A Coopetitive Game Model for Asymmetric R&D ...

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metric R&D alliances (alliances between young small firms and large Multinational Enter- prises firms ... and cooperation in business networks in the spirit of game theory.”). ..... APPS | Applied Sciences, Balkan Society of Geometers, 14: 1-14.
A Coopetitive Game Model for Asymmetric R&D Alliances within a generalized “Reverse Deal” Daniela Baglieri University of Messina, Via dei Verdi, 98122 Messina (Italy) E-mail: [email protected]

David Carfì University of California Riverside, 1200 University Ave (USA) University of Messina, Via dei Verdi, 98122 Messina (Italy) E-mail: [email protected]

Giovanni Battista Dagnino University of Catania Corso Italia, 55 95129 Catania (Italy) E-mail: [email protected]

Abstract The core argument in this paper is a coopetitive game model for the description of asymmetric R&D alliances (alliances between young small firms and large Multinational Enterprises firms for knowledge exploration and exploitation). Our model requires the adoption of a coopetitive framework, which considers both collaboration and competition, in the general quantitative setting constructed and conceived by David Carfi. We draw upon the literature on asymmetric R&D collaboration and coopetition to propose a new special mathematical model of coopetitive game, which is particularly suitable for exploring asymmetric R&D alliances. We model a specific case: the R&D strategies a big player (Large Firm, LF) has decided to adopt in an horizontal alliance with a smaller firm (Small Firm, SF). We assume that, to achieve its goals, LF, our first player, is forming horizontal alliances (that is, alliances between producers of the same good), instead of acquiring new scientific knowledge, with a small (but research-oriented and highly efficient) firm, our second player. The SF firm (II player) is engaged in the discovery, development, manufacture and marketing of highly technological good. To cope with global competitive pressures, LF is actively engaged in the so-called "reverse deal" (McKinsey, 2011), which consists in allying in triad with another mid-size or small-size firm (our SF) and with a venture capitalist (let us call VC or Cap), our fourth player (which we won’t consider one of our principal players, because of its elementary actions and simple payoffs) in order to spin out a new high-tech development program into a new SF joint venture firm (we call RJV, research joint venture), our third player.

Keywords: asymmetric alliances, R&D, normal-form games, coopetitive games, solutions of a game.

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1.

Introduction

Attention to coopetition has increased with the practical significance of collaboration among competitors (Brandenburger & Nalebuff, 1996; Sakakibara, M. 1997; Padula & Dagnino, 2007) and competition among “friends” (i.e. university-industry relationships, Carayannis & Alexander, 1999; Baglieri 2009). Despite the increased importance of coopetition, limited research has examined factors that may drive coopetition, particularly in high technology industries where R&D alliances seem to be growing rapidly. A notable trend is the rapid growth of R&D alliances between large, well-established firms and small, growing firms. We term these alliances asymmetric R&D alliances. These inter-organizational arrangements rise a number of open questions related to the disparately partners bargaining power which affect, among others, alliances outcomes. Are asymmetric R&D alliances a win-win or win-lose partnerships? What are the main firms’ strategies partners may deploy to “enlarge the pie” and create more value? The answers to these questions are important for both larger and smaller firms to better select their partners, the scope and type of alliance, and the resources to be allocated for new product development. This paper aims at developing a mathematical model for the coopetitive games, which is particularly suitable for exploring asymmetric R&D alliances. Despite the classic form games involving two players that can choose the respective strategies - cooperatively or notcooperatively -, we propose that players have a common strategy set C, containing other strategies (possibly of different type with respect to the previous one) that must be chosen cooperatively. Consequently, for any coopetitive game, we necessarily build up a family of classic normal-form games which determines univocally the given coopetitive game. Thus, the study of a coopetitive game is reduced to the study of a family of normal-form games in its completeness. In this paper, we suggest how this latter study can be conduct and what are the concepts of solution of a coopetitive game corresponding to the main firms’ strategies, potentially deployed in asymmetric R&D settings.

2.

Literature review

In this paper we shall use a wide range of scientific literature, especially from coopetitive studies. In particular, we shall present and use fundamental works in coopetition, in Game Theory and applications, in a perspective feasible to represent coopetitive interactions; we shall concentrate on papers regarding the coopetitive game model introduced by D. Carfì and on the asymmetric R&D alliances, because we need to construct models of coopetition in asymmetric R&D alliances using Game Theory. In this section we shall present such complex and wide-range scientific literature. 2.1. Literature on Coopetition Althought game-theoretical models are not sistematically applied in coopetition studies, Game Theory has proved to be extremely useful for coopetition analysis. For example, Brandenburger and Nalebuff (1996, pp. 5–8) argued that game theory is useful for understanding coopetitive situations (Stein (2010: p.257) mentioned that Brandenburger and Nalebuff (1996) “explain ‘co-opetition’ as an approach that intends to explain competition and cooperation in business networks in the spirit of game theory.”). Lado et al. (1997, p. 113) argued that game theory can explain behavior in the context of interfirm relationships.

