Dynamics of Costs and Revenue Sharing Schemes in Open Innovation: an Evolutionary Game Approach

Transcription

1 Dynamis of Costs and Revenue Sharing Shemes in Open Innovation: an Evolutionary Game Approah Daqing He, Yiding Yue, Ying Wang * Business Shool of Central South University Changsha, Hunan Provine 40083, China Shool of Eonomis & Management Changsha University of Siene & Tehnology Changsha, Hunan Provine 404, China Abstrat The onept of open innovation has reently gained widespread attention It is partiularly relevant now beause many firms are required to implement it In order to investigate the inentives of open innovation, this artile analyzed ompanies' hoie to open innovation in an evolutionary game setting using repliator dynamis It disussed how osts and revenue alloation shemes affet the final equilibrium Evolutionary game analysis shows that partiipants hoies are related to shemes of ost sharing The probability of hoosing open innovation is positively related to exess benefits, and negatively related to total osts There exists an optimal exess benefits alloation, so that firms tend to adopt open innovation strongest The probability of both firms adopting open innovation is greater in punishment ase This artile shed some light on how to promote ompanies to hoose open innovation Keywords - Open innovation; Evolutionary game theory; Repliator dynamis I INTRODUCTION Traditionally, industrial firms have developed new tehnologies for their own produts internally [, ] Thus, most ompanies have pursued relatively losed innovation strategies, and had limited interations for the purpose of developing new tehnologies In reent deades, the innovation strategies have begun to hange as firms aross different types of industries have inreasingly aquired external tehnologies to omplement their internal knowledge bases [3] In light of these developments, Professor Henry Chesbrough oined the term open innovation to desribe innovation proesses in whih firms interat extensively with outsiders for ideas and methodology [4] With the growing importane of open innovation, some pioneering ompanies, suh as Proter & Gamble and Eli Lilly, have ahieved great benefits from the new tehnologies that have developed from these interations [5, 6] Open innovation is vital for ompanies whose produts have short life yles (for example software and onsumer eletronis) An example of a typial produt that has utilized open innovation is Android, whih uses Open Soure software, whose soure ode has been partially or ompletely released [7] A poliy of Open Innovation poliy allows ompanies to obtain external tehnologies and have ontrol over the release of its own knowledge with outside partners [8,9] Through the use of external expertise, Open Innovation stimulates advanes by sharing the ost and risk assoiated with developing new tehnologies, offering aess to new ontat networks through intermediaries and information pools [0] A few reent studies examine the underlying fators affeting the degree of openness of a firm from a strategi point of view [,] These authors identify souring and aquiring as the typial inbound proesses and revealing and selling as the typial outbound proesses, and investigate the advantages and disadvantages of eah form of openness Open innovation helps ompany to share external tehnologies and absorb outside knowledge with other partners, it has been examined to play a role on value oreation, wealth spillover and ompetitive advantage [3,4,5] Open innovation an be seen as an innovation in itself, beause it evokes new issues on distributing the ost and risk, offering aess to new ontat networks [6] It finds out open innovation in small and medium-sized firms (SMEs) is attrative when initiating a risk and revenuesharing agreement with partners sharing ost of open innovation sometimes indues new ost suh as transation osts as ollaborating partners may free-ride [7] External resoures of outbound open innovation an be pereived as a publi good, so innovating partners an free-ride on ollaborated ativities [8] Sine Open Innovation has been studied theoretially and empirially in reent deades, a few models have already appeared in eonomi literature The most ommon frameworks have been the stati games It has investigated aspets of tehnology transfers and differentiated Cournot duopolies, whih lead to asymmetri equilibrium strutures [9,0,] One of the few studies to work with a dynami model of Open Innovation has been established [] In this work, the authors determine the optimal strategy of a firm when it has to hoose between proprietary and Open Soure software Tehnially, their model is an optimal ontrol DOI 0503/IJSSSTa ISSN: x online, print

