Networked innovation and coalition formation: the effect of group-based social preferences

ABSTRACT

In this paper, we study the production and dissemination of public knowledge goods, such as technological knowledge, generated by a network of voluntarily cooperating innovators. We develop a private-collective model of public knowledge production in networked innovation systems, where group-based social preferences have an impact on the coalition formation of developers. Our model builds on the large empirical literature on voluntary production of pooled public knowledge goods, including source code in communities of software developers or data provided to open access data repositories. Our analysis shows under which conditions social preferences, such as ‘group belonging’ or ‘peer approval’, influence the stable coalition size, as such rationalising several stylized facts emerging from large-scale surveys of open-source software developers, previously unaccounted for. Furthermore, heterogeneity of social preferences is added to the model to study the formation of stable but mixed coalitions.

KEYWORDS:

• Coalition formation
• networked innovation
• open-source software (OSS)
• public knowledge goods
• private-collective model
• social preferences

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 We also refer to Swan and Scarbrough (2005) for an exhaustive literature review on networked innovation.

2 As shown by Harison and Cowan (2004), open-source software projects have also become relevant to firms in the sense that a certain degree of disclosure of development processes can boost profit margins when revenues are responsive to this kind of ‘openness’.

3 David and Keely (2003) use the same definition of coalition-building (‘network’ formation) used in our paper. However, they model the process of coalition formation among research units that seek competitive funding from a supra-regional program rather than developing new technology.

4 See, e.g. Lessig (2001), Benkler (2006), Hess and Ostrom (2007) or David (2008).

5 The latter, however, does not imply that the core group of developers remains invariably composed of the exact same people over time, as shown by Dalle and David (2008) in a simulation model of large-scale open-source software projects. Because of this ‘turnover’ of developers, the core group is more accurately described as a ‘quasi-stable’ community of agents, which nonetheless always has the appropriate size to intervene in the accessible parts of the code-base requiring further development.

6 As has been shown elsewhere, this joint public/private character can have different effects on contributions. If the private benefit has a market substitute, the joint character can undermine the willingness to contribute to the public good in situations where the market price of the substitute is sufficiently low (Cornes and Sandler 1984). See also Andreoni (1988), Kotchen (2006, 2009) and Vicary (1997, 2000) for opposite effects in the absence of market substitutes.

7 More generally, the private benefits to voluntary cooperation in this context are emphasised in many other studies of public knowledge goods. One can think for example of open access databases with tailor-made data management tools that benefit specific communities and individuals (David 2005), or hybrid funding arrangements – including both market and non-market tools – for openly available culture products on the internet (Lessig 2008).

8 This individual level need not be purely self-interested in the negative sense of the word, but can also have an altruistic quality. See, e.g. Gächter, vonKrogh, and Haefliger (2010) and Garriga et al. (2012) for a discussion on the effects of inequality aversion, fairness and reciprocity in the private-collective context.

9 Along these lines, Benkler (2006) has found that, in mixed or complex incentive schemes, such as those at stake in these large-scale digital collaboration networks, participants are driven more by social motivations (especially reputational benefits) and intrinsic motivations (such as ethics, curiosity and other personal values) than by the prospect of direct monetary rewards alone. In the life sciences, where potential commercial rewards from basic research are always a factor, especially with regard to university-driven research, Allarakhia found that the reciprocity benefits to be gained from participation in research consortia are often the key motivational factor (Allarakhia, Marc Kilgour, and David Fuller 2010).

10 Hoel (1992), Carraro and Siniscalco (1993) or Barrett (1994) laid the groundwork here, followed by e.g. Barrett (2003), Ulph (2004) or Kolstad (2007). Finus (2008) or Hovi, Ward, and Grundig (2015) provide a survey of this large body of literature.

11 David and Keely (2003) evaluate alternative possible external public R&D funding rules to determine the impact on coalition formation.

12 See, e.g. also Kosfeld, Okada, and Riedl (2009) or McEvoy (2010) on this issue.

13 In Sandler and Arce (2007), such impure public good production is set in the context of international development cooperation. Here, donor countries can also derive private benefits – e.g. through the sale of technology – in addition to the global public good benefits related to the increase in economic development and poverty alleviation. Finus and Rübbelke (2013) go on to study such ‘ancillary benefits’ of public good provision in a setting of international environmental agreements.