Clarke-Hill et al. (2003) and Gnyawali and Park (2009) explained game theory approach in coopetition situation (however, Clarke-Hill et al. (2003) used both cooperation and competition instead of coopetition). Okura (2012, 2009, 2008, 2007), Ngo and Okura (2008) and Ohkita and Okura (2014) explained the advantages of using game theory in coopetition studies. Pesamaa and Eriksson (2010) explained the usefulness of game theory for investigating actors’ interdependent decisions. Rodrigues et al. (2011) applied game theory for investigating strategic coopetition. Ghobadi and D’Ambra (2011) summarized the characteristics, strengths and limitations to use Game Theory in coopetition studies. Bengtsson and Kock (2014) pointed out that game theory is one of the research perspectives in coopetition studies. D. Carfi (2012a, 2010a) has defined and applied a new analytical model of coopetitive game, after that he and various collaborators have developed the applicative aspects of the new model in several directions, such as Management, Finance, Microeconomics, Macroeconomic, Green Economy, Financial Markets, Industrial Organization, Project Financing and so on – see, for instance, Carfì and Fici (2012), Carfì and Lanzafame (2013), Carfì, Magaudda and Schilirò (2010), Carfi and Musolino (2015a, 2015b, 2014a, 2014b, 2013a, 2013b, 2013c, 2012a, 2012b, 2012c, 2012d, 2012e, 2011a, 2011b), Carfì, Patanè and Pellegrino (2011), Carfì and Perrone (2013, 2012a, 2012b, 2011a, 2011b, 2011c), Carfì and Pintaudi (2012), Carfi and Schilirò (2014a, 2014b, 2013, 2012a,2012b, 2012c, 2012d, 2011a, 2011b, 2011c), Carfì, Musolino, Ricciardello and Schilirò (2012), Carfì, Musolino, Schilirò and Strati (2013), Carfi and Trunfio (2011), Carfì and Okura (2014). Further, secondary but useful, material – which we have analyzed for our general setting – can be found in Asch (1952), Biondi and Giannoccolo (2012), Musolino (2012), Porter (1985), Shy (1995), Stiles (2001) and Sun, Zhang and Lin (2008).

2.2. Literature on coopetitive games Here, we present an original recent definition of a coopetitive game, in normal form, given by David Carfì. The model can suggest useful solutions to a specific coopetitive problem, defined by the set of strategy profiles at the disposal of the two players and by a set of possible convenient ex ante agreements on the common strategy set. This analytical framework enables us to widen the set of possible solutions from purely competitive solutions to coopetitive ones and, moreover, incorporates a solution designed “to share the pie fairly” in a win–win scenario. At the same time, it permits examination of the range of possible economic outcomes along a coopetitive dynamic path. We also propose a rational way of limiting the space within which the coopetitive solutions apply. The basic original definition we propose and apply for coopetitive games is that introduced by Carfi and Schilirò (2014a, 2014b, 2013, 2012a, 2012b, 2012c, 2012d, 2012e, 2011a, 2011b, 2011c, 2011d) and Carfì (2012a, 2010a, 2009a, 2009b, 2009c, 2009d, 2009f, 2008a). The method we use to study the payoff space of a normal-form game is due to Carfi (2012b, 2010b, 2010c, 2009e, 2008d, 2008e, 2008f, 2008g, 2007a, 2006a, 2006b, 2005a, 2005b, 2005c, 1999), Carfi and Musolino (2015a, 2015b, 2014a, 2014b, 2013a, 2013b, 2013c, 2012a, 2012b, 2012c, 2012d, 2012e, 2011a, 2011b), and Carfì and Schilirò (2014a, 2014b, 2013, 2012a, 2012b, 2012c, 2012d, 2012e, 2011a, 2011b, 2011c, 2011d). Other important applications, of the complete examination methodology, are introduced by D. Carfì and co-authors in Agreste, Carfì, and Ricciardello (2012), Arthanari, Carfì, and Musolino (2015), Baglieri, Carfì, and Dagnino (2010, 2012a, 2012b, 2015),Carfì and Fici (2012), Carfì, Gambarelli, and Uristani (2013), Carfì and Lanzafame (2013), Carfì, Patanè, and Pellegrino (2011). A complete treatment of a normal-form game is presented and applied by Carfì (2015a, 2015b, 2012a, 2011a, 2011b, 2011c, 2011d, 2010a, 2009a, 2009b, 2009c, 2009d, 2009f, 2008a,2008b,2008c,2007b, 2007c, 2006c, 2006d), Carfi and Musolino (2015a, 2015b, 2014a, 2014b, 2013a, 2013b, 2013c, 2012a, 2012b, 2012c, 2012d, 2012e, 3

