Hybrid competition, innovation outcomes and regulation: A duopoly model

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‘Hybrid’ competition, innovation outcomes

and regulation: A duopoly model

Thomas LE TEXIER



GREDEG - CNRS - Université de Nice Sophia-Antipolis 250, rue Albert Einstein, F-06560 Valbonne Cedex

E-mail: thomas.letexier@gredeg.cnrs.fr First draft – Please do not quote – January 2010

Abstract

This article aims at better understanding the impact of an institutional regime shift on commercial, innovation and social outcomes. To do so, we introduce a duopoly model in which a commercial organization and a community compete by providing digital products while being able to share – under some circumstances – their innovation outputs to develop their own activities. Our results reveal that the commercial organization always benefits from either a ‘closed’ or an ‘open’ regime shift. They also evidence that the commercial organization and the community both have higher-leveled incentives to innovate when they act in a ‘closed regime’ framework. From our numerical analysis, we observe that the ‘closed shift’ provides the best levels of both global innovation and welfare whereas such a shift is not found to be profit-improving when product differentiation is small. This result clearly exhibits a potential conflict of interest between commercial players and policy makers and partially qualifies the conventional idea according to which public policies may be designed to defend private – commercial – interests rather than public ones.

Keywords: Digital products; Pricing; Innovation; Communities; Duopoly

JEL Codes: D43 – L13 – L86

Corresponding author. Tel.: +33(0)493954330; Fax: +33(0)493653798.

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1. Introduction

The introduction of new appropriation channels for goods has led to fierce opposition between traditional commercial-oriented players and less traditional ones. In the case of digital diffusion, the advent of the Internet as a new transactional space is not only directly based on new patterns of consumption but on productive ones too. Indeed, the development of new compression standards highlights the shift to the ‘dematerialization era’ which leads to the widespreading of digital files online and to new technological adoption issues (Shapiro and Varian, 1998; Varian, 2000; Hui and Png, 2003; Chellappa and Shivendu, 2005; Peitz and Waelbroeck, 2006). In this context, new competition patterns have also emerged inasmuch as non-commercial players have shown that their user-centric production activities may threaten those of traditional commercial entities (Toffler, 1980).

The example of Napster represents an innovation case which has clearly shown that good ideas may be developed outside the boundaries of commercial organizations. The way commercial players first fought against that online music file-sharing before intending to integrate it into their business scheme reveals to what extent ‘outlaw’ innovations may be good enough to be considered for profit-enhancing purposes (Flowers, 2008). As an illustration, the success of iTunes as a commercial distributive digital platform mostly derives from that of its illegal ancestors, such as Napster, Gnutella and eDonkey. In a similar fashion, the developing success of the VoD – Video on Demand – commercial activity expresses the market-based attempts of some commercial players to react to the ‘pirate’ threat by exploiting the innovation outputs that online communities initially developed for their own – non-commercial – needs. As such, one may see a shift in the manner non-commercial organizations consider appropriation schemes. Therefore, an increasing number of commercial players are nowadays likely to co-operate with the external sources of innovation they previously competed with, evidencing other potential cases of either ‘democratized innovation’ (von Hippel, 1986; 1988; 2005) or ‘open innovation’ (Chesbrough, 2003; 2006).

A first key research question aims at analyzing if such emerging hybrid – both private and public – production patterns are likely to provide the best outcomes to commercial players (Grand et al., 2004; Bonaccorsi et al., 2006; Economides and Katsamakas, 2006). Indeed, one may attempt to find out if developing an asset-sharing view of carrying out for-profit

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activities necessarily leads commercial organizations to achieve larger profits than they would within the old-fashioned ‘closed innovation’ framework.

A second key research question is to study the impact of the closeness and openness of both commercial players and communities on their motives to innovate when they evolve on the same market. Indeed, such results have to be considered for policy applications to identify whether a ‘closed innovation’ or an ‘open innovation’ regime is likely to stimulate pro-innovation behaviors (Nelson, 1959; Merton, 1973; David, 1998; 2004; Nelson, 2004).

We analyze the impact of an institutional regime shift (i.e., ‘open shift’ or ‘closed shift’) on the profits of commercial organizations as well as on the level of innovation they are likely to provide. For this purpose, we present a duopoly model which depicts a ‘hybrid’ competition framework. By ‘hybrid’ competition framework, we here refer to a specific framework in which two types of producers (i.e., a commercial organization and a community) compete while being able to share – under some circumstances – their innovation outputs to develop their own activities. Competition outcomes (i.e., market shares) are identified according to the objective functions of each type of players, namely profit and surplus functions. We identify the optimal pricing strategy of the commercial organization and its related profit, as well as the optimal surplus of the community. The innovation levels delivered by the commercial organization and the community at the optimal state are also presented to provide regulatory insights.

Our results reveal that the commercial organization always benefits from either a ‘closed’ or ‘open’ regime shift. They also evidence that the commercial organization and the community both have higher-leveled incentives to innovate when they act in a ‘closed regime’ framework. From a numerical illustration, we observe that the ‘closed shift’ provides the best levels of both global innovation and welfare whereas such a shift is not found to be profit-improving when product differentiation is small. This result clearly exhibits a potential conflict of interest between commercial players and policy makers and partially qualifies the conventional idea according to which public policies may be designed to defend private – commercial – interests rather than public ones.

