Academic commercialization and changing nature of academic cooperation

Abstract

Recent economic policies emphasize the role of academic science in technological innovation and economic growth and encourage universities and individual academics to engage in commercial activities. In this trend of academic commercialization, a growing concern has been expressed that its potential incompatibility with the traditional norms of open science could undermine the cooperative climate in academia. Drawing on the framework of evolution of the cooperation, this study examines the changing nature of academic cooperation under the current policy trend. In an ideal state of open science, academics are supposed to cooperate gratis and unconditionally. However, results predict that the commercialized regime could compromise underlying mechanisms of cooperation and allow defectors to prevail. As the trend further grows, academics would become more demanding of direct reward in exchange for cooperation, and they would refrain from engaging in cooperation but would prefer to work independently. Some interventions (e.g., centralized rewarding) could mitigate the problem but require delicate system design.

1 Introduction

Recent economic policies emphasize the role of universities and academic science in economic growth and encourage direct interaction between industry and academia (Argyres and Liebeskind 1998; Jensen and Thursby 2001; Etzkowitz 1998; Grimaldi et al. 2011; Poyago-Theotoky et al. Hauert et al. 2002). Consequently, in the trend called academic entrepreneurship or commercialization, universities and individual academics have increasingly been engaging in industry collaboration, technology transfer, and other commercial activities (AUTM 2007; OECD 2003). While this might increase the social contribution of academic science, a growing concern has been voiced that the commercialized regime could develop a self-regarding climate and compromise the basis of academic science (Dasgupta and David 1994; Nelson 2004). Behind this is a notion that the progress of science is critically underpinned by the norms of open science, and potential conflict between open science and the emerging regime has spurred intense debate (Murray and Stern 2007; Thursby and Thursby 2011; David 1998; Nelson 2004).

Under the norms of open science, scientific achievement is regarded as the property of the scientific community, not of individuals, and thus academics are expected to share their knowledge and resources with one another gratis and unconditionally (Merton 1973; Dasgupta and David 1994). This altruistic practice is crucial in academia, where individuals are highly specialized and often need cooperation, even from strangers (Walsh et al. 2007; Shibayama and Baba 2011). While the underlying norms seem reasonably respected, empirical studies have shown that academics engaging in commercial activities, industry collaboration, and other for-profit activities (commercial academics, hereafter) tend to deviate from the norms; i.e., they are non-cooperative and unwilling to share their knowledge and resources so that they can earn personal profit (e.g., Campbell et al. 2000; Walsh et al. 2007).

While non-cooperative behavior of commercial academics has been repeatedly reported, little attention has been paid to a graver consequence that commercialization could deteriorate cooperation even among ordinary academics who do not engage in any commercial activities, and fundamentally compromise the norms of open science (Shibayama et al. 2012). To fill this gap, the current study offers a model of academic cooperation drawing on the framework of the evolution of cooperation (Nowak and Sigmund 1998; Sigmund 2010). Evolutionary games allow rich predictions to various economic issues (e.g., Friedman 1998; Arce 1996). Exploiting the feature, this study aims to predict a broader impact of academic commercialization on the norms and practices of academic cooperation. In so doing, this study provides implications for science and technology policies and future empirical research. Results suggest that, under the commercialized regime, ordinary academics would become unwilling to cooperate gratis, become more demanding of direct reward in exchange for cooperation, and be hesitant to participate in cooperation. This study also evaluates the efficacy of some policy interventions to mitigate these issues.

2 Academic cooperation as indirect reciprocity

Academic science relies on various forms of cooperation. Some are continuous, such as collaboration between a pair of laboratories, while others are temporary, such as material transfer. In general, a mechanism behind continuous cooperation between a fixed pair of players and that behind one-time cooperation between a random pair are considerably different (Sigmund 2010). The focus of this study is the latter, where one academic needs expertise or resources that he does not have and has to receive cooperation from another academic. This is pivotal in open science characterized by extreme specialization and active interaction (Merton 1973). Particularly in natural sciences, academics frequently share various types of resources such as cells, chemicals, reagents, software, and data (Walsh et al. 2007; Campbell et al. 2000), and importantly, the majority of such transactions occur between strangers, not between fixed collaborators (Shibayama and Baba 2011). This practice sustains the progress of science by allowing academics to avoid redundant efforts, reproduce previous findings, and standardize research methods (Walsh et al. 2007).

In the ideal state of open science, academics are supposed to cooperate gratis and unconditionally. Thus, donors bear the cost of cooperation while recipients benefit by advancing their research. In general, such altruistic behavior is vulnerable to free riders, who receive cooperation but refuse to give. However, the reality is that the compliance is fairly high; for example, in life sciences, average academics make 3–5 requests for research tools and data every year, and greater than 80 % of the requests are fulfilled (Walsh et al. 2007; Campbell et al. 2000).