2011a, 2011b), Carfi and Perrone (2013, 2012a, 2012b, 2011a, 2011b, 2011c), Carfi and Ricciardello (2013a, 2013b, 2012a, 2012b, 2012c, 2012d, 2012e, 2012f, 2012g, 2012h, 2012i, 2012l, 2011a, 2011b, 2010, 2009) and Carfi and Schilirò (2014a, 2014b, 2013, 2012a, 2012b, 2012c, 2012d, 2012e, 2011a, 2011b, 2011c, 2011d). Carfi (2008a) proposes a general definition and explains the basic properties of Pareto boundary, which constitutes a fundamental element of the complete analysis of a normal-form game and of a coopetitive interaction. The possible dynamical evolution models of our game theory framework could be developed by using the methodologies and tools introduced and exploited in Carfi (2011c, 2009c, 2008b, 2008c, 2007b, 2007c, 2006c, 2006d, 2004a, 2004b, 2004c, 2004d), Carfi and Caristi (2008) and Carfi and Cvetko-Vah (2011).

2.3. Asymmetric R&D alliances: literature review We see a range of studies that focus on the collaboration among competitors (Brandenburger and Nalebuff, 1996; Sakakibara, M. 1997, Padula and Dagnino, 2007).The literature focuses on coopetitive tension in vertical alliances (Walley,2007), considering to integrate complementary resources within the value net (Nalebuff and Brandeburger, 1996; Wilkinson and Young, 2002; Laine, 2002), to increase learning opportunities; to improve firm's R&D capabilities and suggest to adopt mechanism to improve the innovation process (Hagel and Brown, 2005). In particular, the majority of the existing game theory literature in R&D strategy setting concentrates on the inter-organizational level and uses noncoperative games which help to determine optimal R&D expenditure, optimal timing of entry for new products into market, but do not provide any information about how much power the different player have in a given setting. This explains why the cooperative games are becoming much more used in R&D settings although they use the less-familiar characteristic-function language (Brandenburger and Stuart, 2007). In other words, cooperative games represent a tool to better understand how competition unfolds among players.

3.

Asymmetric R&D Alliances: a Coopetitive perspective

Several researchers have clearly indicated the importance of co-opetition for technological innovation. Jorde and Teece (1990) suggested that the changing dynamics of technologies and markets have led to the emergence of the simultaneous innovation model. For firms to pursue the simultaneous innovation model and succeed in innovation, they should look for collaboration opportunities that allow them to bring multiple technologies and diverse and complementary assets together. Von Hippel (1987) argued that collaboration for knowledge sharing among competitors occurs when technological progress may be faster with collective efforts rather than through individual efforts and when combined knowledge offers better advantages than solo knowledge. More recent research clearly shows the importance of co-opetition in technological innovation. Quintana-Garcia and Benavides-Velasco (2004) empirically show that collaboration with direct competitors is important not only to acquire new technological knowledge and skills from the partner, but also to create and access other capabilities based on intensive exploitation of the existing ones. Similarly, Carayannis and Alexander (1999) argue that co-opetition is particularly important in knowledge intensive, highly complex, and dynamic environments.

By extending these ideas further, we focus on asymmetric R&D alliances, widely recognized as critical to technological innovation. These alliances are prominent since they involve large, well-established firms and small, growing firms, that are endowed with intangible resources and unique technological capabilities in niche areas (Chen and Hambrick 1995; Stuart 2000). Gomes-Casseres (1997) notes that, although larger firms have been traditionally dominant players in the information technology and pharmaceutical industries, the advent of new technologies such as microelectronics and biotechnology presents unique opportunities for smaller entrepreneurial firms to pursue targeted innovation. Research on entrepreneurship (Alvarez & Barney, 2001; Gulati & Higgings, 2003) suggests that ties with larger firms are vital to the growth of smaller firms for at least two reasons. Firstly, smaller firms, looking for funds, use the alliances with larger firms to get access to the key tangible resources for commercializing their innovative efforts. Secondly, partnerships with prominent partners, such as larger established firms, buffers smaller firms from their liability of smallness, enhances their chances of survival, and boosts sales growth (Baum, Silverman, and Calabrese 2000; Stuart 2000). In this vein, cooperation with larger, and established firms, may be seen beneficial for enlarging the pie and putting into action value creation strategies. On the other hand, some competitive pressure can arise between partners, in order to getting the “right” balance of control on innovation (i.e. patents ownership; exclusive control rights on future innovative efforts). These pressures call for a more scholarly attention on rent capture strategies and how coopetitive strategies emerge, balancing “partially convergent interests” between partners (Padula and Dagnino 2007: 32). In this setting, exploring managerial issues concerning rent appropriation is beneficial for young and small firms’ survival. In this respect, we propose to integrate and broaden the theoretical lens of R&D alliances taking into consideration a recent set of papers which rejuvenate the coopetative approach (see special issue “Coopetition Strategy”, International Studies of Management and Organization, vol.37:2, 2007). Following the seminal work of Nalebuff and Brandenburger (1996), some scholars have analysed how firms cooperate in the upstream activities and compete in the downstream activities (Walley, 2007), in order to pursuit several goals:  to integrate complementary resources within the value net (Nalebuff and Brandenburger, 1996; Wilkinson and Young, 2002; Laine, 2002);  to increase the heterogeneity of the resources needed to successfully compete in convergent businesses;  to enhance learning opportunities;  to boost firm’s R&D capabilities;  to speed up innovation (Hagel III and Brown, 2005). This broad range of goals explains why coopetition is common in several industries. Sakakibara (1993) describes R&D cooperation among competing Japanese semiconductor firms. Hagedoorn, Cyrayannis, and Alexander (2001) document an emerging collaboration between IBM and Apple that resulted in an increasing number of alliances between the two for joint technological development. Albert (1999) points to the coopetitive relationship between Dell Computers and IBM. Coopetition is common in mature industries too. Recent works examine coopetition in soft drink and beverage industry, in carbonated soft drink industry, and in tuna industry. Therefore, the idea to “working with the enemy” is not new, although it has been a “an under researched theme”. What it is new in this paper is the attempt to apply coopetition in a asymmetric R&D alliances setting, theme which has been more investigated in industrial organizational literature that largely explores how increases in cooperative activity in the 5