The organization of the paper is as follows. We first present the settings of the model (2.). We secondly analyze the optimal pricing and innovation strategies as well as the ensuing optimal profits and surpluses according to the three institutional regimes we specify (3.). We thirdly identify profit-improving and innovation-enhancing regimes and a numerical analysis is

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carried out to illustrate our comparative study. Welfare results are also discussed (4.). We fourthly conclude and provide directions for further research (5.).

2. The model – Settings

We present a market in which two producers act as duopolists when providing digital products via their own dedicated distribution channels. Although each producer provides digital products users may adopt to meet their entertainment-related consumption expectations, they differ in their intrinsic nature. Indeed, we introduce two types of producers in the model, since one of the producers is set to be a commercial organization ( ) and the other is set to be an online community ( ). As such, both producers differ in the nature of their incentives to produce inasmuch as commercial organizations are driven by traditional profit-oriented motives whereas community-based production activities are rather driven by altruistic, ideological or signaling purposes (see Rossi, 2006 and Flowers 2008 for general insights about motives and incentives to produce within online communities).

F

C

From an output-related point of view, we suggest that both producers deliver different services according to their nature. We hence state that commercial organizations are more likely to produce high-quality digital goods and that communities are more likely to build up innovative distributive tools for users to easily get access to the content they provide. The products we consider here are not only batches of files but also the distribution channels that are developed by both organizations to diffuse digital goods. As a consequence, each organization sells a differentiated product in a ‘à la’ Hotelling framework, the firm (resp. the community) being located at 0 (resp. 1).

On the demand side, we consider adopters who are uniformly distributed on the Hotelling line and whose total mass is equal to 1. They adopt one product that is provided by either the commercial organization or the community. We define x as the location of each product on

the line (x

 

0;1 ). Consumers whose x is close to 0 exhibit preferences for the digital

product provided by the commercial organization whereas consumers whose x is close to 1

are more interested in adopting the digital product provided by the community. Utility functions are defined as follows:

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if adopts product from 1 if adopts product from

F C x C F r q q tx p F U r q q t x s C          

 

1

r is the gross utility adopters derive from digital consumption. tx (resp. ) is the

transportation disutility adopters get from adopting the product provided by the commercial organization (resp. the community).

1

tx

x (resp.

1x

) represents the distance between any

adopter’s ideal product and that provided by the commercial organization (resp. the community) and t is the traditional transportation cost parameter used when formalizing

product differentiation. p( ) is the price the firm charges to consumers when adopting

their product and s( ) represents the cost adopters have to face when adopting the

product provided by the community. For instance, refers to the opportunity costs an adopter has to face when adopting a product provided by the community (e.g., the amount of time she needs to assimilate and to be able to efficiently use community-based services). ( ) (resp. , ) is the level of quality that is provided by the commercial organization (resp. the community) when releasing its product. Such levels are positively appreciated by adopters when consuming one of the two products. In our general framework (

0 p 0  s s F q qF 0 C q qC 0

 

1 ), we also suppose that the commercial organization (resp. the community) can catch innovation outputs from the production activity of the the community (resp. the commercial organization) to enhance its own activity. In other words, we here define a situation in which both producers may freely appropriate innovation outputs that are developed outside their production boundaries.

 (

 

0;1 ) represents the share of innovation outputs that the commercial organization appropriates from the production activity of the community and (

 

0;1 ) represents the share of innovation outputs that the commercial organization appropriates from the production activity of the commercial organization. Such appropriation schemes are taken into account in the adopters’ decision-making and shape adoption patterns. Specific cases are next analyzed. As we previously underlined, both producers (i.e., the commercial firm and the community) differ in their motives to provide digital products. The commercial firm is driven by pure for-profit purposes whereas the community is generally perceived to carry out production activities for rather altruistic or signaling reasons. Yet, although such a viewpoint may lead one to define distinct objective functions for these two types of producers, we consider that the objective function of the community can be defined as a traditional profit function. Indeed,

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although one may think that community-based activities are not carried out for pecuniary reasons, we observe that such activities require funds to be carried out, mostly for technical reasons. For instance, since servers are costly to acquire and maintenance activities are often required to avoid traffic overloads, financial aspects also have to be taken into account. As a consequence, both production activities are led so that these remain sustainable. In the case of commercial organizations, profit-maximizing decision-making is likely to shape the level of innovation effort. In the case of community-driven production activities, innovation decision-making is led for sustainability-related reasons and pecuniary resources are apprehended as a means of meeting technical constraints and dealing with external ‘disturbing’ effects (e.g., server crashes or legal penalties when activities are shown to be illegal). As such negative externalities are likely to occur at any time, we suggest that administrative players acting within online communities seek to raise funds from various sources to prevent uncertainty and meet technical imperatives. We define the producers’ objective functions as follows:

2 2 1 2 1 2 F F C C n p q S n a q          

 

2

 is the profit function of the commercial organization when supplying its product. We define nF (nF

 

0;1

S is the surplus function of the community when providing its product online. nC (

) as the mass of consumers who adopt the product provided by the firm.

 

0;1

C

n  )

the mass of consumers who adopt the product released by the community. a is the

Contrary to

is marginal

the adopters. – pecuniary – reward the administrative staff of the community collect from

p, a (a0) is not a retail price (i.e., a price that any adopter has to pay to get

the product) but can be seen as a ‘participation’ price. By ‘participation’ price we mean the advertising banner ‘clicking’-behaviors. We suggest that such a ‘participation’ price is not set by the community from market-based mechanisms, as donations are not likely to be imposed within the community and advertising-issued revenues depend on the price set by external players. As generally assumed, we suppose that both producers face innovation production costs whose shapes are quadratic.

marginal reward the community earns from either adopters’ donations and adopters’

 and S differ in the nature of the gross benefit both organizations generate from production.

