the game. The second form of learning is of generous bigger significance during this setting. This can be the case once each corporation decides to continue investment. The naive firm two will imply a distribution of firm one's product quality relative to its own product quality. We introduce the RLSM technique to include the incomplete information framework in our valuation procedure. The rule is predicated on the principle that exercise choices of the naive firm two should take previous choices under consideration. Thus, the RLSM rule solely uses methods that are in-the-money.

(13) With the border state given by the value of the project when it is completed:

ω2D ( yT1 , yT2 , T ) = qT2 C

(14)

ω2D

* ω2D

and as all information The border condition is similar for is revealed at time T. The free border states are given by:

ω2D ( yt1, yt2 , t ) ≥ 0

(15)

and *

ω2D ( yt2, Ut , t ) ≥ 0

(16)

Solutions to these equations cannot be got analytically and so we apply a discrete time Monte Carlo method to estimate the project values. 4.3. Stopping time game Applying given valuations we can focus the interactions between the two firms. As stated by Fine and Li that commonly, any stochastic dynamic game where a firm's strategy is a single dichotomous decision can at each period be expressed as a stopping time problem [10,41]. At each time t, the active firm notes the information available to them and then resolves whether to stay in the market or leave. The Perfect Bayesian decisions can be stated in the game given in Table 2 below. Having organized the model, the next section expands on implementing the model.

5.4. Recursive Least Squares Monte Carlo Algorithm (RLSM) 5.4.1. Way selection mechanism What it all comes right down to, as mentioned above, is that methods are in-the-money and so to be enclosed within the regression. The naive approach represented above uses the whole set of methods within the simulation since the procedure performs backward mentioned at any given time has not been determined whether or not the choice ought to be exercised in any respect earlier times. Thus, it's not (yet) given whether or not a particular way is in-the-money or not. For the delicate approach, we tend to apply an associate extended algorithmic variant of the LSM rule (RLSM) that permits us to embrace the extra info (besides the state variable) clear to firm two. We’d like to develop a structure such gaining the valuation on yt1 > yt1 is feasible. In

5. Implementation 5.1. Degree of deduction sophistication Including this information framework in our numerical procedure is the subject of this section. In our implementation of the model, we attend a two-step procedure. The first step is a standard implementation of the Longstaff and Schwartz [26] Least Squares Monte Carlo algorithm which is performed in various real options papers, among others in Schwartz [34], Miltersen and Schwartz [27] and Grenadier and Malenko [15]. The second method is an extended recursive version of the Longstaff & Schwartz algorithm. It is used to sum up the information that can be gathered from firms (in)actions in an incomplete information game. We identify this procedure as the advanced naive firm two.

different words, we’d like to condition on the idea that ways of yt1 having stayed among a continuation region up till the time once the choice is to be created. Definition. The continuation tunnel at time t is the region where the informed firm continues investing during the time interval s = [0, t ] and is represented as. Table 2 Normal form representation of the game. Firm 1

5.2. Naive firm In the first application, firm two makes use only of the information it can note at time t, i.e. t and yt2 . Based on the value estimation, firm two specifies whether to continue investing or whether to abandon the market as shown in Table 1. The naive firm two so does not use the information that can be finding from the game in each period. So, the informed firm one's (in)actions are not used to update the naive firm

Firm 2

Invest

Abandon

Invest

∼ D ( y1, y 2 , t ); ω 1 t t ∼ D* ( y 2, U , t ) ω

ω1N (t ); 0

Abandon

0;

0; 0

2

t

ω2N (t )

7

t

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Vt = {yt1 ∈ R| y s1 < ys1}

Table 3 Ways involved in the information set of the two firms in the sophisticated and naive implementation method. The ways are those that will be involved in the RLSM regression.

(17)

5.4.2. Matching ways In Fig. 1 two different way understanding of the informed firm one's product quality and the free boundary are sketched. Once applying the LSM rule we forbid our attention to methods that have stayed among the continuation region up till the time the choice is taken. This means the similar way realization one in every of the naive firm two's product quality y 2 , to way understanding, one y11 of firm one, portrayed in Figure three, ought to be excluded from our regression for selections taken on the far side the 11th time period as way understanding one leaves the continuation region. Within the Monte Carlo procedure j = {1, ... ,M} way, sets {y1j , yj2} are simulated.

