Evolutionary stable strategies for business innovation and knowledge transfer

International Journal of Innovation Studies xxx (xxxx) xxx

Contents lists available at ScienceDirect

International Journal of Innovation Studies journal homepage: http://www.keaipublishing.com/en/journals/international-journal-of-innovation-studies

Evolutionary stable strategies for business innovation and knowledge transfer Ela Ozkan-Canbolat a, Aydin Beraha b, * a

Faculty of Economics and Administrative Sciences, Department of Business Administration, Cankiri Karatekin University, Uluyazi, Cankiri 18100, Turkey b Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri Karatekin University, Uluyazi, Cankiri 18100, Turkey

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 January 2019 Accepted 3 September 2019 Available online xxx

Evolutionary game theory expands into a number of areas that go beyond the biological concept of evolution to include sociology, economics, and business management. Social networks determine definite interactions between individuals in social settings. The common nature of these two broad areas of research generates interest in applying the approaches of evolutionary game theory to social network-based problems. Knowledge transfer that occurs in the process of social interaction improves a company's innovation capability. This paper attempts to explore ways in which networks relate to knowledge transfer on the basis of evolutionary game theory. We offer a simple mathematical model to examine the interaction of knowledge transfer and actor behavior in games of coordination. © 2019 Publishing Services by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Keywords: Evolutionary game theory Social networks Knowledge transfer Company innovation capability

1. Introduction Organizational studies examine the relationships and interactions between nodes. In some cases, actors deliberately design entire networks; in other cases, these networks emerge from the collective action of organizations pursuing individual interests. Learning alliances and alliance portfolios, the exploration and exploitation of knowledge, and the role of network position on knowledge transfer are among the crucial forms of social networks. The web of interpersonal relationships within and across organizations is another important form of social networking. Exciting topics in this domain include the role of internal networks and absorptive capacity, crowdsourcing, and interpersonal relationships in inter-organizational networks (Easley & Kleinberg, 2010). Social networks have crucial impacts on the generation of technological innovations and the evolution of commercial knowledge. To highlight the effects of network characteristics and network evolution on the formation and transfer of new knowledge, scholars should study the actions of individuals and organizations in inter-organizational relationships and networks over time. In this study, we intend to explore the manner that networks relate to the transfer of knowledge within the fields of business and management.

* Corresponding author. E-mail addresses: [email protected] (E. Ozkan-Canbolat), [email protected] (A. Beraha). https://doi.org/10.1016/j.ijis.2019.11.002 2096-2487/© 2019 Publishing Services by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

2

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

Evolutionary game theory studies populations that play games and is also useful for studying other social conventions that have game-like characteristics. Some may define a convention as a systematically derived balance point of a coordination game. Convention-based problems may occur when traders in a market must decide the extent to which they can aggressively bargain or when drivers who casually meet at an intersection must decide who will yield to the other. In our model, a conventiondor the systematically derived balance point of a gamedis the point at which knowledge is prevalent. Briefly, it is the “transfer zone” of new knowledge. If there is an obvious way to play in a game, then regardless of the structure or setting of that game, actors will know what the other actors are doing; this understanding of other actors' moves is called “focal point justification” (Schelling, 1960). Consequently, actors are able to guess what other actors are doing on the basis of their past experiences in the population. In addition, the focal point (Schelling, 1960) is presumably the site of knowledge evaluation. We develop a simple mathematical model to examine the interaction of knowledge transfer and individual behaviors in games of coordination on the basis of evolutionary game theory in order to analyze the implications of network characteristics and network evaluations on the knowledge of knowledge. The main aims of this paper are as follows: (a) to survey the recent literature on evolutionary game theory and network analyses; (b) to gather insights into the effects of network characteristics and network evolution on the formation and transfer of new knowledge; (c) to illustrate the application of evolutionary game theory to network evolution through the formation and transfer of new knowledge; and (d) to develop a basic mathematical model that illustrates the applicability of evolutionary game theory in organizational networks.

2. Game theory and evolutionary game theory Game theory is an approved tool for studying a mathematically formalized theory of strategic interactions. Its purpose is to model situations in which decision makers must make choices that have mutual and possibly conflicting consequences (Fudenberg & Tirole, 1991; Gibbons, 1992). Game theory is the study of ways in which strategic interactions among actors (also called nodes, agents, players, or members) produce outcomes with respect to their preferences (or utilities); in some cases, the actors might not have intended the outcomes in question. Scholars have primarily used game theory in economics to model competition between companies (e.g., to analytically answer questions such as should a particular company enter a new market, given that its competitors could make similar or different moves?). Game theory is particularly useful in the study of organizational networks. In recent years, scholars have primarily applied game theory to problems in intra-organizational network relations. In a classical game theory approach, actors are rational decision makers that select a single action from a set of convenient actions. Interaction between the actors is a crucial component of this process. After all, actors have selected their actions and each actor has an effect on and evaluates the resulting outcome through a payoff or utility function that represents her/his objectives. There are two ways to represent the different components (e.g., actors, actions, and payoffs) of a classical game: 1) as normal/strategic forms or 2) as extensive forms. Evolutionary game theory has developed into an active area of research that brings together concepts from biology, evolution, non-linear dynamics, and game theory. Evolutionary game theory provides a different approach to the classic analysis of games. Instead of directly calculating the properties of a game, the theory simulates populations of actors using different strategies and uses a process similar to natural selection to determine how the population evolves. Evolutionary game theory can explain the varying degrees of complexity that multi-actor games with differing strategic methods require to represent populations (Gale, Binmore, & Samuelson, 1995). The two concepts of an evolutionarily stable strategy (ESS) and an evolutionarily stable state are nearly linked but exploit different situations and meanings. In an ESS, all the members of a population adopt this strategy so no mutant strategy can invade (Maynard Smith, 1982). Once virtually all members of the population use this strategy, there is no “rational” alternative. Thus, ESS is part of classical game theory. In an evolutionarily stable state, however, if the disturbance is not too large, then a population's genetic composition will be restored after a disturbance by selection. An evolutionarily stable state is a dynamic property of a population that returns to using a strategy, or mix of strategies, if it is altered from its initial state. This is evolutionary stable strategy equilibrium, so it is a part of population genetics, dynamical systems, and evolutionary game theory. Thomas (2007) applies the term “ESS” to an individual strategy that may be mixed and “evolutionarily stable population state” to a population mixture of pure strategies that may be formally equivalent to a mixed ESS. This theory determines the relationships between evolutionarily stable strategies and Nash equilibria. The theory also identifies replicator dynamics as a static game factor. In the first approach in evolutionary game theory, a population experiences an evolutionarily stable state when all actors adopt an ESS (the abbreviation of ESS is expressed as evolutionary stable state by some authors in natural sciences. On the other hand, it is expressed as evolutionary stable strategy by some authors mostly in social sciences. From here, we will express it as “evolutionary stable strategy”). Even if a few members apply malformed, curious, or novel strategies, these members cannot prevail and will disappear. Natural selection is, thus, sufficient in keeping the population in ESS equilibria. Therefore, the populations in ESS are in a subset of Nash equilibria (Robson, 1992; Zeeman, 1981). The second approach in evolutionary game theory describes cooperation problems using replicator dynamics analyses. This part of the theory utilizes replicator equations to analyze the behaviors of populations affected by selection. This approach distinguishes differential equations depending on the population's strategy distribution and exploits the dynamics Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