Whereas p is a control variable endogeneously set by the commercial organization,

represents an exogenous variable that the community cannot set. Such a difference introduces

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in our m

e

to produce or not to produce;

community simultaneously set

t and each producer can use them in the product they odel an asymmetry in the abilities a producer has to carry out innovation-based production activities while attempting to remain sustainable on the market. Indeed, th commercial producer can maximize her profit by setting both her retail price and quality whereas the community is only able to set the quality it provides to maximize its surplus. We define the adoption decision process as a four-step game:

- at step t0, both the commercial organization and the community decide whether

- at step t 1, the commercial organization and the

their qualities qF and qC; producers fully have mutual knowledge of the qualities

that are produced in the marke

individually release if the institutional regime allows them to do so; - at step t2, the commercial organization sets its retail price p;

- at step t3, consumers adopt the product released by either the commercial

organization or the community.

Our model stands in a framework in which all agents have both full and common knowledge

th qualities are defined do apply.

(i.e., ) into its roduct whereas the com ial organization only uses its own innovation effort (i.e., ). of the production outcomes, whether they concern prices and qualities. We here suppose that

eir expectations about the way prices and

We consider three cases in our model. In the first case (case 1), the community integrates both its innovation effort (i.e., qC) and that of the commercial organization qF

p merc qC

Such a case refers to the actual situation one may easily observe in the market of digital goods in which community-based activities are presented to be illegal – ‘pirate’ – activities (e.g., peer-to-peer networks, illegal streaming websites). In the second case (case 2), communities are not able to appropriate innovation efforts that are made by commercial organizations. This particular case represents the situation one would observe if copyright enforcement is efficient enough to prevent community-based organizations from illegally appropriating commercial innovations, as officially wished by an increasing body of commercial players. In the third case (case 3), both producers are able to integrate both their own innovation effort and a – more or less high-leveled – share of that delivered by the competitor into their products. Such a third case depicts a situation in which outputs are shared and can be used by both producers.

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Our model aims at analyzing to what extent a paradigm shift may be profitable for the two types of producers. To put it simply, we here intend to know whether a ‘closed’ innovation paradigm (case 2) or an ‘open’ innovation paradigm (case 3) is likely to deliver (i) a better level of profit (resp. surplus) and (ii) a higher-leveled joint-innovation outcome than those achieved in the current – somehow ‘asymmetric’ – situation (case 1). Moreover, we analyze the impact of closeness and openness on the incentives of both producers to innovate when they are likely to evolve on the same market. Such results have to be considered for policy applications to measure whether a ‘closed’ or an ‘open’ regime stimulates pro-innovation production behaviors while being profit-improving.

3. Optimal quality and pricing strategies

e intend to identify the optimal quality strategies that the commercial organization and the ommunity have to set to maximize their profit/surplus as well as the optimal retail price the W

c

commercial organization can charge its consumers. To do so, the four-step game we previously presented is solved by backward-induction. From the general case captured in

 

1

(3.1.), we consider three specific cases, namely the ‘current situation’ case (case 1), the ‘closed regime’ case (case 2) and the ‘open regime’ case (case 3). For these three cases, we identify the optimal outcomes (i.e., retail price, quality strategies, profit and surplus) both players achieve depending on the environmental parameters (i.e.,  and ) they face (3.2.).

3.1. Analysis – General case

nctions of the adopters are expressed as follows:

Here, values for

In the general case, the utility fu

1

if adopts product from

x

C F

r qq t x s C

     



if adopts product from

F C

r q q tx p F

U     

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The adopter’s choice is considered at step t3. The adopter who is indifferent between the

two products is located at location x, given by:

 

1F C C F rq q    t x p r q qtxs We find that 

1

1

( ) 1 2 F C q q s t 2 x p t         

 

3  xx

All the adopters who are characterized by parameter adopt the product that is provided

ssumption 1a.The market for digital products is fully-served, i.e., is sufficiently large.

ts by the commercial organization and all the other adopters adopt the product that is provided by the community. We make three assumptions about the structure of the market for digital products.

A r

Assumption 1a stresses that all the adopters are likely to adopt one of the two produc released on the market, i.e., rqF qC   tx p 0 and/or rqC qFt

1x

 s 0 .

Such fully-serving adoption patterns occur when is sufficiently large.

ssumption 1b. No competition crowding-out effect applies on the market for digital

Assumption 1b suggests that both producers share the market, i.e.,

r

A

products.

 

0;1

x . Assumption 1b

implies that the difference between retail price p and opportunity costs is lower and upper

bounded so that

s

1

1

1 

q

1 

F C F C

q  q   t p sq   t

tion is all the more lik ansporta 

ely to apply as tr

 

tion costs t

. Let us note that

such an assump are shown to be

ssumption 1c. The commercial organization and the community serve the market with

high-leveled.

A

differentiated products whose level of differentiation t is sufficiently large, i.e.,

2 1 3 s t     .

We here explicitly specify a level of differentiation above which both commercial and t

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Figure 1 presents the adoption patterns which apply under assumptions 1a, 1b and 1c.