Firm 1

Firm 2

Naive

( y1j , yj2)

( yj2)

j = {1, ...,M}

j = {1, ... ,M}

Sophisticated

( y1j , yj2)

( yj2)

j = {1, ...,M}

j ∈ {l{jτ ≤ s} = 1} l

5.4.4. Set of ways The LSM rule is recursively applied to include information from the unfinished info game within the naive firm two's information set. This is often worn out an order to form its potential to return the investment/ abandonment choices of the naive firm two with several precise beliefs about the wise to firm one's product quality yt1. At any given time t, solely those ways in which wherever firm one has invested with altogether periods from time zero up to time t those that have remained within the continuation region. These ways are inthe-money and therefore similar yj2 ways are therefore to be enclosed within the regression. The continuation region at a time t , Vt is outlined as a continuation set in R+. We show the set of the way that has remained within the continuation region at time t by Wt = {( y1j , yj2)|yj1 ∈ Vt}. Within iterating the LSM rule we base solely the regression on this set of ways. The essence of the consideration is to see what ways that ought to be enclosed in Wt . Because the rule is applied recursively we show the set of ways within the k’th iteration by Wtk , k = {1, 2, ... ,K}.

For selections before the 11th time period, each relating yj2 ways are to be employed in the regression, as we have a tendency to use all ways that are in-the-money. At that point in time, none of the y1 ways have left the continuation area. The above discussion about that ways are to be used are summarized in Table 3. The principle of the RLSM rule is to provide an approximate Markov structure by solely involving the set of ways that has remained within the continuation region throughout the game. Within the following section we tend to elaborate on our technique for determining these thresholds [40,42,43]. 5.4.3. Recursive nature To embrace the equilibrium beliefs of the corporations we have a tendency to define an extended LSM rule that is applied recursively. The goal is to work out the triggering boundary of yt1 stemming from the dynamic incomplete information game. The order of the rule is as follows:

5.4.5. Regression As the naive firm two begins including other exact ideas about its informed competitor, it becomes aware that confident low realizations of the informed firm's product quality cannot have occurred at confident times throughout the game. This suggests the naive firm's expectation of the naive firm's product quality will increase because distributing attainable results is shortened from below. Ceteris paribus, this results in the naive firm abandoning at a better frequency. Therefore the advised firm abandons less often compared to things once it competes with a naive competitor. Our iteration procedure for showing the exercise choices follows in two steps. First, we base our regression on method understandings, π ∈ Wtk , wherever abandonment has not occurred from time zero up to the time wherever the investment/abandonment decision is created, as it is merely these ways in which in-the-money. We decline the discounted values of ωiD (Wtk ; t ) onto the premise functions of the governing state variables, L, to get the continuation price to base our strategic choice exercise incision as mentioned in Section 3:

1. At first, formula is dead within the commonplace LSM fashion. The primary time the LSM formula is dead, a range of that methods area unit inside the boundary isn’t potential because it remains to be determined at this stage. 2. The formula is applied iteratively (K times) whenever using the updated choices and trigger threshold to base the regression on a replacement set of methods. Once every iteration an updated candidate for the equilibrium methods (and exercise threshold) is getting. The iteration procedure for the way to update the boundary is explained below.

N *

ω2D (Wtk ; t ) =

∑ ah L 2,h (Wtk ) h =0

(18)

Selecting premise functions is the set of polynomials up to the fourth degree and the cross products for the noticeable state variables L2 for firm two. As the two firms differ on their informedness the set of premise functions in L are not similar for the two firms. In the second step we use the regression coefficients to specify whether to continue investing or abandon the investment. As the abandonment decisions in one run for the informed firm one might need to be revisited for the following run, we use the whole set of ways of resolving the continuing value of the two firms. The regression coefficients, βˆh , from Eq. (18) that were relied on Wtk to reflect the incomplete information framework, are used to specify the suitable values by:

Fig. 1. Continuation and stopping region separated by the abandonment threshold. Alongside the free boundary, two-way realizations of the product quality of the informed firm are depicted with one of the ways leaving the continuation region and the other way staying within it throughout the time interval.

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ωˆ 2D (Wt0; t ) =

∑ βˆh L 2,h (Wt0 ) h =0

6.1. Parameters selection (19)

Our selection of parameters shows the condition where it is always useful to be a monopolist. Table 4 outlines the set of parameters. Our emphasis is not on regulating unlimited project values that can be nearly confirmed. Rather the emphasis is on understanding the relative value the strategic options bring to the table.