markets for technology (i.e licensing) affect levels of competitive activity in “product markets”. In this paper, we adopt another option which addresses the question how firms manage simultaneously patterns of cooperation and competition in their R&D relationships (firm level) and, thus, how firms “enlarge the pie” (cooperation) and “share the pie” (competition). 4.

The economic model

We model a specific case: the R&D strategies a big player (Large Firm, LF) has decided to adopt in an horizontal alliance with a smaller firm (Small Firm, SF) – here we follow the lane of thoughts expressed below by our original and quite general assumptions.

4.1 Assumptions Assumption 1. We assume that, to achieve its goals, LF, our first player, is forming horizontal alliances (that is, alliances between producers of the same good), instead of acquiring new scientific knowledge, with a small (but research-oriented and highly efficient) firm, our second player. Assumption 2. The SF firm (II player) is engaged in the discovery, development, manufacture and marketing of highly technological good. Assumption 3. To cope with global competitive pressures, LF is actively engaged in the so-called "reverse deal" (McKinsey, 2011), which consists in allying in triad with another mid-size or small-size firm (our SF) and with a venture capitalist (let us call VC or Cap), our fourth player (which we won’t consider one of our principal players, because of its elementary actions and simple payoffs) in order to spin out a new high-tech development program into a new SF joint venture firm (we call RJV, research joint venture), our third player. 4.2 Semi-quantitative description of the payoff functions. After the exposed R&D alliance, the benefits for the various interaction-participants can be summarized as follows: -

LF buys a certain amount x of the new highly technological good from RJV and gains from the selling of the product x on the Market; SF produces a new highly technological good and gains by selling a quantity z to RJV; SF firm cannot, by contract, sell in the Market for a certain amount of time; RJV gains by selling x of the SF production to LF and z – x of the highly technological good on the Market. Cap receives from LF (at time 2) the capitalization C’ of its initial investment C (money given to LF at time 1); Market gains from the sunk costs C of RJV, from the research-costs y of SF and it gains an ‘money equivalent’ value bz, by improving the quality of life of its citizens.

4.3 Analysis the contract The contract imposes the following assumptions. Assumption 4. LF purchases the highly technological good from RJV, and shares profits of time 2 with SF, according to a percentage pair (q, 1 - q). This percentage pair will be determined by using the game itself, not a priori. Assumption 5. SF firm cannot, by contract, sell in the Market for a certain amount of time. Assumption 6. Sharing pair (q, 1 - q) will be deduced by a feasible Kalai-Smorodinsky bargaining solution in a coopetitive transferable utility context. 5.

The formal construction of the game model

Axiom 1. We consider a five-player game. The players are: 1. LF (or LF, large firm); 2. HT firm (or SF, small firm); 3. the third player is the RJV (Research Joint Venture) constituted by LF and HT; 4. VC (capitalist) 5. Market We distinguish between principal players and side players, principal players are LF and SF: side players are RJV, VC and the Market (civil society).