3

of strategies for specific individuals (Taylor & Jonker, 1978; Zeeman, 1980). This paper presents the mechanisms important to the structure of an evolutionary analysis of games. 3. Knowledge transfer in social networks A considerable amount of research has examined the structural (e.g., Grant, 1996; Jensen & Meckling, 1995) and capacitysupporting components (e.g., Grant, 1996; Inkpen & Tsang, 2005; Wang, Lin, Jiang, & Klein, 2007) that facilitate knowledge transfer. Some studies focus on obstacles and difficulties (e.g., Dyer & Nobeoka, 1998; Spraggon & Bodolica, 2012) or on behavioral aspects (Liu, Gao, Lu, & Wei, 2015) with respect to the knowledge transfer. Inkpen and Tsang (2005) indicate that organizations may have to proactively manage and create social capital in order to realize effective and efficient knowledge transfer. Of course, a relationship must exist between the actors involved in the said transfer (Darr, Argote, & Epple, 1995). One node within this relationship becomes the transmission actor while the other becomes the recipient actor (Grant, 1996). The results of previous studies (Chen, Hsiao, & Chu, 2014; Lane, Salk, & Lyles, 2001) suggest that mutual trust, frequent communication, and effective coordination can improve the effectiveness of knowledge transfer. Similarly, Tushman (1977) and Darr et al. (1995) stress that social networks require the maintenance of regular communication and personal acquaintances because both play primary roles in knowledge transfer. Communication is an especially important factor in the process of knowledge transfer. A common knowledge base for communication between two network actors positively affects the process of transferring related knowledge (Weber & Weber, 2007). A knowledge-based view of networks suggests that knowledge transfer between organizations via information sharing requires a routine. This view evaluates the quality of the shared information in terms of the frequency and intensity of routines (Weber & Weber, 2007). Wang et al. (2007) indicate that actors can improve knowledge transfer to achieve higher capacity and competence levels. On the other hand, the process introduces various difficulties, including the source's willingness to transfer and attractiveness, the recipient's absorptive capacity and intention to learn, and the quality of the relationship and its causal ambiguity (Liu, Lu, & Wei, 2015). Absorptive capacity refers to an actor's ability to value and then apply the source's knowledge. In other words, absorptive capacity is the recipient's ability to grasp the transferred knowledge, which requires an existing knowledge stock in order to frame and retain additional knowledge. The recipient's absorptive capacity and the source's competence support the effectiveness of knowledge transfer (Wang et al., 2007). Tidd and Bessant suggest networks as one of the factors that foster companies' innovation capabilities (Ferreira, Fernandes, Alves, & Raposo, 2015). External networks are research-based and can enhance the innovation capabilities of a company (Ferreira et al., 2015). Kim and Lui (2015) and Gupta and Maltz (2015) suggest that companies need knowledge networks to improve their innovation capabilities. Gupta and Maltz (2015) argue that company innovation capabilities improve through interactional, networked, and systemic phenomena. Ahuja (2000) argues that these networks are shaped through companies' commercial, social, capital, and technological realities (Ferreira et al., 2015). Gupta and Maltz (2015) also state that companies need external resources and funds to improve upon their innovation capabilities. Thus, companies also reduce risks and share innovation costs (Olalla, Rota, Sanchez, & Menendez, 2015). In this study, we intend to determine how knowledge flows through a social network, how different nodes can play structurally distinct roles in this process, and how these structural considerations shape the formation and transfer of this knowledge over time. In general, knowledge transfer with respect to many organizational structures is observable, but to simplify our analysis and to determine how particular strategy preferences affect relationships, we explain knowledge transfer in terms of social network games. 4. Why use an evolutionary knowledge network model for innovation? There has been a renewed interest in developing networking games in order to analyze innovation and networks (Nowak & May 1992; Ohtsuki, Hauert, Lieberman, & Nowak, 2006; Skyrms, 2004; Nowak & Sigmund, 1998, 2005). These models are adequately generalizable as the number of actors (nodes) increases, but they have also attracted attention because they allow us to investigate how actors' selfish behaviors may affect inter-organizational relations. Not surprisingly, researchers (Gintis, 2006; Mailath, 1998a; 1998b) have also applied game theory to networking, primarily to solve routing and resource allocation problems in competitive environments. There are hopes that evolutionary game theory will provide tools to address a number of deficiencies in the traditional theory of games. Three of these tools are listed below (McKenzie, 2009): 1. Solution concepts and equilibria problems: The most-used solution in game theory is the concept of a Nash equilibrium. The selected strategies of a group of actors are said to be in Nash equilibrium if each actor's strategy is the best response to the strategies that other actors have chosen. Game theorists use the Nash equilibrium concept to analyze the outcome of the strategic interaction of several decision makers as it provides a way to predict what will happen if several people or several institutions are making decisions simultaneously and if the outcome depends on the decisions of others (Fudenberg & Tirole, 1991; Nash, 1953; Osborne, 2004). By best response, we mean that no individual can improve his or her payoff by switching strategies unless at least one other individual also switches strategies. If actors must use pure strategiesdwhich refer to 2*2 games for our mathematical modeldthen actors may engage two knowledge transfer Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

4

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

strategies (sharing knowledge and not sharing credible knowledge) and two funding strategies (funding or not-funding credible knowledge), and not every game has a Nash equilibrium. On the other hand, a more significant problem associated with invoking a Nash equilibrium as the appropriate solution concept arises because some games have multiple Nash equilibria. When several different Nash equilibria exist, how does a rational actor decide which is the optimal choice (Samuelson, 1997)? 2. Rationality problem, rationality, or bounded rationality? Traditional game theory imposes a very high rationality requirement on actors. Evolutionary game theory may have greater success in describing and predicting human subjects' choices because it is better equipped to handle the appropriate assumptions of bounded rationality (Mailath, 1998a; 1998b). 3. The lack of dynamic conditions problem: Neumann and Morgenstern (1953) describe classical game theory as a static theory, whereas the theory of evolution is a dynamic theory. The second approach to evolutionary game theory explicitly reveals an evolutionarily dynamic model in the interactions among individuals in a population. For this reason, evolutionary game theory may fill an important void in traditional game theory. In terms of the relationships that independent node systems create, network theories (Wellman, 1988) analyze interpersonal relations, including the characteristics of these relations. Most studies on network theory depend on network outputs; thus, they are output-oriented studies. Why is characterizing network anatomy so important? It is important because structure always affects function. A network's anatomy affects the spread of activities. For example, in some types of networks, information, innovation, and technology can spread throughout society. Social network analyses offer a way to understand the complex connectedness of modern society. Social networks can simply and easily explain how organizations' or individuals' expectations and incentives are related to others' behaviors and how these organizations' structures or interactions arise within a population. Social interaction enables companies to foster the kinds of knowledge-intensive relationships from which innovations emerge (Gupta & Maltz, 2015). Knowledge transfer is critical for product innovation. Gupta and Maltz (2015) recommend institutional relationships between companies to foster their product innovation. Gupta and Maltz (2015) argue that market network is not only related to organizational innovation and business group affiliation but also to both product and organizational innovation. Organizational innovation comprises a company's management practices, processes, structures, and its external relations (Kim & Lui, 2015). In our model, we use company innovation capability as meaning both product and organizational innovation that emerge through networked and interactional relationships between companies.