The procedure is repeated for each time step for one specific iteration. The entire procedure is then repeated K times, till convergence is got and the incomplete information structure is included.

6.2. Results

5.4.6. Exercise border As the algorithm is often appealed the exercise border moves as the decisions of the firm's change. This relies on incorporating the incomplete information framework. Firm two's supposition of the firm one's exercise border Δsk is explained as the noticeable actions of firm one where k depicts the k’th time the LSM algorithm has been run:

Δsk ({ys2 , Usk , s}|s ∈ [0, t ])

We choose the values from our simulation procedure by the different implementation methods in Table 5. We find the option to abandon adds value for both firms and the skill in the thinking procedure presents the naive firm with a value raise. For the base case set of parameters, it is not useful for the firms to begin their R & D projects if they depend on the standard NPV method. Although, by involving the value of the strategic flexibility to leave the market, it gets useful to manage the investment. This is right for the incomplete information besides the complete information case which we only leave in as a benchmark. As the firms have symmetric technologies accessible, their simple NPV and symmetric complete information values are similar. In the following, we consider the results given above to find different features of the strategic investment game.

(20)

As the border is updated by iterating the algorithm, the best investment decisions change. The sign function Usk is so changed, which potentially changes the shape and level of Δk . In Fig. 2 the condition where the border moves fall is shown.

5.4.7. Convergence As we use a recursive variation of the LSM algorithm to hold the incomplete information framework, we depend on an estimation of the project values. We need some procedure to influence an enough level of convergence in our model. It appears difficult to state a generalized evidence of convergence in option game models with the incomplete information given the number of state variables of our model. So, we appeal a simple measure of convergence. It is a productive research avenue to build a generalized method to hold these kinds of problems with many absorbing tasks in several areas of economics. The iteration is set to stop when the value of the projects alters less than 0.1% from one iteration to the next.

6.2.1. The value of strategic options Regardless of the implementation method the abandonment option carries important value to both firms. In the base case, the market is competitive and firms will abandon the market if they are behind with their development of the product quality. Given the availability of the abandonment option, both the informational strong and weak firm will begin their project [1,5,6,9]. That is, option values rely on how informed firms are, as we would expect. Our modeling structure permits us to understand how this value comes about and under what circumstances it is high and when it is low.

6. Numerical results 6.2.2. The value of information As the supposed technological rank of the two firms are similar, the

In this section, we give a numerical illustration of the model. The richness of the modeling framework permits a notable number of considerations that could be achieved. We concentrate on distinguishing the distinctions in the option values as a function of the level of experience of the naive firm. Besides, the value gap between the firms caused by the distinct availability of information is explored. In the following, we explain selecting parameters for the base case of our model.

Table 4 Base case parameter values market. Market Market size Product quality of firms Initial value Deviation parameter Spread parameter Other parameters Competition parameter Discount rate Investment cost per year Numerical procedure parameters Number of simulated ways Duration of each time step Length of R & D phase (years)

C

80

y0 d σ

100 0 0.25

α i v

1 5% 14

U Δt T

150.000 0.1 3

Table 5 Values for a base case set of parameters.

Fig. 2. The exercise boundary is shown in the ex-ante case and when it shifts downwards as the naive firm updates its beliefs.

9

Value with option to abandon

Firm 1

Firm 2

Naive firm 2 Sophisticated firm 2 Value with complete information Value with no optionality NPV

12.61 12.33 8.1

5.40 6.28 8.1

−4.371

−4.371

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tendency to have an interest in understanding, however, the worth of the companies and their ways reply to variations in a very variety of the driving parameters. A variety of attention-grabbing findings may be extracted from distressing the key parameters.

only point of difference in the incomplete information case is the information accessible. As the informed firm, one is the informational strong firm it normally has a higher project value than the naive firm two. In the standard NPV setting the extra information of firm, one does not bring any value as it may not strategize on its benefit. Our modeling framework can aid in responding questions on which strategic dominance can be got because of an informational benefit and by that means which assets should be spent in getting such benefits [7,21,22]. When contrasting the values got to the complete information benchmark, it is clear the informed firm one profits and the naive firm two avoid value when moving to the incomplete information setting. This is what we would suppose, as firm one gives an informational benefit and firm two an informational drawback.