The paradoxical fact that altruistic cooperation is very common in the human society (e.g., blood contribution, donation), despite the temptation to free-ride, has provoked extensive debate in economics as well as sociology and biology, and several mechanisms behind altruistic cooperation have been proposed (e.g., Blau 1964; Bowles and Gintis 2011; Nowak 2012). Among others, Trivers (1971) showed that a cooperative strategy (i.e., tit-for-tat) can be evolutionarily stable in iterated Prisoner’s Dilemma Games. This form of cooperation is called direct reciprocity, since a fixed pair of players cooperate with each other. Going beyond this restricted player matching, Nowak and Sigmund (1998) developed a pioneering theory on indirect reciprocity. In this model, a player encounters a different opponent in each round of repeated games, so donors cannot be rewarded directly by their recipients. Instead, they are indirectly rewarded by someone else, where social information plays a key role. Simply put, players are assigned reputation based on their history of cooperation so that free riders are denied cooperation. Hence, defection based on bad reputation functions as a punishment. This model has offered a foundation for subsequent theories on the evolution of cooperation (Seinen and Schram 2006; Nowak 2012).¹ Another mechanism to sustain cooperation is network reciprocity, which relies on a spatial structure or network between players. Ohtsuki et al. (2006) suggest that a cooperative strategy can be sustained in structured network, where players’ interaction is not completely random. Further, a line of literature emphasizes the role of explicit forms of punishment and reward in sustaining cooperation (Fehr and Gachter 2000; Fehr and Fischbacher 2004; Sefton et al. 2007).

These theories explain academic cooperation to some extent. Direct reciprocity is widely observed as bilateral continual collaboration. Network reciprocity is also relevant, since real cooperation is influenced by social networks. There are some official sanction mechanisms; for example, funding agencies require their recipients to share their resources for open use after project completion. If academics do not comply with the rule and such an incident is reported, they could be stripped of their right to future funding. Many scientific journals have similar guidelines. Still, the effectiveness of these mechanisms may be questionable for the practical difficulty of policing and punishing defectors. Among others, I draw on indirect reciprocity to model the focal form of cooperation in this study. The principle of gratis cooperation is clearly articulated in various guidelines (National Academy of Sciences 2003), and non-cooperative behavior is generally despised. Academics who encounter non-cooperative donors sometimes spread a negative word, whereby not only direct victims of non-cooperation but also other academics in the community could eliminate free riders (Shibayama et al. 2012). Thus, a reputation mechanism appears to be at work in academic cooperation.

3 Model

This section formulates a model of unconditional cooperation under ordinary circumstances, and the following sections analyze how it is affected by academic commercialization. This study draws on a well-established model of indirect reciprocity based on the Donation Game (Sigmund 2010; Nowak and Sigmund 1998). From an infinitely large population of players, two players are randomly chosen as a donor and a recipient to engage in a one-shot game. Each player is endowed with a type, based on which a donor decides whether to cooperate with his recipient or to defect (i.e., deny cooperation). If the donor cooperates, he pays a cost (c) for preparing and providing the resources, and the recipient receives a benefit (b) by advancing his research. I assume b > c so that cooperation is collectively beneficial. If the donor defects, he pays no cost and the recipient receives no benefit. Apparently, defection is dominant in a one-shot game, but cooperation can emerge in iterated games with the aid of reputation. To illustrate this, the first model involves three types (Table 1) following the convention of prior literature (Sigmund 2010; Nowak and Sigmund 1998). One extreme type is ALLD, who is myopically self-regarding and always defects as a donor, representing free riders. The other extreme is ALLC, who indiscriminately cooperates as a donor. ALLD dominates ALLC because ALLD receives full cooperation from ALLC but does not bear the cooperation cost. The third type, DISC, is a discriminate cooperator. A DISC donor cooperates with recipients with good reputation but refuses to help those with bad reputation. Thus, DISC can avoid being exploited by ALLD. For simplicity, I use dichotomous reputation, zero (bad) and one (good). Reputation is evaluated on the basis of the last game in which a player participated as a donor. This study draws on a reputation rule consistent with the cooperation behavior of DISC; i.e., cooperation with good players and defection with bad players are regarded as good, while defection with good players and cooperation with bad players are regarded as bad (Table 2).² Although the literature on indirect reciprocity offers a great variety of model settings, I follow as simple and established a model as possible because the goal of this study is not to study indirect reciprocity of itself.

Table 1 List of player types

Table 2 Reputation rule

The evolutionary dynamics are analyzed as follows. Let x _i denote the frequency of i-th type (1: ALLC, 2: ALLD, 3: DISC), where x _i  ≥ 0, ∑x _i  = 1. Donation Games are repeated for multiple rounds, where g _n denotes the frequency of good players at the n-th round in the whole population and g _i,n denotes that among the i-th type (g _n  = ∑x _i g _i,n ). As an ALLC donor always cooperates, his reputation becomes good when encountering a good recipient and becomes bad when encountering a bad recipient; g _1,n  = g _n − 1. To the contrary, since an ALLD donor always defects, his reputation becomes bad when encountering a good recipient and becomes good when encountering a bad recipient; g _2,n  = 1 − g _n − 1. Since the action of DISC agrees with the reputation rule, DISC should always be good. However, the reputation of other players may not always be available. Following Nowak and Sigmund (1998), this study introduces a parameter, q ∈ (0, 1), the probability that donors know the recipients’ reputation. When the reputation is unknown, a DISC donor assumes that his recipient is bad.³ With this setting, g _3,n  = 1 − (1 − q)g _n − 1. Further for simplicity, the following analysis draws on the equilibrium reputation (Brandt and Sigmund 2005). That is, the above difference equations are solved with the assumption that g _n  = g _n − 1 = g and g _i,n  = g _{i,n − 1} = g _i .⁴ The equilibrium frequencies of good players are given by

$$ g=\left({x}_2+{x}_3\right)/\left\{2{x}_2+\left(2-q\right){x}_3\right\},\kern0.5em {g}_1=g,\;{g}_2=1-g,\kern0.5em \mathrm{and}\kern0.5em {g}_3=1-\left(1-q\right)g. $$