5. Model The paper's strength is that it proposes a theory-based mathematical model that can help companies understand the results of a decision according to the model. This model explores the effects of network evolution on the formation and transfer of new knowledge; therefore, we study the actions of actors in inter-organizational relations and networks over time. Scholars have acknowledged that inter-organizational cooperation and innovation networks are very important in knowledge transfer and innovation (Gemünden, Ritter, & Heydebrech, 1996; Gintis, 2000; Gupta & Polonsky, 2014; Inkpen & Tsang, 2005). An innovation network is a system of innovations designed to meet basic institutional arrangements, whereas a cooperative relationship between enterprises is the main connection mechanism of a network's structure (Freeman, 1991). Cooperation is widespread in the real world; therefore, understanding the emergence and persistence of cooperation among inter-organizational relationships is a fundamental and central problem in understanding networks. The mathematical approach has the advantageous claim of the language it uses. It is brief, comprehensive, and literaldit is an instrument to single out the most essential factors and relationships. As a result, mathematical modeling reveals the tricks and vital points that are free from the many real-world complications (Chiang, 1984). It is the job of empirical researchers to determine if a mathematically derived theory is useful. Linear equations can describe actual economic and managerial relationships with respect to the nature of the relationships among variables. Cost and gain functions are behavior equations that specify the manner in which a variable behaves in response to changes in other variables. Formation and diffusion of innovation according to many organizational structures is observable, but to make our analysis concise and to determine how particular strategy preferences affect relationships, we explain innovation in terms of linear gain functions at the innovation level. Game theory explains situations in which the utility of an actor's decision depends not only on how an actor chooses among several options but also on how the actors with whom they interact choose. Searching equilibria is generally difficult for n-actor games (McKelvey & McLennan, 1996). When there are more than two actors, mathematical and computational complexity rises along with the number of actors. One way to solve this problem is to use Boolean functions to represent individual decisions in a network. For the sake of conceptual simplicity and in an effort to understand general relationships, we will determine all relations in terms other than Boolean mathematics. In addition, a drawback of the algorithm in Boolean representation is that it cannot solve mixed-strategy equilibria (Chung, 2012). We focus on pure strategy equilibria; therefore, the evolutionary game approach mathematical representation will be an effective model. Evolutionary game theory assumptions are relevant in settings in which anyone tacitly makes decisions. In addition, evolutionary game theory provides a powerful framework within which we can solve our problem. In this problem setting, Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

5

the strategy used is one of cooperative knowledge transfer behaviors between organizations; thus, organizations that use this strategy are members of an innovation network. Determining the formation and rules of an innovation network and regulating the key factors affecting the formation of this knowledge transfer within networks is not easy. We use evolutionary game theory in innovation networks to better understand the nodes' expected behaviors in order to induce a socially desirable equilibrium. Evolutionary game theory provides a powerful framework to determine companies' knowledge-sharing behaviors based on cooperative innovation. It is also novel in that bounded rational actors with particular cooperation strategies choose their moves; the number of copies of a particular strategy that remain to play in the games of succeeding generations, given a population in which other strategies with which the selected strategy acts are distributed at particular frequencies, acts as a measure of that strategy's success (Hofbauer & Sigmund, 1988). This paper is based on the work of Ozkan-Canbolat and Beraha (2016) who describe the knowledge games in social networks. Distinctively, this paper attempts to progress the mathematical model to exhibit the results of cooperative and noncooperative relationships of companies in terms of an ESS. 5.1. Outline of the knowledge network model We start by characterizing the networks that emerge from our model. Subsequently, we introduce organizations that adopt definite strategies and make bounded rational decisions by engaging in games with others and study how strategy and structure coevolve. Let us consider a 2*2 games with two pure strategies, Company A and Company B. Each individual uses either strategy of fund or not fund and share or not share. We do not consider mixed strategies. We study the evolution of innovation cooperation modeled as an asymmetric 2*2 games in a population. Organizations play the game with all of the organizations in the interaction network. These interrelations determine the total payoff of each actor (Ohtsuki, Nowak, & Pacheco, 2007; Pacheco, Traulsen, & Nowak, 2006). Company A has strong ties in a network in which the nodes have a detailed understanding of what others in the network are doing and can easily accelerate any type of information flow through their direct relationships. The strong relationships between the nodes eliminate the problem of their confidence in each other (Granovetter, 1983). As the dominant enterprise, Company A has two options: to fund or not to fund. If it funds an innovative activity, then other companies throughout the network will rapidly imitate their innovation. If it does not fund the innovation, then the knowledge may not move through the network effectively. Company B has weak ties within the network. Burt (1997) notes the importance of weak edges in a network's ability to interact with organizations that are not directly connected to it. He mentions that a considerable amount of interorganizational cooperation improves as a result of these weak edges. An organization with more weak ties generates new ideas more easily. In social networks, actors with whom the nodes less frequently relate are the new sources of information. Company B is the non-dominant enterprise; as such, it has the ability to acquire and provide new knowledge to the network. It has two options: to share new knowledge or not to share new knowledge. To determine how particular strategy preferences affect relationships, we explore the actors' knowledge transfer strategies. Because an actor's strategy depends on her/his partner's strategy, the formation and diffusion of innovation among actors changes dynamically. To examine the interaction among actors, we model a framework comprising companies with different strategies (not/funding innovations and not/transfer knowledge to these innovations) repeatedly. This is the “evolutionary knowledge network game” chain structure model. When one actor knows something that others do not, sometimes he wants to reveal it credibly. Organizations sometimes transfer knowledge and use an action as a credible “signal”; i.e., a warning that something will not be desirable if the circumstances were otherwise. For example, an extended warranty is a credible signal to the consumer that the organization believes it produces a high-quality product (Nalebuff & Brandenburger, 1997). Formation and diffusion of innovation with respect to many organizational behaviors is observable. Actors can improve knowledge transfer with higher capacity and competence levels (Wang et al., 2007). One way to increase capacity in an industry is to use the alternative capacities of others if given credible knowledge. Trust is another critical factor related to knowledge-sharing between actors. There is a distinction between tie strength and perceived trustworthiness (Levin & Cross, 2004). Levin and Cross (2004) suggest that actors could benefit from developing trusted weak ties, not just strong ties. The authors also indicate that this strategy does also carry the risk of misplaced trust. 5.1.1. General assumptions We assume that models of networked behavior should include aspects of strategic behavior and we take strategic reasoning into account. Every actor targets maximum utility but cannot make totally rational decisions or predictions of the future. We assume that actors have bounded rationality. Actors lack information about other actors in the network. We do not consider mixed strategies. Actors may engage two knowledge transfer strategies: sharing or not sharing credible knowledge. Actors may engage two funding strategies: funding or not-funding credible knowledge. Cooperation is a pattern of innovation and cooperation for innovation will not remain stable. The risk coefficient with respect to funding and knowledge-sharing companies may decrease to increase the possibility of cooperation between companies. Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