6.3.1. Market value As the extent of the underlying market varies, the worth of the firms’ comes respond in keeping with the depictions in Fig. 3. Within the high left, the worth of the two companies is shown for each the naive case (F1, Naive, and F2, Naive) and the sophisticated case (F1, Sophis and F2, Sophis). Also, the change within the NPV is shown to the high right. 6.3.2. Variance To specify to what area the values of the firm's R & D projects are affected by the variability of the product quality we differ the variance parameters σ1 and σ2 in Fig. 4.

6.2.3. The level of sophistication Comparing the two distinct methods of performing the LSM algorithm in the incomplete information case, a few things can be mentioned. Moving from the naive to the sophisticated implementation method the informed firm one's value reduces whereas firm two gets value.

6.3.3. Technology In Figure five we have a tendency to consider concurrent changes to each firms’ technology. Within the left figure we differ the variance parameters. We see the informed firm profits mostly from extended uncertainty about the result of the product development. This can be since its informational benefit. Within the figure on the right, moving the product quality equations is differed (Fig. 5).

6.3. Sensitivity analysis To test the robustness of the base-case results, we stock out a sensitivity analysis with relevance the model parameters. We have a

Fig. 3. Sensitivity of the project value to changes in the underlying market value. The value of both firms’ projects is positively influenced by an expansion in the underlying market. Fairly, the naive firm two benefits the most as the revelation optionality benefit vanishes the higher the market size becomes.

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Fig. 4. Sensitivity to the variance of the product quality. Both firms benefit from their product quality development becoming more variable, as the abandonment option truncates the project value distribution in the lower end.

Fig. 5. Sensitivity to technology changes. Increasing the variability of the technology for both firms concurrently causes a benefit to the informed firm because of its informational benefit and ability to abandon the market in a better fashion. General expected growth in the product quality does not change the game between the players and so does not affect the project values.

ability under which governments and private associations do need to settle on their venture choices. Furthermore, the globalization and consequent rise of some creating nations as imperative financial players on the planet's economy has increased rivalry among nations

7. Conclusion The 2007 financial crisis and resulting monetary stuns everywhere throughout the world expanded fundamentally the levels of vulner11