(1)

Based on this reputation and the payoff of a single game (Table 3), the average payoff for the i-th type (P _i ) is computed. As a donor, ALLC always bears cooperation cost (− c). As a recipient, ALLC gains cooperation benefit from an ALLC donor (bx ₁) but never receives cooperation from an ALLD donor. An ALLC recipient, only if his reputation is good and known, receives cooperation from a DISC donor (bg ₁ qx ₃). All taken together,⁵

Table 3 Payoff matrix^a

$$ {P}_1=-c+b{x}_1+b{g}_1q\ {x}_3. $$

(2a)

ALLD and DISC recipients receive cooperation in similar ways, while ALLD donors never cooperate and DISC donors cooperate only with good recipients whose reputation is known. Thus,

$$ {P}_2=b{x}_1+b{g}_2q\ {x}_3, $$

(2b)

$$ {P}_3=-cgq+b{x}_1+b{g}_3q{x}_3. $$

(2c)

The evolutionary dynamics are computed with the continuous replicator dynamics (Hofbauer and Sigmund 1998):

$$ {\overset{\cdot }{x}}_i={x}_i\left({P}_i-\overline{P}\right), $$

(3)

where $\overline{P}={\displaystyle \sum }{x}_i{P}_i$ (the mean payoff) and ${\overset{\cdot }{x}}_i=d{x}_i/dt$. Based on (1) – (3), Figure 1 illustrates a numerical phase plot. It shows two evolutionarily stable equilibria, pure ALLD and pure DISC, and two unstable equilibria, pure ALLC and a mix of ALLD and DISC. If the reputation availability is sufficiently high (i.e., q > c/b), the phase space is split into two parts; the initial state in the shaded part leads to a non-cooperative regime (ALLD) and the other to a cooperative regime (DISC). Thus, a certain frequency of DISC is necessary to maintain cooperation.

Fig. 1

Numerical Phase Plot of ALLC, ALLD, and DISC . The pure ALLD, (0,1,0), and the pure DISC, (0,0,1), are stable equilibria. A mix of ALLD and DISC, (0, 1 − c/qb, c/qb), and the pure ALLC, (1,0,0), are unstable equilibria. b = 1.0. c = 0.2. q = 0.8

4 Cooperation under academic commercialization

4.1 Increasing defection

Based on the above model, this section examines the impact of commercialization on the cooperation behavior of non-commercial academics. To model the commercialized environment, this study introduces a player type, COM (Table 1), representing commercial academics with the following assumptions. First, they earn certain commercial profit (e.g., licensing income) aside from the cooperation benefit. Second, they do not cooperate because cooperation decreases the commercial profit. They would rather sell their resources than give them away for free. Thus, their behavior is the same as that of ALLD. This is a simplification of the empirical observation that commercial academics tend to withhold their resources (Walsh et al. 2007; Campbell et al. 2000). I further assume that the transition between commercial and non-commercial academics should occur significantly slowly compared to that among non-commercial academics. In reality, starting commercial activities takes various kinds of initial time-consuming effort such as patenting, business planning, and fund raising; once starting a business, they would not abandon it immediately when it makes a loss. Thus, in the following analyses, the rate of adjustment between COM and other types is set infinitely small. In other words, the frequency of commercial academics is exogenously controlled, and the evolutionary dynamics of only non-commercial academics are analyzed.⁶

First, I analyze the impact of COM on the dynamics between ALLD and DISC. ALLC is neglected for simplicity as it is dominated by both ALLD and DISC. A modification of (2b) and (2c) gives the payoff for i-th type as follows:

$$ {P}_2=b{g}_2q\ {x}_3, $$

(4a)

$$ {P}_3=-cgq+b{g}_3q{x}_3. $$

(4b)

Let x ₀ ∈ [0, 1) denote the frequency of COM and z _i  ∈ [0, 1] the relative frequency of the i-th type among non-commercial players; i.e., z _i  = x _i /(1 − x ₀). The dynamics of non-commercial types are described as ${\overset{\cdot }{z}}_1={z}_i\left({P}_i-\overline{P}\right)$ where $\overline{P}={\displaystyle \sum }{z}_i{P}_i$. To examine the impact of COM, Fig. 2a illustrates the reputation, rate of receiving cooperation, payoff, and phase diagram for DISC (black) and ALLD (gray) with and without COM (solid and dashed, respectively). The invasion of COM improves the reputation of both types with a greater extent for ALLD (Column 1). ALLD gains in reputation because it always refuses to help COM, who is likely to be bad. While DISC recipients become more likely to be denied due to the invasion of COM, ALLD recipients are less affected thanks to improved reputation (Column 2). This is directly reflected in the payoff for each type (Column 3). The intersection of the payoff curves is the unstable interior equilibrium, which corresponds to the z ₃-intercept (z ^*₃ ) in the phase diagram (Column 4). With a greater frequency of DISC than the equilibrium, DISC earns higher payoff than ALLD, growing its frequency until it dominates the whole population. On the other hand, a smaller DISC frequency leads to pure ALLD. Since the invasion of COM causes a rightward shift of the equilibrium, it enlarges the basin of attraction for ALLD. The transition of this equilibrium (Column 5) suggests that a greater frequency of COM creates a more favorable condition for ALLD. Formally, dz ^*₃ /dx ₀ > 0 (proof in Math Appendix A).⁷