Figure 1. Adoption patterns

ithin this framework, the market shares and held by each type of producers are low

W nF nC

defined to be strictly positive and are expressed as fol s:

1 1 ( ) 1 F C q  q   s t  if 2 2 1 1 1 ( ) 1 if 2 2 i F C F C p i F t t n n n q q s t p i C t t                 

 

4

From

 

2 and

 

4 we obtain

2 2 1 1 ( ) 1 1 , , 2 2 1 1 ( ) 1 1 , , 2 2 F C F C F F C F C C q q s t q q p p p q t t q q s t S q q p p a q t t                                     2 2  

 

5

At step , the commercial producer sets her optimal pricing strategy. Let us bear in mind that the co munity is not able to design such a pricing strategy inasmuch as ‘participation’

rice t as a parameter. 2 t  m is se p a

The profit-maximizing program of the commercial producer is:

1

1

( ) 1 1 2 max , , 2 2 F C F C F p q q s t q q p p p q t t             

e shown that the Nash equilibrium at t 2

2

It can b  is characterized by the following price:

* , 1 1 ( 2 F C F C q q s p q q      t)

 

6

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* ;

F C

p q q depicts a maximum state since

2 2 1 0 p t       . We verify that

Equation

 

6 provides preliminary insights about the impact of the quality of the products deliver the two players on the retail price * *

;

F C

pp q q charged by the commercial

ed by

organiza On the one hand, we observe that rice positively depends on both the qu lity the commercial organization se ing its product (i.e., ) and the share of innovation outputs that it appropriates from unity’s activity (i.e.,

tion. a

the level of such a p ts when releas

the comm

F

q

). On innovation output provided the other hand, its level negatively depends on the quality of the

by the community (i.e., qC ) as well as the share of commercial innovation outputs the

community is able to integrate into its product (i.e.,  ). Overall effects are nevertheless more likely to be apprehended when optimal quality-based strategies are identified.

When the commercial organization charges retail price *

F, C

pp q q , optimal levels of

profit and surplus are defined so that

2 * 2 * 2 ; 1 1 8 2 1 1 ; 1 1 3 4 2 F C F C F F C F C C q q q q s t q t S q q q q t q t                        1 1 s

t step , both producers set their optimal quality strategies, namely, and . Optimal e 1 tq*F qC* A

* * ; F C pp q q

levels for quality are set according to the optimal retail pric the commercial organization is expected to charge at step t2.

he profit-maximizing program of the commercial producer is T

2 * 1 1 2 max ; 1 1 8 2 F F C F C F qq qt  q   q  s t   q

and the surplus-maximizing program of the community is defined by:

* 1 2 4 C F C F q t 1 max ; 1 1 3 2 C C S q q    q   q   s t  q

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The quality-related reaction functions of both producers are

  



  

2 1 1 1 ( 1 4 1 4 C F C C F q s q q t q q a t                     ) t

 

7

y solving system

 

7 we find that the Nash equilibria at step t1 are as follows:

B

2 * * 1 2 1 4 1 4 1 4 C q a t           4 F q a t s t t t          

 

8

Under assumption 1c, we find that

2 2 * 2 1 4 0 4 F t q t         and 2 * 2 1 0 C S q      . As such, Nash

equilibria and depict maximum states when the commercial producer (resp. the ze

Let us note that an asymmetry in the design of optim

occurs. Indeed, we see that the community does not take the quality strategy of the commercial organization into account whereas the commercial player integrates that of the community into her own quality strategy. Such an asymmetry here results from the differing

et their prices at ste

* F

q qC*

community) optimi her profit (resp. surplus) function.

al quality strategies of the two producers

abilities of both producers to s p t2 (i.e., retail price p and

quality to th th mmercial organization. When retail price

‘participation’ price ). being exogenous, the community is not able to align its level of at of

a

e co

a

pis set so that the profit of

the commercial org nization reaches its optimal statea **

qF;qC

, optim

positive or null.

al quality strategies are defined so that the commercial organization benefits from a positioning advantage. This positioning advantage allows it to set its level of quality according to the level provided by the community and prevent the community from doing so. The optimal pricing strategy of the commercial organization thus allows it to consider the community as a productive entity which is not able to react to the quality strategy it sets.

As already suggested by assumption 1c, we restrict our analysis to high levels of transportation costs. Moreover, we suppose that optimal quality levels are always found to be

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Assumption 2.Both producers serve the market with differentiated products so that optimal quality strategies do not apply for negative levels, i.e.,

2 2 1 2 s s a t       .

From assumption 2, we define an analytical framework within which the two types of producers maximize their profit/surplus by setting qualities whose levels are positive or null. Although *

1

4 C q a t  

 is found to be positive or null for any values of t,  and a, we

2 * 2 1 1 4 0 1 4 4 F q a t s t t t  

characterize the values of tabove which   

 , i.e.,

ly

 

 

1

2a4t s t

 

0. We find that qF* 0 if and on

2 2 1 2 s s a t  .      ls are charact

From assumption 1c and assumption 2, we now restrict our analysis to transportation costs

whose leve erized so that

2 2 2 1 1 max , ; 3 2 s ts sa                        

Some comments have to be made about the weight of the share of innovation outputs provided by the community (i.e., the commercial organization) the commercial organization

(resp. the community) is te into i.e.,

.

able to integra its product (  , resp. ).