5.1 Strategies Axiom 2 (strategies of the first player). Any positive real number x represents the production that LF decides to buy (x in a certain compact interval [a’, b’]) from the Research Joint Venture founded by LF and SF. Axiom 3 (strategies of the second player). Any positive real number y represents investments for research and service production (y in a certain compact interval [c’, d’]) employed by SF, we assume that an investment in research of at least c’ > 0 is needed for creating the new highly technological good. Axiom 4 (strategies of the third player, i.e., coopetitive strategies of the first two players). Any positive real z represents production of the RJV (z in a certain compact interval [0,M]), decided together by LF and SF. Axiom 5 (coopetitive strategies of the first two players). We shall use the strategy z of the third player as a cooperative strategy of the couple (LF, SF) in a coopetitive game. Axiom 6 (strategies of the fourth player). The number C represents the loan that VC de7

cides to offer to the LF (the strategy set of VC is reduced to the singleton {C}). Axiom 7 (strategies of the fifth player). Any real z represents the production of the RJV (z in [0, M]), that the Market decides to buy: we assume, by classic microeconomic assumption, that this z coincides with production of the RJV (z in [0, M]), decided together by LF and SF.

5.2 Payoffs Axiom 8. The payoff function of LF is defined by f1(x, y, z) = (p - p') x - C' - ay, where: 1. px is the profit from selling x at price p in the Market; 2. p’x is the cost to buy x from RJV at price p’; 3. C’ are the sunk costs faced by LF itself; 4. ay is the extra-payment to SF for research and development y (a > 1).

Axiom 9. The payoff function of SF is defined by f2(x,y,z) = p''z + ay - y - f, where 1. p''z is the payment received from RJV selling the product z, 2. ay is extra-payment for research y, a >1, received from LF, y is the investment in research. 3. f is the fixed cost to produce the highly technological good, this cost is not afforded by RJV, which pay only the variable cost. Axiom 10. The payoff function of the RJV is defined by f3 (x,y,z) = p'x + p(z - x) - cz - p''z, where : 1. p’x is the profit from selling x at price p' to LF; 2. p(z – x) is the profit from selling z - x at price p > p' on the Market; 3. cz is the variable cost for the production of z, faced by SF and paid by RJV; 4. p’’z is the payment paid to SF to buy the product z, with p > c + p''.

Axiom 11. The payoff function of the Market is defined by f3(x,y,z) = - p(z - x) + cz + C – px +y + kz, where : 1. px is the cost from buying x at price p from LF; 2. p(z – x) is the cost from buying (z – x) at price p from RJV; 3. cz is the indirect gain from the production of z, faced by SF and paid by RJV; 4. y is the indirect gain coming from the research activity of SF; 5. C is the indirect gain coming from the foundation of RJV; 6. kz is the social indirect gain (beneficial effects) coming from the use of the quantity z of the new high-tech good.

5.3 Economic interpretation Axiom 12. In this model we have four formal players interacting together and one player, the venture capitalist VC, acting only at the beginning of the interaction (time 0) and at its end (time 1). Axiom 13. We assume that: - our first player is a Large Firm (LF) (in our study case, it is the LF) that, in order to develop new products, decides to form an horizontal alliance with a Small Firm (SF) (in our case, it is the SF), our second player, operating in the same sector. - first and second player, in order to cooperate, constitute a Research Joint Venture (RJV), our third player. The RJV is financially supported by the VC, our fourth player, at the level of initial costs, and it supports SF, at the level of variable costs. The second player produces a quantity z (decided together by I and II player) of high-tech good and sells it to the RJV, at price p’’ (fixed by contract). - when the research of the RJV of the good (in our case the high-tech good) has concluded, then the production of the high-tech good is conducted by second player and the Large Firm decides the amount x of production to buy from the RJV. - The revenue of LF is given by the difference between the sale price p’x and the purchase price px, of the quantity x of production bought by the RJV at price p’. - To begin the RJV research, the VC offers a financial support K (million dollars) to RJV, via LF, to cover the initial sunk costs. - After the cooperative production of II player is started. The first player pays the capitalized sunk costs K’ > K to the RJV, in order to compensate the VC and to conclude the participation of the VC in the game. 9

- Moreover, at the beginning of the RJV, first player funds directly the researches of the small firm SF: by a sum ay, for any investment y in research of the second player, with a > 1. - When, cooperatively, player I and II has decided the quantity z that the II player has to produce and sell to RJV. Revenues for the second player are equal to p’’z, where p’’ is the unit price (in dollars) at which SF sells to RJV, and z is the total quantity of production (in million of pieces). The cost is represented by the investment for research and is equal to y. - For the Research Joint Venture revenue is calculated as p’x + p(z – x) + (K + cz) where p’x is the profit from selling x (in million of pieces) at price p’ to LF and p(z – x) represents the profit from selling (z – x) at price p > p’ on the market. - Lastly, we assume that the variable cost cz for the production of z (by the second player) is paid by the RJV and so the costs for the RJV are equal to: (K + cz) + p’’z, where: cz is the cost of z (at the end of the day, paid to RJV by the II player), in dollars; p’’z is the payment due to the small firm for the product z; K is a positive constant, it should be added, in the payoff of RJV, when it represents the sunk costs are paid by the first player, but they are also employed by the RJV to start the business. Solution. We propose a model in which the sharing-pair (q, 1 – q) is determined by a KalaiSmorodinsky coopetitive solution.

6.