Fig. 2

Impact of COM on Evolutionary Dynamics . Solid line: x ₀  = 0.25 (with COM) and dashed line: x ₀  = 0 (without COM) in Columns 1–4. In Column 4, to the right of unstable interior equilibria, the dynamics move rightwards, while, to the left, it moves leftwards. The z _i coordinate of unstable equilibria is denoted by z ^* _i . In Column 5, z ^* _i is illustrated as a function of the frequency of COM (x ₀ ). b = 1.0. c = 0.2. β = γ = 0.3. σ = 0.1. p = 0.3. q = 0.8

In summary, the commercialized environment with a greater number of commercial academics is more advantageous for defectors than for cooperators for two reasons. First, prevailing commercial academics, who tend not to cooperate, directly decrease the cooperation benefit for cooperators. Second, commercial academics compromise the reputation mechanism. Academics gain reputation by cooperating with good academics or not cooperating with bad academics. Increasing commercial academics, who tend to be non-cooperative and thus bad, gives defectors a greater chance of gaining in reputation. In other words, altruistic punishers and selfish defectors become less distinguishable once defection by commercial academics becomes common. Therefore, with an increasing number of commercial academics, even non-commercial academics are more inclined toward defection.

Prediction 1

With a greater prevalence of academic commercialization, academics become less willing to engage in unconditional cooperation.

4.2 Bilateral rewarding

In the face of malfunctioning indirect reciprocity, recipients who need others’ resources have a few alternatives. For one, they can directly offer some rewards to donors, such as coauthorship, acknowledgments in their publications, and a promise of future support (Shibayama and Baba 2011). This can be appealing to self-regarding donors in that the risk of non-reciprocity is mitigated through negotiation. As long as the reward is larger than the cooperation cost, reward-based cooperation is more profitable than defection. The literature suggests that bilateral rewarding could sustain cooperation (Sefton et al. 2007; Sigmund et al. 2001). To incorporate this possibility, I extend the Donation Game with the option of bilateral reward, where a recipient who receives cooperation may return a part of his benefit to the donor. For this, the fourth type, PAY, which favors reward-based cooperation is added (Table 1).⁸ PAY is also myopically self-regarding; PAY donors cooperate only for their own benefit (i.e., when reward is expected and it exceeds the cooperation cost), and PAY recipients give reward only when necessary (i.e., when reward is demanded and it is smaller than the cooperation benefit). Let β and γ denote the values of reward for donors and recipients. Reward-based cooperation yields payoff of β – c and b – γ for donors and recipients, respectively. I assume β ∈ [c, b] and γ ∈ [0, β] so that both sides do not make a loss from this transaction, and that rewarding of itself does not decrease the total payoff.

While indirect reciprocity has the limitation of incomplete reputation, reward-based cooperation has its own limitation. In academic cooperation, unlike economic exchange, money is almost never used and a universal currency does not exist (Shibayama and Baba 2011). Thus, as in barter exchange, two players have to find each other’s resources valuable simultaneously. However, such barter exchange may be difficult in academia, where individuals specialize in a narrow research area and recipients may possess nothing valuable for donors. Coauthorship in expected publications might function as a currency, where a recipient gives away a certain credit in his publication, but donors may not appreciate coauthorship (e.g., due to an expected low quality of publication) and may doubt that recipients could really publish. To incorporate this limitation, I introduce a parameter, p ∈ (0, 1), the matching rate at which a donor finds his recipient’s reward valuable. For simplicity, I assume that the contract of bilateral rewarding is binding,⁹ and thus PAY is immune to the risk of non-reciprocity.

With this setting, I analyze how gratis cooperation competes with reward-based cooperation under the commercialized regime. I focus on the evolutionary dynamics of DISC and PAY.¹⁰ The payoffs of both types are given by

$$ {P}_3=-cgq+b{g}_3q{x}_3, $$

(5a)

$$ {P}_4=p\left(\beta -c\right)\left({x}_0+{x}_4\right)+b{g}_4q{x}_3+p\left(b-\gamma \right){x}_4, $$

(5b)

where x ₄ denotes the frequency of PAY. Figure 2b illustrates how the invasion of COM affects the dynamics. The reputation of DISC is not largely affected while that of PAY is improved. Successful transaction for DISC declines to a greater extent than for PAY. Taken together, the payoff of DISC decreases to a greater extent especially when the frequency of DISC is high. The phase diagram shows that the unstable equilibrium shifts rightwards. Therefore, the invasion of COM expands the basin of attraction for PAY (i.e., dz ^*₃ /dx ₀ > 0), producing a more favorable condition for PAY than for DISC (see Math Appendix B).

This result suggests that the increase in commercial academics weakens the reputation mechanism and undermines their potential benefit from indirect reciprocity, which forces academics to depend on safer transactions conditioned on direct rewarding. This bilateral transaction resembles an economic exchange, but only incomplete economic exchange is achievable due to the limitation of barter exchange (modeled as low p). Consequently, the shift toward reward-based cooperation can result in a socially undesirable state with fewer fulfilled transactions.¹¹ Even so, academics would resort to such a suboptimal option to avoid being exploited by free riders.