2 problem for a firm in the market subjet to the quality of its produt as it evolves Their analysis fouses on the essential role of researh and development osts, and works to determine when it is onvenient to open the soure ode for the firm However, these studies all think about single hoie, neglet interation in long period Evolutionary games promise riher predition than orthodox game models, evolutionary game analysis of open innovation may turns out new outomes [3,4] What leads a firm to hoose a poliy of Open Innovation? The establishment of partnerships is an essential issue The question is whether outside partners will alter their hoies In this paper, we will take into onsideration osts sharing and exess benefits between firms and their outside partners, Sine the reviewed literature either builds on the stati game theory, or on optimal ontrol, without strategi interation among firms, we adopted a differential game This artile establishes an evolutionary game model It analyzes different equilibrium results, and explores optimal inentive and punishment shemes between firms and outside partners Our study ontributes to the open innovation literature by providing new insights on ollaboration league form, introduing evolutionary game analysis makes out different outomes Additionally, we also ontribute to game theory by adding to the body on knowledge on how ompanies an benefit from utilizing open innovation ativities From a overall perspetive, our study provides new insights to mangers in ompanies and governors about how they an alloate limited resoures for pratiing open innovation and share innovation spillovers to ahieve and sustain ollaborated innovation The rest of artile is organized as follows Next, we will outline the setup of our model In the third setion, the analytial study of equilibrium are desribed Setion 4 subsequently presents the results and disussions on punishment ase Conlusions, limitations and suggestion for future studies are offered in the final setion II THE SETUP Whether or not firms implement Open Innovation ould be onsidered as the results of mutual games between firms and outside partners They an adopt strategi alliane, joint ventures, tehnology transfer or outsouring researh in form of Open Innovation They an also stik to the traditional losed innovation by their own resoures Given inomplete information and limited rationality of game players, it s diffiult for players to ensure that their hoie of strategies is the best In the innovation proess, the players need to repeat games to look for better strategy by learning Based on the nature of the issue, we have two assumptions to simplify the situation: ) Consider the market is only omposed by two firms, denoted as firm and firm Eah firm has two strategies to hoose from open innovation and losed innovation If the firm hooses losed innovation, it have to bare R&D ost by itself and get produt wholly If the firm hooses open innovation, it will share produt as well as osts ) Revenue and osts vary by firms hoie If both firms hoose losed innovation, they get benefits from different new produts, denoted as and If both firms hoose open innovation, they an get exess benefits, besides and The firm an get, the outside partner will get ( ), epresents exess benefits alloation ratio; the osts will shared by ratio, the firm bares osts ( ), the outside partner bares If they hoose different strategies, the player who adopts open innovation will share osts without exess revenue, the player of hoosing losed innovation an get additional benefits r for tehnique spillover from other side All above is ommon knowledge The osts and benefits matrix is shown in table TABLE THE PAYOFF MATRIX OF TWO FIRMS Firm Firm Open innovation Closed innovation Open innovation, ( ) ( ) Closed innovation, ( ),, r III EQUILIBRIUM ANALYSES The basi onept of the evolutionary game theory The evolutionary game theory is the ombination of game theory and dynami evolution It differs from game theory to fous on the stati equilibrium and omparative stati equilibrium, but to emphasize the dynami equilibrium [5] Currently, evolutionary game theory has been widely applied in ooperative behavior and strategy seletion problem [6,7] The ore ontent of the evolutionary game model is the evolutionary stable strategy(ess), it haraterizes the dynami onvergene proess to the steady state The repliator dynami equations desribe the steady state of the evolutionary game The dynami pae of hange is expressed as dx( t) / dt x( Us U), x is the proportion of the individuals who hoose the poliy s, U s is the expeted revenue of the hoose the strategy s, dx( t) / dt is the average benefit of all strategies for the player, shows the hange of ratio that selet the strategy s over time Evolutionary game analysis of open innovation of simplified ase DOI 0503/IJSSSTa ISSN: x online, print

3 In order to simplify the problem, we assume that firm adopting open innovation aounts for x, while firm adopting losed innovation aounts for x Firm adopting open innovation aounts for y, while firm adopting losed innovation aounts for y The respetive expetation values of open innovation and losed innovation strategy for firm are u o Governments average value is u u y () o u yr () u x[ y( ) ] yr (3) In the same way, The respetive expetation values of open innovation and losed innovation strategy for firm are uo Governments average value is u u x( ) ( ) (4) o u xr (5) u y{ x[( ) ] ( ) } xr (6) Further, the repliator dynamis equation to hoose open innovation are as follows dx x( u o u) x( x)[ y( ) ] (7) dt dy y( uo u) dt y( y){ x[( ) ] ( ) } (8) Aording to state of ESS, when 0 and ( ) 0,we get onlusions as follows: If y,then dx dt 0,whih means that all games are stable; If games are stable; If y, then x,whih means that all y,then x 0,whih means that all games are stable ( ) If x ( ),then dy dt 0,whih means that all games are stable; ( ) If x ( ),then y,whih means that all games are stable; ( ) If x ( ),then y 0,whih means that all games are stable the dynami tendeny and stability of firms population are shown in Figure The game has five equilibrium points: A(0,0), B(,0),C(0,), D(,), ( ) E( ( ), ) E is saddle point Figure Populations evolutionary game route Aording to Figure, if initial statement is loated in area ABEC, the evolution system will onverge to point A(0,0), it means firm and firm will both adopt losed innovation; if initial statement is loated in area CDBE, the evolution system will onverge to point D(,), it means firm and firm will both adopt open innovation 3 Analysis of osts sharing and benefits alloation effet on open innovation Aording to analysis of evolution equilibrium, although the optimal strategy is (open innovation, open innovation), stable strategies for firm and firm are (open innovation, open innovation) and (losed innovation, losed innovation) The tendeny of evolution result is determined by size of region ABEC and region CDBE If S ABEC <S CDBE, the probability of both firms adopting open innovation is bigger than that of losed innovation, if S ABEC >S CDBE, otherwise If S ABEC =S CDBE, probability will be equal Aording to Figure, S ABEC an be desribed as follows ( ) SABEC [ ] (9) s ( ) s Aording to equation (9), there are five variables influening the area We an get results by mathematial analysis Proposition : With the inrease of R&D osts, the probability of both firms adopting open innovation is smaller S ABEC ( ) [ ] 0 So s ( ) s is a monotonially inreasing funtion of It means that with the inrease of open innovation osts of both firms, DOI 0503/IJSSSTa ISSN: x online, print