* 2 * 1 1 2 1 1 F C q q a 4 1 4 4 t t a t                   

 

 

2 1  a 4t s t * 2 2 2 * 2 1 1 4 4 8 1 1 4 0 F C q t t t t q                               

From , we unsurprisingly find that the optimal level of quality provided by the community negatively depends on the share of commercial appropriation

 

8

 whereas the optimal level of quality set by the commercial organization positively depends on such a share. In a similar

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fashion, we observe that the optimal level of quality provided by the commercial organization negatively depends on the share that the co munity appropriates from the commercial player. Yet, one striking result is that the way the commercial organization appropriates community-based innovation outputs does not directly shape the level of innovation outputs

the community sets. At optimal states, the pricing strategy m

* C

q p*  p*

qF;qC

l innovation outputs for llingness to innovate. has a positive ef

pact on the comm

of the commercial organization is defined so that appropriating commercia

munity-based purposes has a utral effect on the community’s wi

Finally, we also unsurprisingly observe that the ‘participation’ price fect on the community’s willingness to vate while it has a negative im ercial

com ne

inno

a

organization’s.

Lemma 1. At the optimal state, the commercial organization sets out strategies

 

2 2 ** ** 2 2 1 1 4 1 4 ; ; 1 4 4 1 4 8 F a t s t a t s t q p t t t t                     

and makes profit

 

2 2 ** 2 2 1 1 1 4 1 4t a t s t     32t                 

whereas the community sets out a quality

strategy **

1

4 C q a t  

and makes surplus

 

 

2 2 2 2 2 ** 2 2 2 2 2 1 1 1 ( 3 ) 1 1 32 1 4 4 1 4 a s t S a a t t t t                         .

When both produ

al pricing and cers maximize their profit/surplus, they set out optim

ovation strategies, namely

** *

and . From

F ** C q

 

6 and

 

8 * ;

q p , we find that the optimal

inn

pricing strategy of the commercial organization is such that

2 ** the ** *; * 8 F C t p p q q         . As a conse ce, com 2 1 a 4t s t t     merc

quen the optimal profit achieved by

organization is 1 4     ial

2 ** ** ** ** 2 2 1 1 , , 1 4 32 1 4 F C q q p t s t t    

t

2 ** a               al level of  

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surplus achieved by the community is

 

 

2 2 2 2 2 ** ** ** ** ** 2 2 2 2 2 1 1 1 ( 3 ) 1 , , 1 32 1 4 4 1 4 F C a s t S S p q q a a t t t t                           . ay iti

Proposition 1. At the optimal state, the level of profit (resp. surplus) the commercial organization (resp. the community) achieves is alw s pos ve if both products are

differentiated enough (i.e.,

2 2 2 1 1 max s, s s a ; t                 ).

** ** **, **, ** 0 F C q q p    and 3 2          

Proof of proposition 1. From assumption 1c and assumption 2, we find that

** ** **, **, ** 0

F C

SS q q p  .■

fit/surplus within the analytical framework we have previously defined. The commercial organization and the Proposition 1 highlights that both producers are able to make positive pro

community are thus always shown to provide innovation outputs, their activities being sustainable if levels of appropriation innovation

 ,

 

0;1 apply. As such, proposition 1 2 stresses that the provision of highly differentiated products always leads both producers to serve the market at step t0.

Our general analysis (i.e., for which

 ,

 

0;12) reveals preliminary results about the

based activities. Indeed, the

weight of innovation appropriation on the sustainability of both commercial and pricing strategy asymmetry we have introduced in our model also induces an asymmetry in the abilities of both producers to set out innovation strategies. Here, the level of quality that is provided by the community into account. We conversely find that al pricing strategy prevents the community from integrating the quality strategy optimal pricing allows the commercial player to set out her optimal quality strategy by taking such an optim

of the commercial organization in its own innovation decision-making. Commercial and community-based activities are nevertheless found to be both sustainable inasmuch as their related optimal level of profit/surplus are always shown to be positive.

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3.2. Analysis – Specific cases

From the results of the general case we have obtained in the previous sub-section (3.1.), we consider three specific cases, namely the ‘current situation’ case (case 1), the ‘closed regime’ case (case 2) and the ‘open regime’ case (case 3). For these cases, we now specify the values of the share of commercial (resp. community-based) innovation outputs the community (resp. the commercial organization) is able to integrate into its product. Hence, table 1 presents the values’ specifications according to the institutional framework we consider.

Table 1. Cases and environmental parameters

‘Actual situation’ ‘Closed regime' ‘Open regime’

Case 1 Case 2 Case 3

 ,

 0,

 

0;1

 0, 0



 

0;1 ,

 

0;1

We distinguish the cases in which appropriation strategies cannot apply (i.e.,  0and/or 0

  ) from those in which such strategies are possible (i.e., 

 

0;1 and/or 

 

0;1 ). Let us bear in mind that our analysis aims at identifying the type of regime that is likely to provide higher-leveled outcomes. As such, we do not consider  and as control variables that can be set out by both players but as parameters whose values depend on the environmental conditions in which the commercial organization and the community carry out

their ctivities. Th hed by bo ell as their trategies,

are defined from the re ressed in lemma 1.

For each case we have to consider values for defined so that both assumption 1c and assumption 2 are respected. Such a range of values depends on the values for

a e outcomes reac th players, as w quality/price s

sults st

t

 and . ysis is carried out in the ‘current situation’ case hold for values t

Therefore, the results that are found when the anal

2 2

(1 ) s s s a

 



 

defined so that max ,

3 2

t  . The results that

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defined so that 2 1 max , 3 2 s s s a t      

  whereas those obtained in the ‘open regime’

framework hold for values t defined so that

2 2 2 1 1 max , 3 2 s s a s t                .