Prediction 2

With a greater prevalence of academic commercialization, academics become more likely to demand private reward in exchange for cooperation.

4.3 Abstention from cooperation

The above argument assumes compulsory participation in cooperation games, where recipient players must request cooperation. In reality, however, academics have the option of not making a request. If academics engage in no cooperation and work alone, their payoff from cooperation is zero, but this could be preferable to being exploited by defectors. In addition, making a request of itself can incur some cost; for example, academics may have to reveal their research plan to donors, which could reduce their scientific lead, and they have to spend time to negotiate the conditions under which the resources are used. Such a cost becomes a burden when cooperation requests are likely to be denied. Thus, the malfunction of indirect reciprocity can affect academics’ willingness to participate in cooperation.

To examine this possibility, I further extend the Donation Game by adding a type, ABST (Table 1), which abstains from participating in the game (Hauert et al. 2002). ABST players do not engage in Donation Games at all and forgo potential benefit from cooperation. Instead, they devote full effort to their own work, whereby they earn a constant benefit (σ) by saving the cost of participating in cooperation.

For mathematical tractability, I analyze evolutionary dynamics for two types at a time. First, the dynamics between DISC and ABST with the existence of COM are illustrated in Fig. 2c. The payoffs of DISC and ABST are given by

$$ {P}_3=-c{g}_{-5}q\left(1-{x}_5\right)+b{g}_3q{x}_3, $$

(6a)

$$ {P}_5=\sigma, $$

(6b)

where g _− 5 denotes the mean reputation of non-ABST players. The invasion of COM decreases successful transaction and the payoff of DISC, while ABST gains constant payoff. Thus, under the commercialized regime, indirect reciprocity becomes more vulnerable to loners, who earn the minimum payoff by avoiding cooperation. That is, the basin of attraction for ABST expands; i.e., dz ^*₃ /dx ₀ > 0 (see Math Appendix C).

Next, the dynamics between PAY and ABST are examined. The payoff of PAY is given by

$$ {P}_4=p\left(\beta -c\right)\left({x}_0+{x}_4\right)+p\left(b-\gamma \right){x}_4. $$

(6c)

Similarly, Fig. 2D shows that the invasion of COM creates a more favorable condition for ABST than for PAY. With limited efficiency of rewarding (low matching rate, p, or low reward value, β), the basin of attraction for ABST expands; i.e., dz ^*₄ /dx ₀ > 0 (see Math Appendix D), and cooperation based on bilateral rewarding becomes more likely to be invaded by loners.

In summary, the commercialized environment, where indirect reciprocity is likely denied and direct reward is demanded, discourages academics from making cooperation requests, and abstention from cooperation becomes a viable option.

Prediction 3

With a greater prevalence of academic commercialization, academics become less willing to engage in cooperation and more likely to refrain from making requests.

For a holistic view, I examine the dynamics of DISC, PAY, and ABST.¹² Figure 3a shows numerical phase plots with and without COM. The phase space is divided into three regions that converge into each of the three types. Figure 3b illustrates the area percentage of each region as a function of COM frequency, suggesting that the basin of attraction for ABST consistently increases at the sacrifice of DISC, and that it also affects PAY with a high frequency of COM. In addition, I examine the sensitivity to parameter settings.¹³ Results suggest that the basin of attraction for DISC consistently shrinks with increasing frequencies of COM, and that DISC is particularly vulnerable with low reputation availability (q). As for the balance between PAY and ABST, a higher matching rate (p) and higher value of reward (β) gives an advantage to PAY, and a higher opportunity cost of cooperation (σ) to ABST.

Fig. 3

Impact of COM on DISC, PAY, vs. ABST . The area percentage of the basin of attraction is numerically computed as follows. For each lattice point in the phase space with the interval of 0.02 (1,326 points) as the initial state, the coordinate (z ₃, z ₄, z ₅) at t = 10,000 is computed based on ${\dot{z}}_i={\mathrm{z}}_{\mathrm{i}}\left({P}_i-\overline{P}\right)$. If it is within the distance of 0.01 from one of the three pure types, it is regarded as a convergence to the type. The percentage of convergence to each type is used as the area percentage of the basin of attraction. b = 1.0. c = 0.2. β = γ = 0.3. σ = 0.1. p = 0.3. q = 0.8. Mathematical detail is given in the Supplementary Material

5 Interventions

With the above predictions for possible deterioration of indirect reciprocity under commercialization, what policy interventions should be taken? A simplistic approach may be to reverse the trend of commercialization. Though completely abandoning it is unrealistic, reducing the incentive of commercial participation may be feasible. In fact, for example, some scientific communities have been trying to discourage academics from excessively patenting research tools if they are used mainly inside academia (Lei et al. 2009). This type of intervention must be implemented swiftly. For, once the norm of unconditional sharing deteriorates to a certain extent, recovering from a non-cooperative equilibrium might be impossible. Such irreversibility has been sometimes observed in reality, where the introduction of economic incentives changes the framing of games and destroys social norms (Gneezy and Rustichini 2000; Frey and Jegen 2001).

More proactive incentive mechanisms may be feasible. Literature suggests that centralized rewarding and punishing contribute to sustaining cooperation (Gintis et al. 2005; Ostrom 1990). Mechanisms to officially punish defectors do exist in academia, though their effect may be unclear (National Academy of Sciences 2003). Alternatively, the central authority could reward cooperators by awards, research funds, and so forth. In what follows, the effectiveness of centralized rewarding is examined.