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[18] Huisman, K. Technology investment: a game theoretic real options approach. Boston: Kluwer Academic Publishers; 2001. [19] Huisman Kuno JM, Kort Peter M. Strategic investment in technological innovations. Eur J Oper Res 2003;144:209–23. [20] Huisman Kuno JM, Kort Peter M. Strategic technology adoption taking into account future technological improvements: a real options approach. Eur J Oper Res 2004;159:705–28. [21] Keser , Claudia Irina Suleymanova, Wey Christian. Technology adoption in markets with network effects: theory and experimental evidence. Inf Econ Policy 2012;24:262–76. [22] Khallaf Ashraf. Information technology investments and nonfinancial measures: a research framework. Account Forum 2012;36:109–21. [23] Kong Jean J, Kwok Yue Kuen. Real options in strategic investment games between two asymmetric firms. Eur J Oper Res 2007;181:967–85. [24] Kramer Thomas, Maimaran Michal, Simonson Itamar. Asymmetric option effects on ease of choice criticism and defense. Organ Behav Hum Decis Process 2012;117:179–91. [25] Lambrecht , Perraudin . Real options and preemption under incomplete information. J Econ Dyn Control 2003;27:619–43. [26] Longstaff , Schwartz . Valuing American options by simulation: a simple leastsquares approach. Rev Financ Stud 2001;14:113–47. [27] Miltersen , Schwartz . R & D investments with competitive interactions. Rev Financ 2004;8:355–401. [28] Morellec , Schürhoff . Corporate investment and financing under asymmetric information. J Financ Econ 2011;99:262–88. [29] Murto , Keppo . A Game Model of Irreversible Investment Under Uncertainty. Int Game Theory Rev 2002;4:127–40. [30] Murto, Pauli, Välimäki, Juuso. Delay and information aggregation in stopping games with private information. J Econ Theory. [31] Pawlina Grzegorz, Kort Peter M. Real options in an asymmetric duopoly: who benefits from your competitive disadvantage?. J Econ Manag Strategy 2006;15:1–35. [32] Paxson Dean, Pinto Helena. Rivalry under price and quantity uncertainty. Rev Financ Econ 2005;14:209–24. [33] Ram Camelia, Montibeller Gilberto. Exploring the impact of evaluating strategic options in a scenario-based multi-criteria framework. Technol Forecast Soc Change 2013;80:657–72. [34] Schwartz . Patents and R & D as real options. Econ Notes 2004;33:23–54. [35] Smets. Exporting versus FDI: the e!ect of uncertainty, irreversibilities and strategic interactions. Yale University; 1991. [36] Smit, Han TJ, Trigeorgis, Lenos. 1997. R & D option strategies. In: University of Chicago Working Paper. [37] Smit, Han TJ and Lenos Trigeorgis. 2004. Quantifying the strategic option value of technology investments. Montreal: 8th Annual International Real Options Theory. [38] Teixeira Bruno OS, Aguirre Luis A. Using uncertain prior knowledge to improve identified nonlinear dynamic models. J Process Control 2011;21:82–91. [39] Weeds . Strategic delay in a real options model of R & D competition. Rev Econ Stud 2002;69:729–47. [40] Xie Li, Yang Huizhong, Ding Feng. Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering. Math Comput Model 2011;54:315–24. [41] Zhang Heng, Yang Ming, Bao Jiye, Gong Pu. Competitive investing equilibrium under a procurement mechanism. Econ Model 2013;31:734–8. [42] Zhang Mingjin, Zhang Shizhi, Iqbal Jibran. Key wavelengths selection from near infrared spectra using Monte Carlo sampling–recursive partial least squares. Chemom Intell Lab Syst 2013;128:17–24. [43] Zhao Wen-Xiao, Zhou Tong. Weighted least squares based recursive parametric identification for the submodels of a PWARX system. Automatica 2012;48:1190–6. [44] Zschocke Mark S, Mantin Benny, Jewkes Elizabeth M. Mature or emerging markets: competitive duopoly investment decisions. Eur J Oper Res 2013;228:612–22. [45] Adkins Roger, Paxson Dean A. Subsidies for renewable energy facilities under uncertainty.. The Manchester School 2016;84:222–50. [46] Aguerrevere Felipe L. Equilibrium investment strategies and output price behavior: A real-options approach.. Review of Financial Studies 2003;16:1239–72. [47] Amador Manuel, Weill Pierre-Olivier. Learning from private and public observations of others’ actions.. Journal of Economic Theory 2012;147:910–40. [48] Scott R. Baker Nicholas Bloom Steven J. Davis Measuring economic policy uncertainty. National Bureau of Economic Research. [49] Bouis, Romain, Kuno JM Huisman, and Peter M Kort. 2005. Strategic real options: three firms. [50] Cabral Luís, Dezső Cristian. Technology adoption with multiple alternative designs and the option to wait. Journal of Economics & Management Strategy 2008;17:413–41. [51] Murray Carlson Adlai Fisher Giammarino Giammarino 2006. SEOs, real options, and risk dynamics: Empirical evidence. working paper, University of British Columbia [52] Casparri, Maria Teresa And Javier Garcia Fronti. 2010. A nanotechnology joint investment framework.pp. 161 in Computational Intelligence in Business and Economics: Proceedings of the MS'10 International Conference, Barcelona, Spain, 15-17 July 2010, vol. 3: World Scientific [53] Chevalier-Roignant, Benoit and Lenos Trigeorgis. 2011. Competitive strategy: Options and games: MIT Press [54] Culík Miroslav. Company valuation under risk and flexibility: discrete models comparison.. International Journal of Risk Assessment and Management 2014;17:268–82.