Recap of the model-recipe

Resuming, we have: 1) x represents production of high-tech good – in million of pieces - the first player has decided to buy from joint venture firm (RJV) in the strategy interval E = [a’, b] (from 0 to 1 million pieces); 2) y represents money – in million of dollars - for research and service production invested by the second player, any y belonging to the strategy interval F = [c’,d’]; 3) z represents total production of high-tech good – in million of pieces - decided by both players I and II (together) of the RJV, with constraint C = [0,M] ; 4) the payoff function of the LF is defined by f1(x,y,z) = (p – p’)x – C’ – ay, for every x in E and y is F; where :

(p – p’)x is the profit from selling x at price p in the market and by buying x at price p’ from RJV; K’ = (1 + i) K is the capitalized sunk cost K, invested by the VC into the foundation of RJV, via the first player LF; - ay is the extra-payment for research, paid to the second player SF by the first one (here we assume a >1); 5) the payoff function of the second player is defined by f2(x, y, z) = p’’z + ay - y - f where : - p’’z is payment (in dollars) received by RJV, for the product z, by first player and Market; - ay is the extra-payment for research y (a >1) received by LF; - f is the fixed cost of the production. 6) the payoff function of the third player is defined by f3(x, y, z) = p’x + p(z – x) – cz – p’’z, where: - p’x is profit from selling x at price p’ to the player 1; - p(z – x) represents profit from selling z – x at price p > p’ in the market; - cz is the production cost of z faced by SF and paid by RJV; - p’’z is the payment received by RJV for the product z, we assume p > c + p’’.

7.

Conclusions

We model a specific case: the R&D strategies a big player (Large Firm, LF) has decided to adopt in an horizontal alliance with a smaller firm (Small Firm, SF) – here we follow the lane of thoughts expressed below by our original and quite general assumptions. We assume that, to achieve its goals, LF, our first player, is forming horizontal alliances (that is, alliances between producers of the same good), instead of acquiring new scientific knowledge, with a small (but research-oriented and highly efficient) firm, our second play11

er. The SF firm (II player) is engaged in the discovery, development, manufacture and marketing of highly technological good. To cope with global competitive pressures, LF is actively engaged in the so-called "reverse deal" (McKinsey, 2011), which consists in allying in triad with another mid-size or small-size firm (our SF) and with a venture capitalist (let us call VC or Cap), our fourth player (which we won’t consider one of our principal players, because of its elementary actions and simple payoffs) in order to spin out a new high-tech development program into a new SF joint venture firm (we call RJV, research joint venture), our third player. At the end of this R&D alliance, the benefits for the three partners can be summarized as follows: -

LF buys a certain amount x of the new highly technological good from RJV and gains from the selling of the product x on the Market; SF firm produces a new highly technological good and gains by selling a quantity z to RJV; SF firm cannot, by contract, sell in the Market for a certain amount of time; RJV gains by selling x of the SF production to LF and z – x of the highly technological good on the Market. Cap receives from LF (at time 2) the capitalization C’ of its initial investment C (money given to LF at time 1); Market gains from the sunk costs C of RJV, from the research-costs y of SF and it gains a value bz by improving the general population quality of life determined by the adoption of the new high-tech good.