First, dynamics between DISC and ALLD are examined. Let r ∈ (0, b) denote the value of reward given by the central authority. I assume that the central authority rewards all cooperation (i.e., cooperation with good recipients is not distinguished from that with bad recipients), and that this fact is publicly known. I slightly modify ALLD’s behavior to make this analysis more meaningful. That is, ALLD donors defect if r < c, but they cooperate if r > c as if they were ALLC because cooperation is more profitable than defection. I assume that DISC’s behavior is not affected since cooperation with bad recipients, rewarded or not, is against the norms of open science. Figure 4A shows the shift of evolutionary dynamics by illustrating the coordinate of the unstable equilibrium (z ^*₃ ) as a function of COM frequency (x ₀). If r < c (left), the curve shifts downwards, indicating that the reward increases the basin of attraction for DISC. This is an apparent result because DISC’s payoff increases by rewarding while ALLD’s does not. Centralized rewarding should be used when DISC’s frequency is between two curves, where the dynamics head toward the defecting equilibrium (pure ALLD) without reward but toward the cooperative regime (pure DISC) with reward. Thus, even after the invasion of COM created a favorable condition for ALLD, DISC could regain its advantage with the aid of centralized rewarding. However, when r > c (right), the effect of rewarding is rather limited because ALLD also receives a reward. Rewarding could even facilitate ALLD to dominate DISC (where the solid curve exceeds the dashed curve). This suggests that the central authority must choose an adequate (not too large) size of reward to maintain indirect reciprocity. Second, the dynamics between DISC vs. PAY are analyzed. I assume that centralized rewarding is given only for gratis cooperation; i.e., if PAY receives a bilateral reward, it is not additionally rewarded by the central authority. With this assumption, PAY’s behavior is not affected if r < c, but PAY acts like ALLC if r > c to exploit centralized rewarding.¹⁴ Figure 4b shows a similar result; while modest rewarding increases the basin of attraction for DISC (left), excessive rewarding can be counterproductive (right). The left graph shows a narrow margin between two curves, suggesting that centralized rewarding is effective in rather limited situations compared to DISC vs. ALLD. In both cases, an inadequate size of rewarding can make a negligible or even negative effect.¹⁵ When too large rewarding helps ALLD or PAY to prevail, the level of cooperation becomes high. Though this may appear socially acceptable, it has two problems. First, it instantly collapses when the centralized rewarding ceases. Thus, it cannot be a solution unless the rewarding mechanism is cheap and sustainable. Second, the central authority may be able to reward only specific forms of cooperation. However, the norms behind indirect reciprocity can be more general, and losing them could affect some forms of cooperation that are not covered by rewarding.

Fig. 4

Effect of Centralized Rewarding. The curves illustrate unstable interior equilibria as a function of the frequency of COM (x ₀ ). Solid line: centralized rewarding is implemented. Dashed line: centralized rewarding is not implemented. The frequency of DISC is decreasing (ż ₃ < 0) below the curves and increasing (ż ₃ > 0) above them. Thus, centralized rewarding is effective between the two curves as a means to reinforce deteriorated indirect reciprocity. b = 1.0. c = 0.2. β = γ =0.3. p = 0.3. q = 0.8. r = 0.15 for r < c and r = 0.3 for r > c. Details are given in the Supplementary Material

A different approach to sustain cooperation is to transfer the cooperation cost from donors to recipients. The cost for donors consists of the direct cost for cooperation and the indirect cost for forgoing scientific lead that could have been maintained by denying sharing. The former can be mitigated by charging recipients minimum fees.¹⁶ However, the cost transfer rarely occurs in reality for some reasons: collecting fees of itself is costly, fair pricing is difficult, and money payment is sometimes prohibited. In this regard, universities or third parties could act as an agent for academics in collecting fees and supplying resources. In fact, central repositories play this role, where donors store their resources in repositories and recipients receive them at cost. Many repositories are already in operation, such as Jackson Laboratory and American Type Culture Collection, though their contribution is still minor (Furman and Stern 2011).

6 Discussion and conclusions

The current economic policies have encouraged academics to engage in commercial activities as a means to increase the contribution of academic science to technological innovation and economies (e.g., Etzkowitz 1998; Poyago-Theotoky et al. 2002), but their potential inconsistency with the norms and practices of open science has been concerned (Dasgupta and David 1994; Nelson 2004). While prior literature shows that commercial academics are less willing to cooperative in favor of commercial profit (Walsh et al. 2007; Campbell et al. 2000), the current study suggests that the commercialized regime could broadly affect ordinary academics and undermine the norms of open science.

This study models the academic cooperation in the ideal state of open science as indirect reciprocity (Nowak and Sigmund 1998; Sigmund 2010) and examines the influence of increasing commercial academics. The analyses predict that growing commercialization could lead to three behavioral changes in cooperation. First, even non-commercial academics could become unwilling to cooperate gratis because increasing commercial academics lower the expected benefit from indirect reciprocity and weaken the reputation mechanism behind indirect reciprocity. Then, the malfunctioning indirect reciprocity could force academics to rely on bilateral rewarding (e.g., coauthorship). That is, cooperation becomes based more on short-term personal profit despite the limitation of barter exchange. Third, consequently, academics might be discouraged from participating in cooperation and would rather work independently. This study also examines potential interventions to mitigate these problems; centralized rewarding may be effective but requires delicate implementation.