and multinational organizations. Real options game models are, consequently, all around put to all the more satisfactorily fit present and future financial specialists' needs with respect to new speculation models for new and exceptionally dynamic venture connections. We expect that new and more complex real options game models will touch base in the coming years given the high number of working papers we highlighted in this examination and the high intrigue the real options point still mix up among set up and new scholarly specialists. Those models will fit essentially a more extensive scope of rivalry settings and monetary connections and make, perhaps, better utilization of the capable game theory mathematical tools. The real options game models evaluated in the writing audit some portion of this paper address cutting edge questions in speculation investigation and give new answers for venture issues, contributing, in this manner, to a superior comprehension of the mind-boggling nature of firms’ venture conduct in business sectors where instability and rivalry hold. This paper considers a method for valuing real options in a dynamic incomplete information game with different state variables and a finite horizon. The method includes the application of an altered recursive LSM algorithm (RLSM) to summarize the information from the dynamic incomplete information investment game. We discover that having the naive firm appeal the guessing method in the RLSM algorithm takes necessary value distinctions. This specifies the importance of accurately including guessing methods in incomplete real options models. When compared to the complete information case, we discover the informed firm one profits from proposing the asymmetry of information whereas firm two losses. Also, we get findings under which conditions firms can best strategize on an informational benefit and how much bang for the buck it brings. References [1] Alvarado Matías, Rendón Arturo Yee. Nash equilibrium for collective strategic reasoning. Expert Syst Appl 2012;39:12014–25. [2] Antoniadou Elena, Koulovatianos Christos, Mirman Leonard J. "Strategic exploitation of a common-property resource under uncertainty. J Environ Econ Manag 2013;65:28–39. [3] Azevedo, Alcino, Paxson, Dean. Uncertainty and competition in the adoption of complementary technologies. Hull University Business School, Hull; 2009. [4] Boyer Marcel, Lasserre Pierre, Moreaux Michel. A dynamic duopoly investment game without commitment under uncertain market expansion. Int J Ind Organ 2012;30:663–81. [5] Christiansen Nels. Strategic delegation in a legislative bargaining model with pork and public goods. J Public Econ 2013;97:217–29. [6] Corsano, Gabriela, Guillén-Gosálbez, Gonzalo, Montagna, Jorge M. Computational methods for the simultaneous strategic planning of supply chains and batch chemical manufacturing sites. Comput Chem Eng. [7] Dehlen, Tobias, Zellweger, Thomas, Kammerlander, Nadine, Halter, Frank. The role of information asymmetry in the choice of entrepreneurial exit routes. J Bus Ventur. [8] Dutta , Rustichini . A theory of stopping time games with applications to product innovations and asset sales. Econ Theory 1993;3:743–63. [9] Fernandes Leão José, Relvas Susana, Barbosa-Póvoa Ana Paula. Strategic network design of downstream petroleum supply chains: single versus multi-entity participation. Chem Eng Res Des 2013;91:1557–87. [10] Fine , Li . Equilibrium exit in stochastically declining industries. Games Econ Behav 1989(1):40–59. [11] Georgiou Ion. Messing about in transformations: structured systemic planning for systemic solutions to systemic problems. Eur J Oper Res 2012;223:392–406. [12] Grenadier . The strategic exercise of options: development cascades and overbuilding in real estate markets. J Financ 1996;51:1653–79. [13] Grenadier . Information revelation through option exercise. Rev Financ Stud 1999;12:95–129. [14] Grenadier . Option exercise games: an application to the equilibrium investment strategies of firms. Rev Financ Stud 2002;15:691–721. [15] Grenadier and Malenko . A Bayesian approach to real options: the case of distinguishing between temporary and permanent shocks. J Financ 2010(5):1949–86. [16] Hahn GJ, Kuhn H. Simultaneous investment, operations, and financial planning in supply chains: a value-based optimization approach. Int J Prod Econ 2012;140:559–69. [17] Hsu , Lambrecht . Preemptive patenting Under uncertainty and asymmetric information. Ann Oper Res 2007;151:5–28.

