انتخاب مشکل متوالی و سیستم پاداش در علم باز

In this paper we present an original model of sequential problem choice within scientific communities. Disciplinary knowledge is accumulated in the form of a growing tree-like web of research areas. Knowledge production is sequential since the problems addressed generate new problems that may in turn be handled. This model allows us to study how the reward system in science influences the scientific community in stochastically selecting problems at each period. Long term evolution and generic features of the emerging disciplines as well as relative efficiency of problem selection are analyzed.

Nelson (1959) and Arrow (1962) first highlighted that the specific characteristics of knowledge considered as a public good result in a default in knowledge creation incentives. Consequently private investment in knowledge creation is below its optimal level. This very well known result appeared as a theoretical justification for public support of research which may (non-exclusively) be undertaken by funding a specific social institution, namely academia. In that respect, modern countries obviously support a network of public laboratories and academic researchers. After having focused on the social returns of public research,1 economists have logically begun to address the issue of the internal organization of the academic institution. Dasgupta and David (1994) have recently synthesized in an economic fashion the mertonian mechanisms at play within academia. According to Merton (1957), the functioning of the academic institution, he labels Open Science, relies on social norms 2 that generate a set of effective rules which stress a specific reward system in which priority is essential. The incentive mechanism at play may be sketched as follows. Peers collectively establish the validity and novelty of knowledge produced (peer review). The attribution of rewards is based on recognition by peers of the “moral property” on the piece of knowledge produced which increases the producer’s reputation within the community (“credit”). Dasgupta and David (1994) highlighted that Open Science functioning has two fundamental and original economic properties that contribute to its efficiency. First of all, it avoids some of the asymmetric-informational problems that might otherwise arise between funding agencies and scientists in public procurement of advanced knowledge: scientists themselves are certainly the most able to carry out verification and evaluation operations in the peer-review like procedures. Secondly, since it is precisely the very action of disclosing knowledge which induces the reward (reputation or credit increase), the reward system thus creates simultaneous incentives both for knowledge creation and for its early disclosure and broad dissemination within the community. That is why this mode of knowledge production has been said to have very interesting efficiency properties (Arrow, 1987) and even to constitute a “first best solution” for the appropriability problem (Dasgupta and David, 1994) as it solves the dilemma between knowledge creation incentives and knowledge disclosure incentives (Stephan, 1996). 3 Several modelling exercises have considered specific dimensions of the academic institution. Carmichael (1988) attempts to explain why does the tenure system exist: it is the only reliable employment contract that guaranties scholars will provide correct advises for employing high quality colleagues who might otherwise challenge their own positions. Lazear (1996) models the effects of several funding rules (e.g. weight more past efforts or the quality of the proposal, engage few big or many small awards, favor junior or senior researchers) on the incentives provided to scholars. Windrum and Birchenhall (1998) study the impact of the credibility based funding pattern on the evolution of a population of research units. Brock and Durlauf (1999) introduce a model of discrete choice between scientific theories when agents have an incentive to conform to the opinion of the community. Levin and Stephan (1991) propose a human capital model of knowledge production which fits the usual inverse-U shape of life-cycle scientific productivity. Carayol (2005) proposes a model of scientific competition in which overlapping generations of researchers compete at the different stages of their career while universities also simultaneously compete to hire the best scientists. In this paper we focus on another dimension of academic organization, namely the sequential determination of research agendas within scientific communities and the subsequent disciplinary knowledge production. Our point of departure is that even though competition between scientists is clearly important (associated with “winner-takes-all” rules and “waiting and racing games” issues, cf. Dasgupta and David, 1987 and Reinganum, 1989), it is only second, while the first and most important decision a scientist has to take is the choice of which research area and which problem she or he will investigate. This issue is usually referred to in the sociology of science as the “problem of problem choice” (Merton, 1957, Zuckerman, 1978 and Ziman, 1987).4 As a matter of fact, a very consubstantial organizational trait of the Open Science is the significant freedom given to scholars in defining and selecting their own research agendas. More, the selection of good problems is far from being marginal from scholars’ points of view in the academic competition: not all problems are the same in their eyes and in the ones of their peers. The model introduced in this paper addresses the issue of the impact of the Open Science reward system on the allocation of attention of the community of scientists ex ante, and on the resulting evolution of disciplinary knowledge ex post. 5 Scientific disciplines are represented as growing tree-like webs of research areas that are the repository of accumulated knowledge. At each period, researchers allocate their attention responding to academic incentives. It leads to the improvement of knowledge in a given area or to the investigation of a new area. Our main results are that the process exhibits path dependency (David, 1985) especially disciplines that are more specialized have a higher chance to become even more specialized. We also find that there is a decline in the generation of new research areas over time which can be balanced by increasing the rewards for performing pioneering research. We also study how the outcoming disciplines are shaped through tuning the various typical incentives of the Open Science rewarding process. Finally, we propose a welfare criterion which assigns a given social surplus to each new problem addressed. We show and discuss how to balance academic incentives for improving the decentralized allocation of scholars’ attention. The paper is organized as follows. The next section discusses the issue of modelling problem choice and subsequent evolution of disciplinary knowledge. The technical presentation of the theoretical model is the purpose of the third section. The fourth section is dedicated to the study of the generic properties of the process, while the fifth section studies parameters effects on the dynamics and discusses the characteristics of the outcoming disciplines. The sixth section introduces a welfare criterion and analyzes how the reward system should be tuned for an efficient allocation of attention. The last section concludes.