Lemma 2a. In the ‘actual situation’ case (case 1), the commercial organization sets out

strategies

** ** 2 2 ; ; 4 1 4 8 F q p t tt t        

and makes profit

1 4 4 1 4 a t s t a t s t                

2 ** 2 2 1 1 4 32t 1 4t a t s t            

  whereas the community sets out a quality strateg

    y

 

2 2 2 1  a 1  (s 3 )t ** 1 4 C q a t

and makes surplus ** 12 2 2 2 2

32 1 4 4 1 4 S a a tt tt                 .

Such results are obtained by substituting  by value and considering 0  so that 

 

0;1 . Let us note that the quality strategy set out by the community is not here related to the level of

novation appropriation c sen by the commercial organization.

in ho

Lemma 2b. In the ‘closed regime’ case (case 2), the commercial organization sets out

strategies

**; ** 4 ; 4 1 4 4 1 4 8 F a t s t a t s t q p t t t t         

   and makes profit

2 ** 2 1 1 4 32t 1 4t a t s t       

  whereas the community sets out a quality strategy

** 1

4

C

q a

t

and makes surplus

 

2 ** 2 2 2 1 1 32 1 4 4 1 4 a s S a t t t t  ( 3 )t a           .

Such results are obtained by substituting both  and  by values 0. Let us note again that the innovat quality strategy set out by the community is not here related to the level of ion appropriation chosen by the commercial organization.

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Lemma 2c. In the ‘open regime’ case (case 3), the commercial organization sets out strategies

 

2 2 ** ** 2 2 1 1 4 1 ; ; 1 4 4 1 4 8 F a t s t a q p t t t t                       profit 4t s t  and makes

2 2 ** 2 2 1 1 1 4 32t 1 4t a t s t                     

whereas the community sets out a

quality strategy **

1

4 C q a t  

and makes surplus

 

 

2 2 2 2 2 ** 2 2 2 2 2 1 1 1 ( 3 ) 1 1 32 1 4 4 1 4 a s t S a a t t t t                        

ontrary to cases 1 and 2, we see that the quality strategy set out by the community is here organization.

The outcomes reached by the commercial organization and the community in the three cases ly to differ. Such varying results may highlight p

the two types of players. We next develop a comparative statics analysis to identify such

4. Identifying profitable and innovation-improving regimes

that we aim at analyzing to what extent a paradigm shift may be profitable for e two types of producers. Moreover, we here intend to know if a ‘closed’ innovation

hift dilemma’ policy makers face when having to choose between a’ closed’ novation regime and an ‘open’ one.

.

C

negatively related to the level of innovation appropriation chosen by the commercial

are like otential conflicts of interest between

conflicts.

Let us remind th

paradigm (case 2) or an ‘open’ innovation paradigm (case 3) is likely to deliver (i) a better level of profit (resp. surplus) and (ii) a higher-leveled joint-innovation outcome than those reached in the current – somehow ‘asymmetric’ – situation (case 1). Figure 2 illustrates the ‘paradigm s

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Figure 2. Paradigm shift dilemma

The way policy makers may decide to choose between the ‘closed’ regime and the ‘open’ regime depends on the outcomes these two are likely to provide. Switching from the current situation to a new regime directly affects the levels of price **

p , profit **, surplus and

innovation outputs (i.e., , and

**

S

** F

q qC** Q**q**Fq**C ). The surplus the com rcial

organization may derive from a regime switch as well as the global innovation effect such a switch leads to allow us to identify the regime which delivers the best outcomes. We next present a comparative statics analysis which presents the outcomes – gains or losses – the ‘closed regime’ and the ‘open regime’ provide when considering optimal surplus, prices and e first present the general results and identify related conditions (4.1.).

4.1. Comparative statics – General results

me

innovation outputs. W

We then illustrate the equilibrium properties by considering a numerical example. Welfare issues are also discussed (4.2.).

We compare the optimal levels reached when shifting from the ‘actual situation’ framework to the ‘closed regime’ (resp. ‘open regime’) one. As such, we distinguish two cases, namely the ‘closed shift’ (denoted by 2,1) and the ‘open shift’ (denoted by 3,1). A comparative

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statics analysis enables us to measure the impact of the paradigm shift on the levels of optimal surpluses (**and **

S ), price (p**) and innovation outputs ( and ).

or comparison purposes, we identify the range of values for tion 1c and ssumption 2 hold. In the ‘closed shift’ case,

** F q t , ** C q Q**q**FqC**

so that both assump

such values have to be defined so that F a

2

2 2 1 (1 ) s 1 s s s       2 2 1 1 max , max 3 3 2 3 2 a  s  s s   a          , . In the  t ,    

‘open shift’ case, values for t have to be defined so that

2

2 2 2 2 1 2 (1 ) max , , max , 3 2 2 3 2 s s a s s s s a s s a t              1    

The impact of the ‘closed shift’ (resp. ‘open shift’) on the optimal

price level is expressed by

 

 

.

Proposition 2. The optimal price level of the commercial organization increases when a shift to either the ‘closed regime’ or the ‘open regime’ applies.

Proof of proposition 2.

** 2,1 1 4 8 2 8 4 1 4 2 1 4 1 4 8 p a t s t t tt t tt 4 4 1 1 1 a t s t a t s t t                                    (resp.