6

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

We accept p as the punishment coefficient for not sharing new knowledge with funding actors when a funding mechanism is active. Games conclude a non-zero/non-constant sum. If actors' interests are not always in direct conflict, then there are opportunities for both to gain. Game repeats constantly (for every node and edge). We refer by repeated games to a situation in which the same stage game (strategic form game) is played at each date for some duration of t periods (Aumann & Maschler, 1995). We assume that innovation cooperation will not remain stable. In repeated games, organizations with limited information about others set their strategies sustainably to improve their utility and reach a dynamic balance in a process known as “ESS equilibrium.” This model requires an asymmetric game where there are not identical strategy sets for both actors and where asymmetries refer to asymmetries in payoffs (Aumann, 1987). This model is an asymmetrical model because actors/companies are not identical and their roles differ; each actor can condition its actions on its strategies and its opponents' strategies. ESS-based evolutionary game theory is not without its problems. In particular, its explanation for the emergence of cooperation in populationsdthrough which individuals increase others' payoffs at their own expensedis inadequate and in obvious contradiction with evolutionary theory (McKenzie, 2009). 5.1.2. Limitations and boundaries This paper does not aim to add the possible influences of internal and external variables (e.g., company age, size, and industry; intensity of competition; or a company's position in the value chain) into the mathematical model. This paper presents a mathematical model and a method. It presents a formal evolutionary game theoretical model. Although both input and output model components are described, output conditions are poor as they are determined with respect to future applications of the model. Boundary conditions of the model are limited to network modalities, i.e., strong and weak ties. The researchers assume only two types of network tie qualities for the sake of simplicity. In most real-life situations, we are involved in different games and each particular game only makes a small contribution to our overall performance. Numerical simulations suggest that these results are usually good approximations for values (Ohtsuki et al., 2006). We examine finite populations because for infinite populations, contributions to knowledge transfer networks may change. We do not consider mixed strategies. 5.1.3. Knowledge network model assumptions Our simple model has some interesting features: the entire evolutionary dynamics are driven by organizations' innovative interrelations such that their payoffs include both their research and fund costs and their cooperation benefits (rewards). In this model, unlike other network studies (Luce & Raiffa, 1957; Ohtsuki et al., 2007; Pacheco et al., 2006; Rapoport & Chammah, 1965) both cooperators and defectors pay costs and provide benefits with respect to their innovative interrelations. Our aim is to calculate the associated rates of organizations' knowledge-sharing behaviors. Therefore, we study the effect of population structure in accordance with evolutionary dynamics:
IA Innovation capability of Company A and Company B, respectively, and IA and IB > 0; IB
KA Absorption and transformation capacity of the new knowledge (innovation income coefficient); KB KA IA Innovation gain of Company A; KB IB Innovation gain of Company B where KA ; KB > 0;
TA Risk coefficient, where TA ; TB > 0; TB
TA ,IA ¼ CA Costs of cooperation and innovation belonging to Company A and Company B, respectively; TB ,IB ¼ CB x ¼ probability that companies with strong ties choose funding; and. y ¼ probability that companies with weak ties choose sharing. These costs represent the funding cost (CA ) and R&D transfer cost (CB ), where CA and CB > 0. p is a punishment coefficient that is the result of not sharing new knowledge with the funding actor when the funding mechanism is active. RA and RB are the shares of the income-reward with respect to Company A and Company B, respectively, and equal the reward share of income. This model assumes that RA , RB , and p > 0. This form does not require that the payoffs for each actor be symmetric, only that the proper ordering of the payoffs is obtained. In what follows, it will be assumed that the payoffs for the game are the same for everyone in the population. This mathematical model is structured to progress the work of Ozkan-Canbolat and Beraha (2016). Our model follows the initial assumptions as 1e4 of Ozkan-Canbolat and Beraha (2016). Assumption 1. If Company A and Company B cooperate such that Company A funds and Company B shares new knowledge, then the gains of Company A and Company B are as follows (Equations (1) and (2), respectively):

Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

7

UA ¼ KA IA  CA þ RA ¼ KA IA  TA IA þ RA ¼ IA ðKA  TA Þ þ RA

(1)

UB ¼ KB IB  CB þ RB ¼ KB IB  TB IB þ RB ¼ IB ðKB  TB Þ þ RB

(2)

Assumption 2. If Company A funds and Company B does not share new knowledge, then the gains of Company A and Company B are as follows (Equations (3) and (4), respectively):

UA ¼  CA  TA IA

(3)

UB ¼ KB IB  pIB ¼ IB ðKB  pÞ

(4)

Assumption 3. If Company A does not fund and Company B shares new knowledge, then the gains of Company A and Company B are as follows (Equations (5) and (6), respectively):

UA ¼ KA IA

(5)

UB ¼ KB IB  CB ¼ KB IB  TB IB ¼ IB ðKB  TB Þ

(6)

Assumption 4. If Company A and Company B do not cooperate such that Company A does not fund and Company B does not share new knowledge, then the gains of Company A and Company B are as follows (Equations (7) and (8), respectively):

UA ¼ 0

(7)

UB ¼ KB IB

(8)

The payoff matrix of the example model for actors is showed in Table 1. 5.2. Evolutionary equilibrium of knowledge network model Evolutionary game theory comprises two approaches. The first approach is static and derives from the work of Maynard Smith and Price (1973), and employs the concept of an ESS as the principal tool of analysis. An asymmetrical model satisfies a conditional ESS equilibrium in which there is only the existence of a strict Nash equilibrium. The Nash equilibrium is used to analyze rival situations like war (prisoner's dilemma game) and how conflict may be diminished by repeated interaction (“titfor-tat”). It is also used to study the extent to which people with different preferences can cooperate (battle of the sexes game) and whether they will take risks to achieve a cooperative outcome (stag hunt game). In this study, the Nash equilibrium is used to study the adoption of innovation standards as well as the occurrence of knowledge transfer (coordination game). This application provides an understanding of how to organize innovation networks and the outcome of efforts exerted by multiple parties in the innovation process when analyzing strategies in management. Samuelson (1997) states that ESS must be a Nash equilibrium; that is to say, an ESS is a refined or modified form of a Nash equilibrium. In a Nash equilibrium, if all actors adopt their respective parts, then no actor can benefit by switching to any alternative strategy. u(x,y) represent the payoff for playing strategy x against strategy y. The strategy pair (x,x) is a Nash equilibrium (Equation (9)) in a two-actor game if and only if this is true for both actors and for all x s x:

uðx; xÞ  uðy; xÞ

(9)

If the strategy pair (x,x) is a strict Nash equilibrium as in Equation (10), then this is true for both actors and for all x s x if and only if:

Table 1 Payoff matrix of the example model. AjB

Share

Not Share

Fund

IA ðKA  TA Þ þ RA IB ðKB  TB Þ þ RB KA IA IB ðKB  TB Þ

 TA IA IB ðKB  pÞ 0 KB IB

Not Fund

Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

8

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

uðx; xÞ > uðy; xÞ

(10)

In these definitions, there is no long-term incentive for actors to adopt x instead of y. This fact represents the point of departure from the ESS. Maynard Smith and Price (1973) specify two conditions for a strategy x to be an ESS as shown as Equations (11) and (12):

uðx; xÞ > uðy; xÞ

(11)

uðx; xÞ > uðy; xÞ and uðx; yÞ > uðy; yÞ for all xsy

(12)

The third condition is a strict Nash equilibrium and is automatically an ESS equilibrium. The fourth condition is that although strategy y is neutral with respect to the payoff against strategy x, the population of actors who continue to play strategy x has an advantage when playing against y. There is also an alternative definition of ESS that place a different emphasis on the role of the Nash equilibrium concept in the ESS concept as shown in Equations (13) and (14) (Thomas, 2007).

uðx; xÞ > uðy; xÞ

(13)

uðx; yÞ > uðy; yÞ for all xsy

(14)