4 size of S ABEC is bigger, the probability of system evolving to point A(0,0) gets bigger, the probability of both firms adopting open innovation is smaller Proposition : With the inrease of exess benefits of open innovation, the probability of both firms adopting open innovation is bigger S ABEC ( )( ) { } 0 ( ) [( ) ] So S ABEC is a monotonially dereasing funtion of It means that with the inrease of open innovation exess benefits, size of S ABEC is smaller, the probability of system evolving to point D(,) gets bigger, both firms have stronger intention to adopt open innovation Proposition 3: With the inrease of benefits of tehnique spillovers, the probability of both firms adopting open innovation is smaller S ABEC ( ) { } 0 s ( ) [( ) ] So S ABEC is a monotonially inreasing funtion of It means that with the inrease of open innovation osts of both firms, size of S ABEC is bigger, the probability of system evolving to point A(0,0) gets bigger, both firms lak motivation to adopt open innovation Proposition 4: There is a optimal ratio of exess benefits alloation, for the probability of both firms adopting open innovation is biggest SABEC ( ) { } [( ) ] ( ) So impat is not monotonially Aording to seond derivative equation SABEC ( ) } ( ) [( ) ] So it exists smallest value for S ABEC Let S ABEC 0,then r ( ) ( ) size of S ABEC is smallest, the probability of system evolving to point D(,) gets biggest, both firms lak motivation to adopt open innovation Proposition 5: osts sharing ratio mathing to exess benefits alloation ratio will help to firms adopting open innovation S ABEC [ ] So if ( ),then S ABEC 0 S ABEC is a monotonially dereasing funtion of osts sharing ratio It means that only when firm gets more exess benefits than firm, with the inrease of sharing osts of firm, size of is smaller, the probability of system evolving to point D(,) gets bigger, both firms have stronger intention to adopt open innovation; if,the situation is quite opposite, with the derease of open innovation osts of firm, system will more likely evolve to point D(,) IV DISCUSSING THE PUNISHMENT SCHEME OF CLOSED INNOVATION In order to enourage enterprisers to take part in open innovation and avoid free-riding behavior, it will be helpful to design punishment sheme we assume that before the ooperation firm and firm have signed ontrat to larify eah one's ommitment to open innovation when innovation ativities is over, the firm whih didn't hoose open innovation will get punishment of paying P to the other firm, the other assumption is the same as basi model All above is ommon knowledge The osts and benefits matrix is shown in table II, TABLE II THE PAYOFF MATRIX OF PUNISHMENT SCHEME Firm Open innovation Closed innovation Open innovation, ( ) ( ) r P, ( ) P Firm Closed innovation P, r P, we assume that firm adopting open innovation aounts for x, while firm adopting losed innovation DOI 0503/IJSSSTa ISSN: x online, print