12

Renewable and Sustainable Energy Reviews xx (xxxx) xxxx–xxxx

A. Arasteh

of Financial Economics 2005;14:209–24. [71] Pedro Pimentel Azevedo-Pereira José Gualter Couto 2008.High Speed Rail Transport Valuation and Policy Decisions [72] Rogova, Elena and Andrey Yarygin. 2013. Valuing Innovative 4G (LTE) Technology with Real Options Approach Pp. 1 in ISPIM Conference Proceedings: The International Society for Professional Innovation Management (ISPIM) [73] Savva, Nicos and Stefan Scholtes. 2005. Real options in partnership deals: The perspective of cooperative game theory. in Real Options Conference [74] Shibata Takashi. Strategic entry in a triopoly market of firms with asymmetric cost structures.. European Journal of Operational Research 2016;249:728–39. [75] Siddiqui, Afzal. 2012. Valuing Managerial Flexibility in Technology R & D. in Proceedings of the 16th Annual International Real Options Conference, London: Citeseer [76] Sneed Katherine A, Johnson Daniel KN. Selling ideas: the determinants of patent value in an auction environment.. R & D Management 2009;39:87–94. [77] Suh Jong Hwan. Exploring the effect of structural patent indicators in forward patent citation networks on patent price from firm market value. Technology Analysis & Strategic Management 2015;27:485–502. [78] Suttinon Pongsak, Bhatti Asif Mumtaz, Nasu Seigo. Option games in water infrastructure investment. Journal of Water Resources Planning and Management 2011;138:268–76. [79] Tallau Linda J, Gupta Manish, Sharman Raj. Information security investment decisions: evaluating the Balanced Scorecard method. International Journal of Business Information Systems 2009;5:34–57. [80] Thijssen Jacco JJ, Huisman Kuno JM, Kort Peter M. Symmetric equilibrium strategies in game theoretic real option models. Journal of Mathematical Economics 2012;48:219–25. [81] John Weyant Tao Yao Strategic R & D investment under uncertainty in information technology: Tacit collusion and information time lag. in Real Options Conference. 2005 [82] Ming-Cheng Wu, Chun-Yao Tseng. Valuation of patent–a real options perspective.. Applied Economics Letters 2006;13:313–8. [83] Wu Ming-Cheng. Antecedents of patent value using exchange option models: Evidence from a panel data analysis. Journal of Business Research 2011;64:81–6. [84] Wu Liang-Chuan, Li Shu-Hsing, Ong Chorng-Shyong, Pan Chungteh. Options in technology investment games: The real world TFT-LCD industry case.. Technological Forecasting and Social Change 2012;79:1241–53. [85] Zhu Lei. A simulation based real options approach for the investment evaluation of nuclear power.. Computers & Industrial Engineering 2012;63:585–93.

[55] Décamp Jean-Paul, Mariotti Thomas. Investment timing and learning externality. Journal of Economic Theory 2004;18(5). [56] Dixit, Avinash K and Robert S Pindyck. 1994. Investment under uncertainty: Princeton university press. [57] Ernst Holger, Legler Sebastian, Lichtenthaler Ulrich. Determinants of patent value: Insights from a simulation analysis. Technological Forecasting and Social Change 2010;77:1–19. [58] Feil Jan-Henning, Musshoff Oliver. Modelling investment and disinvestment decisions under competition, uncertainty and different market interventions. Economic Modelling 2013;35:443–52. [59] Foster Lucia, Haltiwanger John, Syverson Chad. The slow growth of new plants: Learning about demand?. Economica 2016;83:91–129. [60] Grullon Gustavo, Lyandres Evgeny, Zhdanov Alexei. Real options, volatility, and stock returns. The Journal of Finance 2012;67:1499–537. [61] Karatzas, Ioannis and Steven E Shreve. 1998. Methods of mathematical finance, vol. 39: Springer Science & Business Media [62] Kauffman Robert J, Li Xiaotong. Technology competition and optimal investment timing: a real options perspective. IEEE Transactions on Engineering Management 2005;52:15–29. [63] Kellogg Ryan. The effect of uncertainty on investment: evidence from Texas oil drilling. The American Economic Review 2014;104:1698–734. [64] Lee Shun-Chung. Using real option analysis for highly uncertain technology investments: The case of wind energy technology. Renewable and Sustainable Energy Reviews 2011;15:4443–50. [65] Lombardi Rosa, Manfredi Simone, Nappo Fabio, Russo Giuseppe. Economic valuation of structural capital through static and dynamic approaches: first evidence. Journal for International Business and Entrepreneurship Development 2016;9:135–51. [66] Robin Mason Helen Weeds The timing of acquisitions. The timing of acquisitions. University of Southampton and University of Essex, January. [67] Yongma Moon Tao Yao 2008. Whimsical or Coherent Offers in Negotiation under Incomplete Information: A Real Option Approach." Pp. 1874 in IIE Annual Conference. Proceedings: Institute of Industrial Engineers-Publisher [68] Odening Martin, Musshoff Oliver, Hirschauer Norbert, Balmann Alfons. Investment under uncertainty—Does competition matter?. Journal of Economic Dynamics and Control 2007;31:994–1014. [69] Park Hyun Woo, Kang Jai. The internal attributes of technology as determinants of economic valuation of technology. International Journal of Technology Management 2015;69:166–86. [70] Paxson Dean, Pinto Helena. Rivalry under price and quantity uncertainty.. Review

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