The fifth condition specifies that the strategy is a Nash equilibrium and the sixth specifies that Maynard Smith's second condition is met. The two definitions are not exactly equivalent. In symmetric games, both actors have identical affordances and goals. The only imbalance is deciding which actor goes first, which gives a slight advantage. On the other side, asymmetrical games give actors different possible moves or different goals to win (Aumann, 1987). If the game is asymmetric, then one approach to modeling assumes that each organism inherits a “conditional strategy” that specifies the action it may face. The assumption that conditional strategies are inherited allows us to model an asymmetric game as an asymmetric game in which each actor's set of actions consists of its conditional strategies. A conditional strategy is an ESS if and only if it is a strict Nash equilibrium (Osborne, 2004). If the strategy pair (x,x) is a strict Nash equilibrium, then the fourth condition is automatically satisfied because no action x s y is the best response to y. If the following condition holds, then two strict Nash equilibria may occur in this model: fund, share (F, S) and do not fund, do not share (NF, NS). If one of the Nash equilibria (F, S) exists, then the payoffs for the actors are as follows: IA ðKA TA Þþ RA and IB ðKB  TB Þ þ RB . The following equations satisfy the required assumptions to find the ESS:

IA ðKA  TA Þ þ RA > KA IA ; IB ðKB  TB Þ þ RB > IB ðKB  pÞ Simplifications of these equations are as follows (Ozkan-Canbolat & Beraha, 2016):

IA ðKA  TA Þ þ RA > KA IA RA > TA IA ;

(15)

IB ðKB  TB Þ þ RB > IB ðKB  pÞ RB > IB KB  IB p RB > IB ðTB  pÞ:

(16)

RA > TA IA ¼ RA > C A and RB > IB ðTB  pÞ ¼ RB > C B  I B :p, where (F, S) is a strict Nash equilibrium and ESS (Equations (15) and (16)). Another Nash equilibrium exists if two other options (NF, NS) are chosen strategies. The payoffs for the actors are as follows (Ozkan-Canbolat & Beraha, 2016): 0 and K B I B . To find the ESS, the following equations satisfy the required assumptions: 0 >  TA IA , another Nash equilibrium for Company A. KB IB > IB ðKB  TB Þ, another Nash equilibrium for Company B with simplifications as follows:

IA TA > 0

(17)

Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

9

KB IB > IB ðKB  TB Þ; TB IB > 0

(18)

CA > 0 C A > 0, C B > 0, where (NF, NS) is another strict Nash equilibrium and ESS as in Equations (17) and (18). According to these mathematical explanations, cooperative relationships (F, S) and non-cooperative relationships (NF, NS) may be ESS equilibriums. The results indicate that the reward share of income (RA ) dependent on Company A's cooperation should be greater than their funding costs (CA ). The results show that if the trust risk increases, then the reward amount should increase for cooperation. The reward share of income (RB ) for Company B depends not only on its costs but also on the punishment amount. Its R&D costs (CB ) should be less than the reward share of income (RB ) plus the punishment amount (the cost of not sharing when the funding mechanism is active). When the knowledge-sharing company is the subject, researchers should also take the punishment amount into consideration. In other words, weakly tied companies' cooperation with strongly tied ones depends not only on rewards and the costs incurred by both but also on the degree of punishment. The second equilibrium shows that the do-not-fund/do-not-share strategy may represent an ESS if Company A's funding cost and R&D costs are positive (also the first assumptions of the model). 5.3. A discussion of the explicit model of evolutionary game theory analysis (dynamic equation of the knowledge network replicator) The second approach in evolutionary game theory assumes that once a population dynamics model has been specified, all the standard stability concepts used in the analysis of dynamical systems can be applied (Taylor & Jonker, 1978; Zeeman, 1980). The population is quite large in this instance and the state of the population emerges by contiguity of what proportion follows the cooperate and defect strategies. If x and y denote these proportions and denote the average fitness of cooperators 0

0

and defectors by UA and U A , respectively, and UA average fitness of the entire population, then the values of UA , U A , and UA can be expressed in terms of the population's proportions and payoff values as follows:

 0 UA ¼ xðUA Þ þ ð1  xÞ U A

(19)

We assume that the proportion of the population in the next generation is related to the proportion of the population following the cooperate and defect strategies in the current generation according to the rule (Equations (20) and (21)): 0

x ¼ 0

y ¼

x UA UA

(20)

y UB UB

(21)

These expressions can be written in the following form: 0

x x¼

x ðUA UA Þ UA

(22)

y ðUB UB Þ UB

(23)

and 0

y y¼

If we assume that the change in the strategy frequency from one generation to the next is small, then these difference equations may be approximated by the differential equations (Equations (24) and (25)):

dx x ðUA UA Þ ¼ dt UA

(24)

dy y ðUB UB Þ ¼ dt UB

(25)

These equations were proposed by Taylor and Jonker (1978) and Zeeman (1980) to provide continuous dynamics for evolutionary game theory, and are known as the “replicator dynamics.” Studies on the evolutionary dynamics of populations underlie the process by which strategies change. In other words, all the standard stability concepts used in the analysis of dynamic systems apply and this explicit model determines the Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

10

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

frequency with which strategies change in a population. Furthermore, evolutionary game theory dynamics explain that actors will repeat previously successful strategies in the present interaction at a greater rate in the immediate future (Mailath, 1992). Our study of evolutionary dynamics is built around the replicator equations and is a set of replicators in a specific environmental setting of interaction among actors. An evolutionary dynamic of a replicator system is a process of change over time in the frequency distribution of the replicators in which strategies with higher payoffs reproduce faster in some appropriate sense. To obtain the stable point of the replicated dynamic equation, according to the stability theorem for differential equations, M(z) ¼ dz ¼ 0 and M'(z) < 0. dt Chiang and Wainwright (1984) explains that “in general, it is the slope of the phase line at its intersection point which holds the key to the dynamic stability of equilibrium or the convergence path. A finite positive slope makes for dynamic instability, whereas finite negative slope implies dynamic stability.” That is, they are the roots of M(z). To test the dynamic stability of an equilibrium, we should check the intersection of the phase line with the z axis or check regardless of the initial position of z. Any root c of M(z) yields a constant solution z ¼ c. The long-term behavior of a particular solution is determined solely from the initial condition z (t0) ¼ c. The behavior can be categorized by the initial value z: If z < 0, then z*/ ∞ as t/ ∞. If z ¼ 0, then z* ¼ 0, a constant/equilibrium solution. If 0 < z < c, then z*/ c as t/ ∞. If z ¼ c, then z* ¼ c, a constant/equilibrium solution. If z > c, then z*/ c as t/ ∞. In this study, a description of the analysis of the knowledge transfer process between cooperative innovation networks in a bounded rational situation appears below. If the probability of a company with strong ties choosing a funding policy is x, then the probability of that company not choosing a funding policy is (1  x). If the probability of company with weak ties choosing to share innovation is y, then the probability of that company not sharing an innovation is (1  y). The expected gains for 0

companies with strong ties choosing a funding policy (UA ) or a non-funding policy (U A ) are as follows:

UA ¼ yðKA IA  TA IA þ RA Þ þ ð1  yÞ ð  TA IA Þ;

(26)

0

U A ¼ y KA IA þ ð1  yÞ0 ¼ yðKA IA Þ

(27)

The average gain for companies with strong ties is as follows:

 0 UA ¼ xðUA Þ þ ð1  xÞ U A

(28)

We try to examine a change in the strategy frequency from one generation to the next using differential equations. According to the formulas derived above, we find a dynamic equation for a funding company replicator as follows:

 0  dx ¼ xð1  xÞ UA  U A dt ¼ xð1  xÞð  yTA IA þ yRA  TA IA þ yTA IA Þ ! ¼ xð1  xÞ yRA  TA IA |ffl{zffl}

(29)

CA

¼ xð1  xÞðyRA  CA Þ; m¼

CA RA

If y ¼ m, then CA ¼ yRA , where all dx ¼ 0 and all x remain stable; thus, we determine the stable strategy of the dynamic dt equation for the replicator (see Fig. 1). 0 0 If y sm, then both x ¼ 0 and x ¼ 1 are stable strategy. 0

< 0 and x ¼ 0, which means that companies with strong ties choose a nonWhen 0 y < m 1 and CA > yRA, then dx dt funding strategy as an ESS (see Fig. 2). When the company's funding costs exceed the critical value (yRA ), the no funding strategy is the ESS. If y s m when 1 y > m 0, then the funding cost CA < yRA. > 0 and ¼ 1, which means that companies with strong ties choose the funding strategy as an ESS (see Fig. 3). When Thus, dx dt the company's funding costs exceed the critical value (yRA ), funding is the ESS. Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

11

Fig. 1. Phase map of the dynamics of Company A's equation when y ¼ m.