In this paper we have presented an original model of knowledge production within scientific disciplines. It is a graph theoretical model in which knowledge production is sequential. The main question tackled in the paper is how the specific incentives provided by the academic reward system influence researchers’ problem choice and thus shape the stochastic process of knowledge generation within scientific disciplines. Let us sum up the main results obtained. We first found that the process exhibits a sustained decline in the generation of new areas. We are inclined to compare this evolution and the progressive shift in the growth of scientific knowledge from “little science” to “big science” described by Price de Solla (1963). Our regime change concerns the rarefaction of new areas investigation while Price deals with articles production. It applies to a given discipline while Price’s statement concerns the whole body of scientific knowledge (though most empirical confirmations were performed of a single discipline, see. the survey of Fernandez-Cano et al., 2004). Lastly and most important, it is mainly due to incentive reasons rather than to a saturation hypothesis. This phenomenon is caused by the specific reward system in science which leads researchers to seek others’ attention. When the discipline grows, the relative rewarding of problems located in already developed fields increases: because their audience becomes larger, contributions to such domains are more likely to be cited. This is not to be seen as a fortiori negative: since more knowledge is likely to be produced in larger domains, early contributions there are likely to benefit to many late improvements. That is directly connected to the fact that the citation system traces and rewards knowledge spillovers. Nevertheless, this first result suggests that the rewards for performing pioneering research should be increased when the discipline grows in order to sustain research areas generation. We next found that the stochastic process exhibits path dependency with regard to the specialization of disciplines. More specialized disciplines tend to become even more specialized through time. We found that this property is enhanced when the concentration of scientists’ attention on the most rewarding areas is stronger. In addition to these first series of results, the study of parameters effects allowed us to highlight the possible occurrence of a quite ‘autistic’ dynamics leading to a ‘well’ form of discipline having left many research opportunities unexplored.21 We found that increasing the relative rewarding of pioneering research is again a key leverage parameter because, under such circumstances, it also (unexpectedly) renders general problems more attractive. We argued that such a situation is more likely when the relative rewarding through recording citations is outweighed by publication counts. Thus reinforcing the former mechanism may partly prevent such ‘science wells’ from occurring. We also provided a measure for social wealth generation for which we assume additionality over research areas, lower social returns of the very first problems resolution and, a limited number of interesting problems on each area. According to that normative criterion, society would like each area to be in turn explored up to a given level. The first best being not implementable, we studied how the tuning of the typical incentives affects the efficiency of the decentralized allocation of attention. Our results legitimate the academic reward system for orienting scientists’ attention. We showed that the three typical incentives of the academic reward system (rewards for novelty, audience and specialization) should be all at play simultaneously and should balance each other. Therefore, if some structural forces that are inherent to the characteristics of knowledge produced or to the historical organization of the community distort the influence of the various incentives of the academic reward system (e.g. prevalence or weakness of one type of incentives) there is room for science policy to correct such distortions. Nevertheless nobody would obviously consider deriving precise sound science policy measures from the very preliminary model presented above—indeed nor would we. Our goal here was mainly to show that models can be built to study and simulate the workings of academic communities: models which, once calibrated using empirical evidence (a crucial aspect of the future research agenda in our particular research area), could open the way for more concrete studies. Among the elements that would be worthily considered in further research are the impact of age and career stage on individual choices, the thematic mobility patterns of scientists, the impact of the academic organization in teams, laboratories and universities and, the strategic citation behaviors. For the time being, we can simply say that the studies of imperfect Open Science are just at their beginning.