5 aounts for x Firm adopting open innovation aounts for y, while firm adopting losed innovation aounts for y The respetive expetation values of open innovation and losed innovation strategy for firm are uo Governments average value is u u o y( P) P (0) u y( r P) () u x[ y( ) P] y( r P) () In the same way, The respetive expetation values of open innovation and losed innovation strategy for firm are uo Governments average value is u u o x[( ) P] ( ) P (3) u x( r P) (4) u y{ x[( ) ] ( ) P} x( r P) (5) Further, the repliator dynamis equation to hoose open innovation are as follows dx x( u o u ) dt x( x)[ y( ) P] (6) dy y( u o u ) dt y( y){ x[( ) ] ( ) P} (7) As in the above analysis, we only disuss situation when, Aording to state of ESS, we have to explore two situation when P and P( ), the game has four equilibrium points: A(0,0), B(,0), C(0, ), D(,) The dynami tendeny and stability of firms population are shown in Figure, aording to the figure, point D is saddle point Proposition 6: when taking ount into punishment sheme, only the punishment is enough to miss the ooperator's loss, P max{,( ) } in the long terms the game's evolutional outome will onverge to {open innovation, open innovation} In the initial situation both firms don't hoose open innovation, the market ompetition impels firms to open innovation gaining extra revenue by designing new produt in shorter time, then firms will both alter their hoie to open innovation When one firm hooses losed innovation while the other hoose the opposite innovation mode, the one opting losed innovation hoie will get server loss beause of high punishment, so it will turn to open innovation in the next time, at the same time, the one hoosing open innovation will get exess revenue from punishment, whih impetus it to insist on open innovation in the later game So in the long term, both firms will hoose open innovation in the game, and they will share the exess revenue from the right hoies when P and P( ), the game has four equilibrium points: A(0,0), B(,0), C(0, ), D(,), E( ( ) P P ( ), ) E is saddle point The dynami tendeny and stability of firms population are shown in Figure3, aording to the figure, point E is saddle point Figure 3 Populations evolutionary game route Figure Populations evolutionary game route Aording to Figure 3, if initial statement is loated in area ABEC, the evolution system will onverge to point A(0,0), it means firm and firm will both adopt losed innovation; if initial statement is loated in area CDBE, the evolution system will onverge to point D(,), it means firm and firm will both adopt open innovation Aording to analysis of evolution equilibrium, although the optimal strategy is (open innovation, open innovation), stable strategies for firm and firm are (open innovation, open innovation) and (losed innovation, losed innovation) The tendeny of evolution result is determined by size of region ABEC and region CDBE If S ABEC <S CDBE, the probability of both firms adopting open innovation is bigger DOI 0503/IJSSSTa ISSN: x online, print

6 than that of losed innovation, if S ABEC >S CDBE, otherwise If S ABEC =S CDBE, probability will be equal Aording to Figure, S ABEC are as follows P ( ) P SABEC [ ] (8) s ( ) s Aording to equation (8), there are five variables influening the area We an get results by mathematial analysis Proposition 7: With the inrease of punishment P, the probability of both firms adopting open innovation is greater Proof: aording to equation (8), S ABEC [ ] 0 s ( ) s So is a monotonially inreasing funtion of It means that with the inrease of open innovation osts of both firms, size of S ABEC is smaller, the probability of system evolving to point D(,) gets bigger, the probability of both firms adopting open innovation is greater From Proposition 6 and Proposition 7, we get breakpoint of punishment, whih is max{,( ) }, when the punishment don't reah this threshold, it should be greater to promote popularity of open innovation, one it passes the threshold, there is no need to set greater punishment, for in this situation open innovation is the last evolutional equilibrium V CONCLUSION In this paper, we analyzed osts and benefits effet on innovation behavior of firms based on evolutionary game theory Through the researh on organization whih omposed by two ompanies, we found that derease total osts of innovation ooperation would promote open innovation strategies beome the ultimate evolutionary stable strategy, as well as that improve exess benefits of innovation ooperation And dereasing tehnique spillover or ontrolling ride-off behavior is essential to boot open innovation Then we onsider there exists an optimal exess benefits alloation, so that firms tend to adopt open innovation strongest With the inrease of punishment, the probability of both firms adopting open innovation is greater Our researh extends and ontributes to the literature in three main ways First we extend the findings of open innovation by aounting for the ost and revenue sharing sheme of open innovation versus losed innovation We find that firms prefer to open innovation in the long term in some situations Seond, we introdue evolutionary game to open innovation analysis, and makes out meaningful outomes Third, we enrih game theory by adding to the body on knowledge on how ompanies an benefit from utilizing open innovation ativities It's helpful for mangers in ompanies and governors to alloate limited resoures for pratiing open innovation and share innovation spillovers to ahieve and sustain ollaborated innovation Nevertheless, we leave ample opportunities for further researh Our artile assumed that the enterprises are homogeneous and ignore the differene between them If fat, the status of eah firm is not onsistent Beause of different absorbing apaity, firms will get different revenues from same tehnique spillover We suggest that the future researh takes more expliit aount of heterogeneity of firms It will, however, be hallenging to find suitable measures in the game ACKNOWLEDGMENT This work 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