Fig. 2. Phase map of the dynamics of Company A's equation when y < m.

We also analyze companies with weak ties, which we assume are knowledge-sharing companies. The expected gains of companies with weak ties (knowledge-sharing companies) that choose knowledge-sharing and knowledge-withholding policies are as follows:

UB ¼ xðKB IB  TB IB þ RB Þ þ ð1  xÞ ðKB IB  TA IA Þ;

(30)

0

U B ¼ xðKB IB  pIB Þ þ ð1  xÞ ðKB IB Þ

(31)

The average gain of companies with weak ties is as follows:

 0 UB ¼ yðUB Þ þ ð1  yÞ U B :

(32)

According to the formulas derived above, we find a dynamic equation that replicates a knowledge-sharing company as follows:

 0  dy ¼ yð1  yÞ UB  U B ; dt n¼

dy ¼ yð1  yÞ½xðKB IB  TB IB þ RB Þ þ ð1  xÞ$ðKB IB  TB IB Þ  ½xðKB IB  pIB Þ þ ð1  xÞðKB IB Þ dt # ! ! "

¼ yð1  yÞ x RB  TB IB |ffl{zffl}

þ ð1  xÞ$

CB

 TB IB |ffl{zffl}

þ ðxpIB Þ

(33)

CB

¼ yð1  yÞ½xðRB  CB Þ þ ð1  xÞð  CB Þ þ ðxpIB Þ ¼ yð1  yÞ½xðRB þ pIB Þ  CB  n ¼ C B =ðRB þ pI B Þ If x ¼ n, then CB ¼ xðRB þPIB Þ; where all ¼ 0, indicating that all y are stable; we also find the stable strategy of the dynamic equation of the replicator (see Fig. 4). 0 0 If x sn, then both y ¼ 0 and y ¼ 1 are stable strategies. Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

12

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

Fig. 3. Phase map of the dynamics of Company A's equation when y > m.

Fig. 4. Phase map of the dynamics of Company B's equation when x ¼ n.

When 0  x < n  1 and CB > ½xðRB þ pIB Þ  CB , then dy < 0 and ¼ 0, which means that companies with weak ties choose a dt knowledge-withholding strategy as an ESS (see Fig. 5). When the company's R&D costs exceed the critical value ðRB þ pIB Þ, the no sharing strategy is the ESS. If x sn when 1 x > n 0, then the R&D cost is CB < ½xðRB þ pIB Þ  CB . 0

> 0 and y ¼ 1, which means that companies with weak ties choose the sharing strategy as an ESS (see Fig. 6). When Thus, dy dt the company's R&D costs exceed the critical value (RB þ pIB ), the sharing strategy is the ESS.

Fig. 5. Phase map of the dynamics of Company B's equation when x < n.

Fig. 6. Phase map of the dynamics of Company B's equation when x > n.

Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

13

Fig. 7. Phase diagram of the dynamics of replication.

The phase diagram of the dynamics of replication appears below (see Fig. 7). Although we find five pointsdA(1,0), B(0,1), C(1,1), K(0,0), and D(m,n)din Fig. 7, only two of them, K(0,0) and D(m,n), form an ESS. K(0,0) refers to a non-cooperative relationship, and D(m,n) refers to a cooperative relationship. In the two-dimensional plane, the dotted line ADB divides the surface into two parts with respect to cooperation. The right region represents cooperative relationships, and the left region represents non-cooperative relationships. The lower-left side shows the convergence of non-cooperation. In the future, we anticipate that companies will be more likely to cooperate, which means that D will shift toward the B lower-left corner. According to the formula of m and n, we determine that m ¼ CRAA and n ¼ RB CþpI . The greater the value of CA and B

CB (i.e., the higher the funding and R&D costs), the higher m and n, thus increasing the possibility of non-cooperation between companies. Furthermore, an increase in the value of RA and RB (the share of income rewards) leads to a decrease in m and n (m,n), thus increasing the possibility of cooperation. We also find that if the punishment amount is high, then n is small, which means that cooperation will occur. We find that if we intend to ensure cooperation between members that have weak and strong ties, then we should aim to decrease their funding and R&D costs (CA and CB ) and to increase their cooperation reward amount (RA and RB ) and their punishment amount p. To conclude, regulating innovation networks may depend on setting cooperation rewards that exceed the funding and R&D costs, which may lead to an increase in innovation performance (Ghoshal & Bartlett, 1990). 6. Discussion In this study, we analyze the implications of network characteristics and network evaluations on the transfer of knowledge, and create a model based on evolutionary game theory. First, we identify ESSs and analyze the frequency of different strategies. Next, we study the evolutionary dynamics of populations. Because evolutionary game theory studies populations that play games, it is also useful for examining social aspects, especially conventions. In this study, we analyze two evolutionarily stable strategies that are also conventions: non-cooperative relationships and cooperative relationships. Cooperative relationships can only occur if the reward for cooperation exceeds funding costs or if R&D costs plus the punishment amount are less than the reward amount. R&D costs are less than the reward amount plus the punishment amount. In the long-term, companies may converge to establish cooperative or non-cooperative equilibria. We conclude that companies' network modalities and strong/weak ties affect their strategies to cooperate or not cooperate. However, they do not choose to fund when others do not share and they do not choose not to fund when others share. If some network members choose funding while others choose to withhold their knowledge, then companies with strong ties pay funding costs but gain nothing. On the one hand, companies with weak ties miss the opportunity to transfer knowledge and they must pay an extra fee; as a result, the proportion of companies that choose to share shrinks and they converge on cooperative relations (F, S). On the other hand, companies with strong ties may decide to choose a non-funding strategy while opponents choose not to share knowledge to eliminate funding costs; in this case, the proportion of companies choosing non-funding strategies shrinks and they converge on non-cooperative relations (NF, NS). If some members do not fund while others share, then those who chose not to fund remember that if they fund available knowledge, then they may gain respect and receive a reward for their cooperation (RA > CA ). The proportion of companies choosing a non-funding strategy shrinks and they converge on a funding strategy (F, S). The other possibility is that companies with weak ties may choose to withhold knowledge to eliminate the amount of R&D costs. In this case, the proportion of companies that choose not to share increases and the population converges on non-cooperative relations (NF, NS). Although research studies on network and knowledge transfer studies determine the effects of network qualities, they do not provide like-minded results. For example, strong ties play a role in the spread of accepted knowledge and innovation; on the other hand, weak edges play a role in providing the nodes with new information and sources (Gulati, Dialdin, & Wang, Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