Though prior empirical studies have rarely tested the effect of commercialization on ordinary academics, the predictions of this study are consistent with some previous observations. For example, Walsh et al. (2007) reported that the defection rate in resource sharing in American genomics increased from 10 % in 1997 to 18 % in 2003, though its cause was not identified. Shibayama et al. (2012) show an association between the defection rate in resource sharing and the frequency of commercial academics by comparing several scientific fields. Shibayama et al. (2012) also compare gratis cooperation and reward-based cooperation and find a positive correlation between the rate of reward-based cooperation and the frequency of commercial academics. Focusing on knowledge sharing, Haeussler (2011) attributes defection to weak norms of open science. The predictions of the current study as well as these empirical observations imply that the commercialized regime could broadly deteriorate open science, which is believed to be the foundation of science (Merton 1973; Dasgupta and David 1994). That is, although the policy intention of academic commercialization is to facilitate the practical application of scientific discoveries made in academia, it could damage the very source of scientific discoveries.

The desirability of open science needs cautious examination. One may argue that economic exchange is more efficient than indirect reciprocity. I argue that the extreme specialization of academic science seems to make barter exchange unfeasible, which justifies the necessity of indirect reciprocity. More in general, the weakening norms of open science could cause an even broader impact on practices in science. For example, it might facilitate other types of self-regarding behavior such as secrecy and misconduct, though this is open to empirical investigation. In addition, open science has its own limitation; for example, cooperation with unproductive academics can collectively cause a loss (i.e., b < c), which might be addressed by economic exchange. Therefore, the balance between the emerging norms of commercialization and traditional norms of open science needs to be examined from a broader perspective.

This study offers some implications for future empirical research. First, the general impact of commercialization on behavior of non-commercial academics needs more empirical investigation. The behavior of ordinary academics in diverse contexts (e.g., different scientific fields, countries) and its intertemporal transition should be examined. Cooperation based on bilateral rewarding and abstention from cooperation are of both theoretical and practical interest. Future research should inquire into the conditions of cooperation in detail and identify the determinants of cooperation forms and propensity to participate in cooperation. The parameters employed in this study give some hints for empirical studies. The extent to which academics share the social information about their peers (availability of reputation, q) should be studied. The efficiency of private rewarding (the matching rate, p) and the values of bilateral and centralized rewarding (β, γ, and r) should be investigated. The cost structure of cooperation also needs more empirical basis: i.e., the breakdown of the cooperation cost (c) into direct cost for preparing resources and perceived cost for forgoing scientific leads.

Mathematical appendix

1.1 Prediction 1

$g=\frac{1}{2-q{z}_3\left(1-{x}_0\right)}$ by solving g ₂ = g ₀ = 1 − g, g ₃ = 1 − (1 − q)g, and g = x ₂ g ₂ + x ₃ g ₃ + x ₀ g ₀. With (4a) and (4b), ${P}_3-{P}_2=\frac{q\left\{qb{z}_3\left(1-{x}_0\right)-c\right\}}{2-q{z}_3\left(1-{x}_0\right)}$. The solution of P ₃ − P ₂ = 0 for z ₃ gives ${z}_3^{*}=\frac{c}{qb\left(1-{x}_0\right)}$. $\frac{d{z}_3^{*}}{d{x}_0}=\frac{c}{qb{\left(1-{x}_0\right)}^2}>0$.

1.2 Prediction 2

I assume that recipients of self-regarding types (PAY and COM) accept paying bilateral rewards, but that DISC does not because it violates the norms of open science.¹⁷ Thus, PAY donors cooperate with PAY and COM recipients with the probability of p but never cooperate with DISC. With this setting, the equilibrium reputation of PAY is given by g ₄ = (1 − g ₃)x ₃ + {pg ₄ + (1 − p)(1 − g ₄)}x ₄ + {pg ₀ + (1 − p)(1 − g ₀)}x ₀, where g ₀ = 1 − g, g ₃ = 1 − (1 − q)g and g = x ₃ g ₃ + x ₄ g ₄ + x ₀ g ₀.

Formally, Prediction 2 states $\frac{d{z}_3^{*}}{d{x}_0}>0$, where z ^*₃ is the solution of P ₃ − P ₄ = 0 for z ₃. From (5a) and (5b), P ₃ − P ₄ = b(g ₃ − g ₄)qx ₃ − p(β − c)x ₀ − p(b − γ + β − c)x ₄ − cgq. This is rearranged as $\frac{f\left({z}_3,{x}_0\right)}{h\left({z}_3,{x}_0\right)}$, where f and h > 0 are polynomials of x ₀ and z ₃.¹⁸ Since $\frac{d{z}_3^{*}}{d{x}_0}>0$ is not analytically provable, I indirectly show this by simulation. From the whole parameter regions, $c\in \left(0,b\right),q\in \left(c,1\right),p\in \left(0,\frac{q}{2-q}\right)$,¹⁹ $\beta \in \left[c,b\right],\ \gamma \in \left[0,\ \beta \right],$ and x ₀ ∈ [0, 1), I randomly choose a set of parameters, with which f(z ₃, x ₀) = 0 is numerically solved for z ₃. If a solution is found in (0,1), the same equation is solved again with the same set of parameters except that x ₀ is replaced by x ₀ + ε, where $\varepsilon =\frac{1}{10000}$. The first solution is denoted by z ^*₃ and the second by z ^* *₃ . This computation is repeated 100,000 times. Approximately 70 % of the time, no solution was found in (0,1). For the rest, a single solution was found in (0,1),²⁰ where z ^* *₃  > z ^*₃ always holds. This implies $\frac{d{z}_3^{*}}{d{x}_0}>0$. Because f is a cubic polynomial of z₃ whose leading coefficient >0 and f(0, x ₀) < 0, z ^*₃ is the unstable equilibrium; i.e., P ₃ − P ₄ < 0 if z ₃ < z ^*₃ and P ₃ − P ₄ > 0 if z ₃ > z ^*₃ .■