14 A Nash equilibrium in this membership game is therefore a set of announcements for which no developer will do better by unilaterally changing his or her announcement.

15 See, e.g. Hoel (1992), Carraro and Siniscalco (1993), Barrett (1994) or Kolstad (2007). For the implications of the formation of multiple coalitions, see Carraro (2003) or Hovi, Ward, and Grundig (2015) for a discussion.

16 Note furthermore that under the current specification it is possible for private benefits to outweigh public benefits to the extent that the reputation effect becomes negative if in Equation (1(1) ). Comparing both equations in Equation (1(1) ), developer welfare could consequently be lower when producing inside the coalition as opposed to outside, given certain parameter values. However, since we have modelled the game in such a way that it never pays for developers to produce public knowledge outside of the coalition, this possibility does not affect our equilibrium results. Indeed, if the coalition is profitable and internally stable – as defined in Section 3.2 and resulting from Assumptions 3.2 and 3.3, and expression (4) – no developer j inside the coalition will have the incentive to leave, whilst no developer i outside of the coalition will want to produce on his own. The situation where, e.g. thus never presents itself. In subgame perfect equilibrium, welfare for developers i outside of the stable coalition is simply and will always be larger than welfare inside the coalition because of the internal and external stabilities implicitly imposed by Assumption 3.3. If one coalition member was to leave the stable coalition to reap these higher benefits, however, cooperation breaks down and overall welfare would be zero. See also Footnote 19 on the importance of the threat point to micro-found such an outcome in a non-cooperative setting.

17 By construction of our finite strategy game, the non-cooperative Nash equilibrium will be unique. With , the vector correspondence of best responses to the strategy profile ) – where is a best response to for each i – and given that is upper semi-continuous and convex-valued, we know by Kakutani's fixed point theorem there is some . Given Assumption 3.2, we also know this equilibrium strategy profile is unique.

18 This assumption is not essential, any bargaining solution in the literature would deliver similar results.

19 As is well known, an outcome under axiomatic Nash bargaining is liable to suppress many details of the decision-making process. In order to rationalise such an outcome using a more strategic approach, the disagreement point is of vital importance. The seminal work of Binmore, Rubinstein, and Wolinsky (1986) for example presents a non-cooperative bargaining model of alternating offers which describes the bargaining process – including initial bargaining positions and motives – explicitly. The bargaining motive identified by Binmore, Rubinstein, and Wolinsky (1986) which arguably resonates the most with our setting of networked innovation relates to the fear of losing the opportunity to reach an agreement if negotiations are drawn out for too long. In this line of reasoning, the threat point can be thought of in its literal sense: in the event of a breakdown of the bargaining process the opportunity developers jointly strive to exploit will be lost, as not a single developer will produce. The threat of breakdown could for example come from another network of developers reaching an agreement sooner, thus gaining first-mover advantage whilst developers of the first community are still bargaining.

20 Building on d'Aspremont et al. (1983), Donsimoni, Economides, and Polemarchakis (1986) shows that stable coalitions exist under fairly general conditions. Alternative notions of stability leading to potentially larger coalitions, such as ‘farsighted stability’, are considered by Osmani and Tol (2009) and in Carraro (2003).

Additional information

Funding

We gratefully acknowledge co-funding from the European Commission, under the contract of three PF7-projects, including MICRO B3 (grant agreement 28758), BIOMOT (grant agreement 282625), GENCOMMONS (ERC grant agreement 284) and co-funding from the National Science Foundation (MIS Global Science Commons). Melindi-Ghidi gratefully acknowledges the support of the A*MIDEX project (n. ANR-11-IDEX-0001-02) and the FamPol project (n. ANR-14-FRAL-0007), both funded by the Investissements d’Avenir » French Government program, managed by the French National Research Agency (ANR). Sas thankfully recognises the financial support of the ‘Steunpunt Beleidsrelevant Onderzoek Fiscaliteit en Begroting’, funded by the Flemish government.