14

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

2002). Conversely, Granovetter (1974) argues that changes in the organizational field are limited; that is, if too many strong ties occur, then knowledge transfer cannot emerge throughout the entire network. There should be other conditions (shares of income-reward, funding cost, and R&D costs and punishment coefficient) that interrelate knowledge transfer in organizational network. Moreover, this study determines that for efficient knowledge transfer network should capture both strongly and weakly tied actors' cooperation. For knowledge transfer to occur in a strategic alliance, strong ties must exist between members of the alliance. Larson (1992) has indicated that strong ties promote trust, reciprocity, and long-term relationships. Uzzi (1997) also suggests that weak ties may occur more often but be of lesser significance in terms of success. Weak ties can produce information sharing within a network. Thus, the scope or size of the network is likely to influence the amount of diverse information available to its members, which will be important. If there is an obvious way to play in a game, regardless of the structure or setting of that game, then actors will know what other actors are doing, which is called “focal point justification” (Schelling, 1960). In this situation, actors will guess what other actors are doing with respect to their past experiences in the population. Successful strategies become more prevalent not only because market forces do not select unsuccessful strategies, but also because actors imitate successful behaviors. When we compare cooperation and non-cooperation strategies, we demonstrate that cooperative relationships are more beneficial and profitable than non-cooperative ones. Therefore, we assume that the focal point of this model is a cooperative relationship in which both knowledge formation and profit occur. On the other hand, if we assume that the focal point is a non-cooperative relationship, then we may not achieve knowledge transfer. For this reason, companies should establish institutions that can maintain both profitability and knowledge transfer sustainability. To conclude, this model's focal pointdcooperative relationships, an area in which knowledge is prevalentdis accepted as a convention. In other words, cooperative relationships represent a new knowledge diffusion area. We find that if we intend to satisfy cooperation between members that have weak and strong ties in an innovation network, then we should aim to increase this punishment amount p. An intra-corporate network with personal transfers between network members functions as an inter-organizational grouping rather than a solitary organization. 7. Conclusions The integration of social network ideas and game theory seems to be one of the most likely ways forward in building a systematic social science. The strength of this paper is that it proposes a theory-based mathematical model that can help companies understand the results of a decision according to the model. This study brings together three disparate strains of literaturedsocial network theory, evolutionary game theory, and the literature on knowledge transfer between corporationsdinto one manuscript. We offer a simple model to examine the interaction of knowledge transfer and individual behaviors in games of coordination. We find a specific area, cooperative relationships, where new knowledge is present. We accept this equilibrium as a focal point such that companies in networks can imitate strategies that may lead them to become sustainable, profitable network members. The main contribution of this paper is that it brings evolutionary game theory and social network theory to bear on issues of organizational cooperation. The two core lessons that we draw from the model seem to be unsurprising. Naturally, firms are more likely to cooperate when the reward is increased and cooperation is more likely when one firm can punish the other; in fact, this case seldom appears in the literature on punishment and cooperation because the more salient case is one in which any of the entities can potentially punish others. For knowledge transfer to occur at the inter-organizational level in a network, social capital must be present at the individual level and/or the organizational level. Depending on the network type, individual and organizational social capital involves different dynamics. For example, organizational social capital is more important in strategic alliances, whereas individual social capital is more important in industrial districts (Inkpen & Tsang, 2005). Future research may include the implementation of social capital in evolutionary games. Research studies can use multiple perspectives to evaluate knowledge transfer in strategic alliances. Lane and Lubatkin (1998) suggest that a relationship exists between absorptive capacity and the characteristics of strategic alliances. An organization may obtain knowledge about its partners' design and management or information about an alliance partner that is able to support its managerial capacity for collaborative tasks. This knowledge may play a significant role in the evolution of strategic alliances. Future research may analyze a social game involving these network types (strategic alliances) and knowledge transfer data. The network-related knowledge transfer model fulfills another researcher's request to adapt this model or build on it based on this description. Declaration of competing interest The authors declaim no conflict of interest. References Ahuja, G. (2000). Collaboration networks, structural holes, and innovation: A longitudinal study. Administrative Science Quarterly, 45(3), 425e455. Aumann, R. J. (1987). Correlated equilibrium as an expression of Bayesian rationality. Econometrica: Journal of the Econometric Society, 55(1), 1e18.

Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

15

Aumann, R. J., & Maschler, M. (1995). Repeated games with incomplete information. Cambridge London: MIT Press. Burt, R. S. (1997). The contingent value of social capital. Administrative Science Quarterly, 42, 339e365. Chen, C. J., Hsiao, Y. C., & Chu, M. A. (2014). Transfer mechanisms and knowledge transfer: The cooperative competency perspective. Journal of Business Research, 67(12), 2531e2541. Chiang, A. C., & Wainwright, K. (1984). Fundamental methods of mathematical economics. Singapore: Mc-Graw-Hill International Editions. Chung, B. (2012). Notes on boolean functions and Nash equilibrium. https://doi.org/10.2139/ssrn.1997067 (February 1, 2012). Available at: http://ssrn.com/ abstract¼1997067. (Accessed 14 March 2015). Darr, E. D., Argote, L., & Epple, D. (1995). The acquisition, transfer, and depreciation of knowledge in service organizations: Productivity in franchises. Management Science, 41(11), 1750e1762. Dyer, J. H., & Nobeoka, K. (1998). Creating and managing a high performance knowledge-sharing network: The Toyota case. Strategic Management Journal, 21(3), 345e367. Easley, D., & Kleinberg, J. (2010). Networks, crowds, and markets: Reasoning about a highly connected world. Cambridge: Cambridge University Press. Ferreira, J. J. M., Fernandes, C. I., Alves, H., & Raposo, M. L. (2015). Drivers of innovation strategies: Testing the Tidd and Bessant (2009) model. Journal of Business Research, 68(7), 1395e1403. Freeman, L. C. (1991). Networks of innovators: A synthesis of research issues. Research Policy, 20(5), 499e514. Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge, MA: MIT Press. Gale, J., Binmore, K., & Samuelson, L. (1995). Learning to be imperfect: The ultimatum games. Games and Economic Behavior, 8(1), 56e90. Gemünden, H. G., Ritter, T., & Heydebreck, P. (1996). Network configuration and innovation success: An empirical analysis in German high-tech industries. International Journal of Research in Marketing, 13(5), 449e462. Ghoshal, S., & Bartlett, C. A. (1990). The multinational corporation as an interorganizational network. Academy of Management Review, 15(4), 603e626. Gibbons, R. (1992). Game theory for applied economists. New Jersey: Princeton University Press. Gintis, H. (2000). Classical versus evolutionary game theory. Journal of Consciousness Studies, 7(1e2), 300e304. Gintis, H. (2006). The evolution of private property. Journal of Economic Behavior & Organization, 64(1), 1e16. Granovetter, M. (1974). Getting a job: A study of contacts and careers. Chicago: University of Chicago Press. Granovetter, M. (1983). The strength of weak ties: A network theory revisited. Sociological Theory, 1, 201e233. Grant, R. M. (1996). Toward a knowledge-based theory of the firm. Strategic Management Journal, 17(2), 109e122. Gulati, R., Dialdin, D. A., & Wang, L. (2002). Organizational networks. In A. C. Baum Joel (Ed.), Companion to organization (pp. 281e303). London, Oxford: Blackwell. Gupta, S., & Maltz, E. (2015). Interdependency, dynamism, and variety (IDV) network modeling to explain knowledge diffusion at the fuzzy front-end of innovation. Journal of Business Research, 68(11), 2434e2442. Gupta, S., & Polonsky, M. (2014). Inter-firm learning and knowledge-sharing in multinational networks: An outsourced organization's perspective. Journal of Business Research, 67(4), 615e622. Hofbauer, J., & Sigmund, K. (1988). The theory of evolution and dynamical systems. Cambridge: Cambridge University Press. Inkpen, A., & Tsang, E. W. K. (2005). Social capital, networks, and knowledge transfer. Academy of Management Review, 30(1), 146e165. Jensen, M. C., & Meckling, W. H. (1995). Specific and general knowledge and organizational structure. Journal of Applied Corporate Finance, 8(2), 4e18. Kim, Y., & Lui, S. S. (2015). The impacts of external network and business group on innovation: Do the types of innovation matter? Journal of Business Research, 68(9), 1964e1973. Lane, P. J., & Lubatkin, M. (1998). Relative absorptive capacity and interorganizational learning. Strategic Management Journal, 19, 461e477. Lane, P. J., Salk, J. E., & Lyles, M. A. (2001). Absorptive capacity, learning, and performance in international joint ventures. Strategic Management Journal, 22(12), 1139e1161. Levin, D. Z., & Cross, R. (2004). The strength of weak ties you can trust: The mediating role of trust in effective knowledge transfer. Management Science, 50(11), 1477e1490. Liu, X. G., Lu, L. J., & Wei, Y. (2015). The role of highly skilled migrants in the process of inter-firm knowledge transfer across borders. Journal of World Business, 50(1), 56e68. Luce, R. D., & Raiffa, H. (1957). Games and decisions. New York: John Wiley Sons. Mailath, G. J. (1992). Introduction: Symposium on evolutionary game theory. Journal of Economic Theory, 57(2), 259e277. https://doi.org/10.1016/00220531(92)90036-H. Mailath, G. J. (1998a). Evolutionary game theory. In P. Newman (Ed.), The new Palgrave dictionary of economics and the law (pp. 84e88). London: The Macmillan Press. Mailath, G. J. (1998b). Do people play Nash equilibrium? Lessons from evolutionary game theory. Journal of Economic Literature, 36(3), 1347e1374. Maynard Smith, J. (1982). Evolution and the theory of games. Cambridge: Cambridge University Press. Maynard Smith, J., & Price, G. (1973). The logic of animal conflict. Nature, 146, 15e18. McKelvey, R. D., & McLennan, A. (1996). Computation of equilibria in finite games. Handbook of Computational Economics, 1, 87e142. McKenzie, A. J. (2009). Evolutionary game theory. In N. Zalta Edward (Ed.), The Stanford encyclopedia of philosophy. Available on http://plato.stanford.edu/ archives/fall2009/entries/game-evolutionary/. (Accessed 14 March 2015). Nalebuff, B. J., & Brandenburger, A. M. (1997). Co-opetition: Competitive and cooperative business strategies for the digital economy. Strategy & Leadership, 25(6), 28e33. Nash, J. (1953). Two-person cooperative games. Econometrica, 21(1), 128e140. Neumann, J., & Morgenstern, O. (1953). Theory of games and economic behaviours. London: Oxford University Press. Nowak, M. A., & May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359(6398), 826e829. Nowak, M. A., & Sigmund, K. (1998). Evolution of indirect reciprocity by image scoring. Nature, 393(6685), 573e577. Nowak, M. A., & Sigmund, K. (2005). Evolution of indirect reciprocity. Nature, 437(7063), 1291e1298. Ohtsuki, H., Hauert, C., Lieberman, E., & Nowak, M. A. (2006). A simple rule for the evolution of cooperation on graphs and social networks. Nature, 441(7092), 502e505. Ohtsuki, H., Nowak, M. A., & Pacheco, J. M. (2007). Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. Physical Review Letters, 98(10), 108106. Olalla, M., Rata, B., Sanchez, J. L., & Menendez, J. F. (2015). Product innovation: When should suppliers begin to collaborate? Journal of Business Research, 68(7), 1404e1406. Osborne, M. J. (2004). An introduction to game theory (3rd ed.). New York: Oxford University Press. Ozkan-Canbolat, E., & Beraha, A. (2016). Evolutionary knowledge games in social networks. Journal of Business Research, 69(5), 1807e1811. Pacheco, J. M., Traulsen, A., & Nowak, M. A. (2006). Coevolution of strategy and structure in complex networks with dynamical linking. Physical Review Letters, 97(25), 258103. Rapoport, A., & Chammah, A. M. (1965). Prisoner's dilemma: A study in conflict and cooperation (Vol. 165). Michigan: University of Michigan Press. Robson, A. J. (1992). An introduction to evolutionary game theory: Secret handshakes, sucker punches and efficiency. In J. Creedy, J. Borland, & J. Eichberger (Eds.), Resent developments in game theory (pp. 78e165). Samuelson, L. (1997). Evolutionary games and equilibrium selection. (Series: Economic learning and social evolution). Cambridge: MIT Press. Schelling, T. (1960). Strategy of conflict. Oxford: Oxford University Press. Skyrms, B. (2004). The stag hunt and the evolution of social structure. MA Cambridge: Cambridge University Press.

Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002

16

E. Ozkan-Canbolat, A. Beraha / International Journal of Innovation Studies xxx (xxxx) xxx

Spraggon, M., & Bodolica, V. (2012). A multidimensional taxonomy of intra-firm knowledge transfer processes. Journal of Business Research, 65(9), 1273e1282. Taylor, P. D., & Jonker, L. (1978). Evolutionary stable strategies and game dynamics. Mathematical Biosciences, 40(1e2), 145e156. Thomas, S. S. (2007). Applied linear algebra and matrix analysis, undergraduate texts in mathematics. New York: Springer-Verlag. Tushman, M. L. (1977). A political approach to organizations: A review and rationale. Academy of Management Review, 2(2), 206e216. Uzzi, B. (1997). Social structure and competition in interfirm networks: The paradox of embeddedness. Administrative Science Quarterly, 42(1), 35e67. Wang, E. T. G., Lin, C. C., Jiang, J., & Klein, G. (2007). Improving enterprise resource planning (ERP) fit to organizational process through knowledge transfer. International Journal of Information Management, 27(3), 200e212. Weber, B., & Weber, C. (2007). Corporate venture capital as a means of radical innovation: Relational fit, social capital, and knowledge transfer. Journal of Engineering and Technology Management, 24(1), 11e35. Wellman, B. (1988). Structural analysis, from method and metaphor to theory and substance. In B. Wellman, & S. D. Berkowitz (Eds.), Social structures: A network approach. Cambridge: Cambridge University Press. Zeeman, E. C. (1980). Population dynamics from game theory. In Z. Nitecki, & C. Robinson (Eds.), Global theory of dynamical systems. Lecture notes in mathematics (pp. 471e497). Berlin: Springer-Verlag. Zeeman, E. C. (1981). Dynamics of the evolution of animal conflicts. Journal of Theoretical Biology, 89(2), 249e270.

Please cite this article as: Ozkan-Canbolat, E., & Beraha, A., Evolutionary stable strategies for business innovation and knowledge transfer, International Journal of Innovation Studies, https://doi.org/10.1016/j.ijis.2019.11.002