2 2 ** 3,1 2 2 2 1 4 4 1 1 1 4 8 1 4 8 1 4 8 a t s t a t s t p a t t t t t t                         ). From assumptions 1c and 2, we find that **

2,1p 0

  (resp. **

3,1p 0

  ).■

Proposition 2 highlights that switching to another regime (i.e., ‘closed shift’ or ‘open shift’)

players nowadays consider shifting to either a ‘closed regime’ or an ‘open regime’.

Proposition The level of profit reached by the commercial provider increases when a shift to whether the ‘closed regime’ or the ‘open regime’ applies.

The impact of the ‘closed shift’ (resp. ‘open shift’) on the optimal ercial organization is expressed by enables the commercial provider to charge a higher price than she does in the ‘actual situation’ context (i.e., case 1). Such a result – at least partially – explains why commercial

level of profit of the comm

3. Proof of proposition 3.

2 ** 2,1 2 2 1 1 1 4 32t a t s t 1 4t 1 4t                  (resp.  

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2 2 2 ** 3,1 2 2 1 1 1 4 4 32 1 4 p a t s t a t s t tt                  ). From assumptions

1c and 2, we find that **

2,1 0   (resp. ** 3,1 0   Such a decrease sts.

pact of the ‘open shif the

).■

ew according to which

Proposition 4.The level of surplus the community generates from its activity decreases

a shift to the ‘open reg is also identified in the ‘closed shift’ case for low-leveled tran o

Proof of proposition 4. t’ (resp. ‘closed shift’) on the optimal

community is expressed From proposition 3, we see that both regime shifts are likely to improve the level of profit of the commercial organization. As such, it qualifies the traditional vi

profits only increase in a framework in which the ‘closed regime’ applies.

when level of surplus of ime’ applies. sportation c The im by

 

 

2 2 2 ** 2 2 3,1 2 2 2 1 1 1 1 1 32 1 4 4 S a a t t t                     (resp.

 

  

2 2 ** 2,1 1 1 4 a S a t s t t    2 2 1 1 1 4 4 1     4 tt              ). From assumptions            

1c and 2, we find that **

3,1S 0

  . **

2,1S 0

  if and only if a

  

4t 2 s t 

0. We easily

  

2

 

show from assumption 2 that a 4t s t

0 for low values of parameter t(i.e., 1

4

t ).■

Proposition 4 reveals that a regime shift is always detrimental to the level of surplus the

suc ehow

when a regime shift d re likely to co-e e regime may be.

innovate.

community derives from its activity. Nevertheless, let us point out – from proposition 1 – that h a level is always found to be positive. Therefore, although a regime shift has a som detrimental impact on the community, it does not lead it to stop providing digital products. Our surplus analysis stresses that the two types of producers both obtain positive surpluses

applies an that they a volve whatever th

Such a shift may however shape their production patterns and influence their willingness to

Proposition 5. The level of innovation outputs the commercial provider delivers at the optimal state increases when a shift to either the ‘closed regime’ or the ‘open regime’ applies.

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Proof of proposition 5. The impact of the ‘closed shift’ (resp. ‘open shift’) on the optimal

level of innovation outputs provided by the commercial organization is expressed by

** 2,1 2 2 4 1 4 4 1 1 1 4 4 1 4 4 4 1 4 1 4 F a t s t a t s t a t s t q t t t t t t t                                           (resp.

 

 

 

2 2 ** 1 1 a 4t s t 1 a 4t s t 1 1 1 q a                 ). 3,1 2 2 2 1 4 4 1 4 4 1 4 4 F t t t t t t               

Again, from assumptions 1c and 2, we find that ** 0

q   2,1 F   (resp. ** 0 q 3,1 F   ).■

Proposition 5 suggests – as this is the case for price levels – that both ‘closed’ and ‘open’ ercial

te

shift to the ‘open regime’ applies.

shifts lead the commercial provider to deliver a higher level of innovation outputs than that she delivers in case 1. Put it differently, switching to another regime motivates comm players to provide higher-leveled qualities.

Proposition 6. The level of innovation outputs the community provides at the optimal sta remains the same when a shift to the ‘closed regime’ applies whereas it decreases when a

Proof of proposition 6. The impact of the ‘closed shift’ (resp. ‘open shift’) on the optimal

level of innovation outputs provided by the community is expressed by

** 2,1 1 1 0 4 4 C q a a t t     (resp. **

3,1 1 1 4 4 C a qa 4 a t t t  

     ). As such, we find that

and ).■

innovate whereas a shift to the ‘closed

Propositions 5 and 6 evidence a conflict of interest between th

the commercial organization and the community) about their willingness to innovate. Indeed, we find that commercial players are clearly motivated to innovate when a regime shift applies

** ,1qC 0 ** 3,1qC 0   2 

Proposition 6 stresses that a regime shift has no beneficial effect on the likelihood of the communities to level their innovation efforts up. Moreover, we point out that a shift to the ‘open regime’ negatively affects their willingness to

regime’ is found to have a neutral effect on the level of innovation efforts they provide.

e two types of producers (i.e.,

whereas communities reduce their innovation levels in such a framework. From a regulatory point of view, one may wonder if both regimes are likely to exhibit ‘pro-innovation’ (i.e.,

** 0

Q

  ) or ‘anti-innovation’ (i.e., ** 0

Q

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Proposition 7. ‘Pro-innovation’ effects are always likely to apply in the case of the ‘closed shift’ whereas ‘anti-innovation’ effects may appear in the case of the ‘open shift’.