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Carfì, D., (1999), Metodi matematici della Fisica, dell’Ingegneria e dell’Economia. Azzeramento. Armando Siciliano Editore. Carfi, D., Caristi, G., (2008), Financial dynamical systems. Differential Geometry - Dynamical Systems, 10: 71-85. http://www.mathem.pub.ro/dgds/v10/D10-CA.pdf. Carfi, D., Caterino, A., Ceppitelli, R., (2015), State preference models and jointly continuous utilities. Researchgate Paper, pp. 1-12. https://dx.doi.org/10.13140/RG.2.1.3689.0966. Carfi, D., Cvetko Vah, K., (2011), Skew lattice structures on the financial events plane. APPS| Applied Sciences, 13: 9–20. Balkan Society of Geometers. http://www.mathem.pub.ro/apps/v13/A13-ca.pdf. Carfi, D., Fici, C., (2012), The government-taxpayer game. Theoretical and Practical Research in Economic Fields, ASERS, 3(1(5), Summer 2012): 13–26. Ed. by L. Ungureanu. http://www.asers.eu/journals/tpref/tpref-past-issues.html. Also available as Researchgate Paper at https://www.researchgate.net/publication/239809951_The_governmenttaxpayer_game. Carfi, D., Gambarelli, G., (2015), Balancing Bilinearly Interfering Elements. Decision Making in Manufacturing and Services, 9(1), 2015. (in print). Carfi, D., Gambarelli, G., and Uristani, A., (2013), Balancing pairs of interfering elements. Zeszyty Naukowe Uniwersytetu Szczeciǹskiego 760 (Finanse, Rynki Finansowe, Ubezpieczenia n.59 (2013)) : 435–442. Available as Researchgate Paper at http://www.researchgate.net/publication/259323035_Balancing_pairs_of_interferin g_elements. Carf , D., Lanzafame, F., (2013), A Quantitative Model of Speculative Attack: Game Complete Analysis and Possible Normative Defenses. Financial Markets: Recent Developments, Emerging Practices and Future Prospects, Nova Science, Chap. 9. Ed. by M. Bahmani-Oskooee and S. Bahmani. https://www.novapublishers.com/catalog/product_info.php?products_id=46483. Also available as Researchgate Paper at https://www.researchgate.net/publication/283010498_A_Quantitative_Model_of_S peculative_Attack_Game_Complete_Analysis_and_Possible_Normative_Defenses. Carfì, D., Magaudda, M., (2009), Complete study of linear infinite games. Proceedings of the International Geometry Center - Prooceding of the International Conference “Geometry in Odessa 2009”, Odessa, May 25-30, 2009, 2(3): 19-30. http://domega.org/category/books-and- papers/. Available as Researchgate Paper at https://www.researchgate.net/publication/283048363_Complete_study_of_linear_i nfinite_games. Carfì, D., Magaudda, M., and Schilirò, D., (2010), Coopetitive Game Solutions for the eurozone economy. Quaderni di Economia ed Analisi del Territorio, Quaderno n. 55/2010, pp. 1–21. Dipartimento DESMaS “V.Pareto” Università degli Studi di Messina, Il Gabbiano. Available as MPRA Paper at http://mpra.ub.unimuenchen.de/26541/1/MPRA_paper_26541.pdf. Carfi, D., Musolino, F., (2015a), A Coopetitive-Dynamical Game Model for Currency Markets Stabilization. AAPP | Physical, Mathematical, and Natural Sciences, 93(1): 1-29, 2015. https://dx.doi.org/10.1478/AAPP.931C1. Carfì, D., Musolino, F., (2015b), Tax Evasion: A Game Countermeasure. AAPP | Physical, Mathematical, and Natural Sciences, 93(1):1-17, 2015. https://dx.doi.org/10.1478/AAPP.931C2. Carf , D., Musolino, F., (2014a), Dynamical Stabilization of Currency Market with Fractal-like Trajectories. Scientific Bulletin of the Politehnica University of Bucharest,

Series A-Applied Mathematics and Physics , 76(4): 115-126, 2014. http://www.scientificbulletin.upb.ro/rev_docs_arhiva/rezc3a_239636.pdf. Carfi, D., Musolino, F., (2014b), Speculative and Hedging Interaction Model in Oil and U.S. Dollar Markets with Financial Transaction Taxes. Economic Modelling, 37: 306-319. https://dx.doi.org/10.1016/j.econmod.2013.11.003. Also available as Researchgate Paper at https://www.researchgate.net/publication/259512278_Speculative_and_hedging_int eraction_model_in_oil_and_U.S._dollar_markets_with_financial_transaction_taxes. Carfi, D., Musolino, F., (2013a), Credit Crunch in the Euro Area: A Coopetitive Multiagent Solution. Multicriteria and Multiagent Decision Making with Applications to Economic and Social Sciences: Studies in Fuzziness and Soft Computing, Springer Verlag, Berlin Heidelberg, 305: 27–48, Ed. by A. G. S. Ventre, A. Maturo, Š. Hoškovà-Mayerovà, and J. Kacprzyk. https://dx.doi.org/10.1007/978-3-642-356353_3. Also available as Researchgate Paper at https://www.researchgate.net/publication/282763897_Credit_Crunch_in_the_Euro_ Area_A_Coopetitive_Multi-agent_Solution. Carfi, D., Musolino, F., (2013b), Game Theory Appication of Monti's Proposal for European Government Bonds Stabilization. APPS | Applied Sciences, Balkan Society of Geometers, 15: 43-70. Ed. by V. Balan. http://www.mathem.pub.ro/apps/v15/A15ca.pdf. Carfi, D., Musolino, F., (2013c), Model of Possible Cooperation in Financial Markets in Presence of Tax on Speculative Transactions. AAPP | Physical, Mathematical, and Natural Sciences, 91(1): 1-26. https://dx.doi.org/10.1478/AAPP.911A3. Carfi, D., Musolino, F., (2012a), A coopetitive approach to financial markets stabilization and risk management. Advances in Computational Intelligence, Part IV. 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9-13, 2012, Proceedings, Part IV, Springer Berlin Heidelberg, 300: 578-592 of Communication in Computer and Information Science. Ed. by S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, and R. Yager. https://dx.doi.org/10.1007/978-3642-31724- 8_62. Also available as Researchgate Paper at https://www.researchgate.net/publication/241765804_A_Coopetitive_Approach_to _Financial_Markets_Stabilization_and_Risk_Management. Carfi, D., Musolino, F., (2012b), Game Theory and Speculation on Government Bonds. Economic Modelling, Elsevier , 29(6): 2417-2426. https://dx.doi.org/10.1016/j.econmod.2012.06.037. Also available as Researchgate Paper at https://www.researchgate.net/publication/257098708_Game_theory_and_speculatio n_on_government_bonds. Carfi, D., Musolino, F., (2012c), Game Theory Models for Derivative Contracts: Financial Markets Stabilization and Credit Crunch, Complete Analysis and Coopetitive Solution. Lambert Academic Publishing. https://www.lappublishing.com/catalog/details//store/gb/book/978-3-659-13050-2/game-theorymodels-for-derivative-contracts. Carfi, D., Musolino, F., (2012d), A game theory model for currency markets stabilization. MPRA Paper 39240, pp. 1-38. University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/39240/.