1.3 Prediction 3 (DISC vs. ABST)

The game involving ABST is played as follows. Two players are randomly chosen from a population of DISC, ABST, and COM. When ABST is chosen as a donor, he always defects, so payoffs for both sides are zero. When ABST is chosen as a recipient, he does not ask for cooperation, where the payoff for ABST is σ while that for a donor is zero. As the donor neither defects nor cooperates, his reputation does not change. Because the reputations of DISC and COM are unaffected by games with ABST recipients, reputation is computed only within non-ABST players; i.e., g ₃ = 1 − (1 − q)g _− 5 and g ₀ = 1 − g _− 5, where ${g}_{-5}=\frac{x_3{g}_3+{x}_0{g}_0}{x_3+{x}_0}$.

Prediction 3 is formally $\frac{d{z}_3^{*}}{d{x}_0}>0$, where z ^*₃ is the solution of P ₃ − P ₅ = 0 for z ₃. From the reputation equations, (6a), and (6b), ${P}_3-{P}_5=\frac{q\left\{\left(b-c\right){\left(1-{x}_0\right)}^2{z}_3^2+\left(b+q-2c\right)\left(1-{x}_0\right){x}_0{z}_3-c{x}_0^2\right\}}{\left(2-q\right)\left(1-{x}_0\right){z}_3+2{x}_0}-\sigma$. Let k(z ₃, x ₀) = P ₃ − P ₅. Since k(z ^*₃ , x ₀) = 0, $\frac{d{z}_3^{*}}{d{x}_0}=-\frac{\partial k}{\partial {x}_0}\ /\frac{\partial k}{\partial {z}_3}$. As $\frac{\partial k}{\partial {z}_3}>0$ is easily shown, proving $\frac{\partial k}{\partial {x}_0}<0$ suffices. $\frac{\partial k}{\partial {x}_0}$ is rearranged as $\frac{k_2\left({z}_3,{x}_0\right)}{k_1\left({z}_3,{x}_0\right)}$, where k ₁ > 0 and k ₂ are polynomials of x ₀ and z ₃.²¹ As $\frac{\partial {k}_2}{\partial {x}_0}<0$ is easily shown, it follows that $\frac{\partial k}{\partial {x}_0}<0\ \forall {x}_0\Leftarrow {k}_2\left({z}_3,0\right)<0\iff {z}_3>\frac{\left(qb-2c\right)\left(1-q\right)}{\left(2-q\right)\left(b-c\right)}$. Since k(z ^*₃ , x ₀) = 0, the sufficient condition for $\frac{\partial k}{\partial {x}_0}<0\ \forall {x}_0$ is ${\left.{z}_3^{*}\right|}_{y=0}=\frac{\left(2-q\right)\sigma }{q\left(b-c\right)}>\frac{\left(qb-2c\right)\left(1-q\right)}{\left(2-\mathrm{q}\right)\left(b-c\right)}\iff c>\frac{qb}{2}$ or $\sigma >\frac{q\left(1-q\right)\left(qb-2c\right)}{{\left(2-q\right)}^2}$. Otherwise, ∃ x ^*₀  ∈ (0, 1) s.t. $\frac{\partial k}{\partial {x}_0}<0\left({x}_0>{x}_0^{*}\right)$ and $\frac{\partial k}{\partial {x}_0}>0\ \left({x}_0<{x}_0^{*}\right)$.²² In sum, if c or σ is sufficiently large, COM offers a favorable condition for ABST regardless of COM’s frequency. Otherwise, with a minimal frequency of COM, ABST gains advantage over DISC.

1.4 Prediction 3 (PAY vs. ABST)

Since DISC is not present, reputation does not play a role. From (6b) and (6c), P ₄ − P ₅ = p(β − c)(x ₄ + x ₀) + p(b − γ)x ₄ − σ. Solving P ₄ − P ₅ = 0 for z ₄, ${z}_4^{*}=\frac{\sigma -p\left(\beta -c\right){x}_0}{p\left(b-\gamma +\beta -c\right)\left(1-{x}_0\right)}$. $\frac{d{z}_4^{*}}{d{x}_0}=\frac{\sigma -p\left(\beta -c\right)}{p\left(b-\gamma +\beta -c\right){\left(1-{x}_0\right)}^2}$ . $\frac{d{z}_4^{*}}{d{x}_0}>0$ if σ > p(β − c). Thus, the invasion of COM is favorable for ABST when the matching rate (p) or the value of return payment (β) is sufficiently small.