Proof of proposition 7. See Appendix.

Proposition 7 suggests that the willingness to innovate of the two types of producers strongly depends on the nature of the regime shift (i.e., ‘closed shift’ or ‘open shift’). From a

shifting-on viewpoint, we find that to the ‘clo

comparis a shift sed regime’ leads to the provision of

es whereas a shift to the ‘open regime’ leads to the provision of

lower-Table 2. Regime shifts and gains

rom table 2, we see th t the ‘closed shift’ is more likely to improve the outcomes reached by e commercial provider at the optimal state than ‘the open shift’ does. Besides, proposition 7 vidences that the c mmercial organization and the community have higher-leveled higher-leveled outcom

leveled ones. Such a result may be taken into account by policy makers when designing suitable innovation-enhancing policies.

The following table (table 2) summarizes the main results we have obtained when analyzing optimal prices, surplus and innovation outcomes while considering the two types of regime shifts.

‘Closed shift’ ‘Open shift'

** p    **     ** S  /?  ** F q    ** C q  0  ** Q    / F a th e o

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incentives to innovate when they act in a ‘closed regime’ framework. Some results however main unclear when we carry out a general comparative statics study. Indeed, the real impact of the ‘closed shift’ on the surp that of the ‘open shift’ on the global innovation outcome are likely to depend on the values of the parameters of the model. re

lus of the community as well as

4.2. Numerical example

We illustrate the equilibrium properties by working on a numerical example. Some diagrams are also introduced. Let us suppose that r10, a1, s0.5, 0.3and  0.8. Our

analysis is here held in a framework in which assumptions 1a, 1b, 1c and 2 are satisfied when

imultaneously dealing with cases 1, 2 and 3. As e

onsidering values fo defined so that

s such, we carry out the num rical analysis by

r t

  

c

 

2 2 0.3  2 0.5 0 0.5 1 0.5 max , , , 3 3          , i.e., 2 (1 0.2) 0.5 1      .5 1  2  0.5 2 t   1 0.5 0.5 3

t    . For illustration purposes, w ri r n is by ring

values for t so that

e rest ct ou umerical analys conside

0.5;1.2

t .

**

Figures 3 and 4 exhibit optimal profits (resp. surpluses ) as functions of the transportation costs. We moreover consider the levels reached in the three regimes

1 to 3).

**

S

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Figure 3. Profits

From figure 3, as found in the general comparative statics study, we see that the level of profit the commercial organization reaches in case 1 is always lower than that reached in cases 2 and 3. Let us note that the profits are all increasing in the transportation costs. Besides, figure 3 shows that there is a value for t above (resp. below) which the commercial provider

receives a higher-leveled profit when a ‘closed shift’ (resp. ‘open shift’) occurs. In our specific numerical example, such a level is equal to t0.62681. We therefore point out that a

‘closed’ regime does not always allow commercial players to reap the highest levels of profits. Indeed, product differentiation has to be taken into account to measure to what extent a ‘closed shift’ has to be preferred to an ‘open’ one. This result presents the benefits the commercial organization may derive from using the innovation outputs delivered by community-based activities when transportation costs are high.

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Figure 4. Community’s surpluses

Figure 4 illustrates the levels of surplus the community generates from its production activity according to the regime that applies. As already pointed out when analyzing profits, surpluses functions are all increasing with transportation costs. We unsurprisingly find that the surplus of the community is higher in case 1 than it is when a regime shift occurs. Following a regime shift, surplus’ levels are moreover higher in an ‘open’ framework than in a ‘closed’ one. We nevertheless observe – as a result from assumption 2 – that the community gets positive surpluses whatever the nature of the regime may be.

Profits’ and surpluses’ analyses confirm the preliminary results we have obtained in the general framework. Indeed, we find that the community better benefits from the ‘actual situation’ framework whereas the commercial organization generates higher-leveled profits when a regime shift occurs. An ‘open shift’ notably enables the commercial provider to reach higher levels when product differentiation is small whereas a ‘closed shift’ allows her to receive bigger profits when transportation costs are large.

Optimal levels of global innovation outcomes are represented in figure 5 as functions of parameter . Their studies allow us to better appreciate the relevancy of the public policies led to switching either to a ‘closed regime’ or an ‘open regime’.

**

Q t

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Figure 5. Global innovation outcomes

Figure 5 shows that global innovation functions are all decreasing with transportation costs. It evidences that the ‘closed regime’ leads both producers to deliver higher-leveled innovation outputs than they would if the ‘actual situation’ and ‘open’ regimes apply. Such a result highlights that the ‘open shift’ generates a global ‘anti-innovation’ effect when taking into account the production activities of both players. The ‘closed shift’ delivers the best level of global innovation effort. These facts contribute to support the policies which have currently been carried out to prevent communities from developing activities that are based on – illegal – appropriation patterns. These findings conversely also qualify the idea according to which open-like cooperation schemes are likely to provide higher innovation levels. Motives and incentives to innovate are thus shown to be weakened when the commercial organization and the community can share their innovation outputs. From a regulatory point of view, these results highlight that pro-innovation oriented policies should be based on a design upon which the mutual sharing of assets is not possible.

In contrast to the previous general framework we have specified, we branch out by discussing welfare outcomes to identify the nature of the regime shift that is likely to be socially-improving. Aggregate adopters surplus is equal to . Producers surpluses are equal to the sum of the commercial organization’s profit

** ** **

F

ASASAS

** C

Figure

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References

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