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Carfi, D., Musolino, F., (2012e), Game theory model for European government bonds market stabilization: a saving-State proposal. MPRA Paper 39742, pp. 1-27. University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/39742/. Carfì, D., Musolino F., (2011a), Fair Redistribution in Financial Markets: a Game Theory Complete Analysis. Journal of Advanced Studies in Finance, ASERS Publishing House, 2(2(4)): 74–100. http://asers.eu/journals/jasf/jasf-past-issues.html. Also available as Researchgate Paper at https://www.researchgate.net/publication/227599658_FAIR_REDISTRIBUTION_I N_FINANCIAL_MARKETS_A_GAME_THEORY_COMPLETE_ANALYSIS. Carfi, D., Musolino, F., (2011b), Game Complete Analysis for Financial Markets Stabilization. Proceedings of the 1st International On-line Conference on Global Trends in Finance, pp. 14–42, ASERS. http://www.asers.eu/asers_files/conferences/GTF/GTF_eProceedings_last.pdf. Carfi, D., Musolino, F., Ricciardello, A., and Schilir , D., (2012), Preface: Introducing PISRS. AAPP | Physical, Mathematical, and Natural Sciences, 90 (SUPPLEMENT N.1, E1 (2012): PISRS Proceedings (Part I)): 1-4. Ed. by D. Carf , F. Musolino, A. Ricciardello, and D. Schilir . https://dx.doi.org/10.1478/AAPP.90S1E1. Carfi, D., Musolino, F., Schilir , D., and Strati, F., (2013), Preface: Introducing PISRS (Part II).AAPP | Physical, Mathematical, and Natural Sciences, 91(SUPP EMENT N.2, E1 (2013): PISRS Proceedings (Part II)). Ed. by D. Carf , F. Musolino, D. Schilir , and F. Strati. https://dx.doi.org/10.1478/AAPP. 91S2E1. Carfi, D., Okura, M., (2014), Coopetition and Game Theory. Journal of Applied Economic Sciences, Spiru Haret University, 9( 3(29) Fall 2014): 457-468. http://cesmaa.eu/journals/jaes/files/JAES_2014_Fall.pdf#page=123. Carfi, D., Patane, G., Pellegrino, S., (2011), Coopetitive Games and Sustainability in Project Financing. Moving from the Crisis to Sustainability: Emerging Issues in the International Context, pp. 175–182. Franco Angeli. http://www.francoangeli.it/Ricerca/Scheda_libro.aspx?CodiceLibro=365.906. Also available as Researchgate Paper at https://www.researchgate.net/publication/254444035_Coopetitive_games_and_sust ainability_in_project_financing. Carfi, D., Perrone E., (2013), Asymmetric Cournot Duopoly: A Game Complete Analysis. Journal of Reviews on Global Economics, 2: 194-202. https://dx.doi.org/10.6000/1929-7092.2013.02.16. Carfi, D., Perrone, E., (2012a), Game complete analysis of symmetric Cournout duopoly. MPRA Paper 35930, University Library of Munich, Germany. http://mpra.ub.unimuenchen.de/ 35930/. Carfi, D., Perrone, E., (2012b), Game Complete Analysis of Classic Economic Duopolies. Lambert Academic Publishing. https://www.lappublishing.com/catalog/details//store/ru/book/978-3-8484-2099-5/game-completeanalysis-of-classic-economic-duopolies. Carfì, D., Perrone, E., (2011a), Asymmetric Bertrand Duopoly: Game Complete Analysis by Algebra System Maxima. Mathematical Models in Economics, ASERS Publishing House, pp. 44–66. http://www.asers.eu/asers-publishing/collections.html. Also available as MPRA Paper 35417 at http://mpra.ub.uni-muenchen.de/35417/. Carfi, D, Perrone, E., (2011b), Game Complete Analysis of Bertrand Duopoly. Theoretical and Practical Research in Economic Fields, ASERS Publishing House, 2(1(3)): 522. http://www.asers.eu/journals/tpref/tpref-past-issues.html. Also available as MPRA Paper at http://mpra.ub.uni-muenchen.de/31302/.

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