Design teams and industry life cycles: The interplay of innovation and complexity

This paper studies how innovation teams can be optimally configured to yield the best possible performance at different stages of a certain technology's life cycle, which correspond to different levels of environmental complexity. To conduct our analysis, we have employed computational simulations of communities searching NK landscapes at varying levels of complexity. We studied how the relative proportion of exploring agents to exploiting agents in a community impacts the evolution of scores over time, and conducted additional investigations into the role of specialization (i.e., the agents' propensity to take their preferred action) and density (i.e., the expected width of social groups within the community).

innovator communities (also called innovation structures) forming either within individual organizations or across them. During the innovation process, innovating agents work as groups to explore complex solution spaces in search of optimal alternatives. Unlike individual search, group search comes with many technical benefits like diversity of skills and distribution of efforts; and social benefits like social facilitation and complementary knowledge. [12][13][14] However, there are also many drawbacks such as the cost of efficient information exchange. 15,16 Multi-agent learning in general (and collective problem solving in particular) has become more relevant in contemporary research due to the rise in popularity of crowdsourcing and sharing economy. [17][18][19] Numerous studies have been conducted on the formation of efficient high-performing teams that can accomplish tasks at varying levels of complexity and technological maturity. Even so, there are still debates about the effectiveness of crowdsourcing programs to solve and mitigate larger and more complex tasks efficiently. 20,21 Recent studies have proposed special system architectures and network structures to facilitate effective crowdsourcing and overcome issues of complexity, 22,23 but even then, their approach might not be broadly applicable outside of well-defined cases. On the other hand, literature from organizational learning and technological evolution can provide sufficiently versatile tools to design innovation communities within and outside of crowdsourcing contexts.
Based on how various innovation structures perform at different stages of technological development, much information can be extracted about how to optimize the composition of innovation teams.
Empirical research has highlighted various interactions between the crowd knowledge base and internal expert knowledge base, based on the differences in innovation search strategies when they work as teams. 22 Furthermore, there is evidence that different team compositions and configurations result in faster technological development when innovators collaborate in specific ways. 24 More in general, innovators in teams choose combinations of strategies that encompass a range of different types of innovation, which at the two extremes can be represented as either pursuit of distant innovations, which require higher effort and risk, or work on incremental innovations, which can be achieved with comparatively less effort. 3 Marginal benefits of effort clearly vary over this spectrum while also depending on the implicit levels of environmental uncertainty. As a result, a variety of types of innovation are observed at various stages of the life cycle and at different levels of maturity. Overall team structure, 25,26 innovation management process, and co-dependency between agents' strategies, behavior, and objectives 27,28 govern the trajectory of technological evolution or the level of effectiveness in task execution in the case of crowdsourcing teams. Taking into consideration the similarity between organically formed innovator communities during typical technology evolution and crowdsourcing teams executing tasks of various complexities, we develop a framework of computational studies to determine the optimal composition of innovator communities at various stages of technological maturity. We believe this study could contribute and provide prescriptive guidelines for the design of organic collaborative structures both for crowdsourcing and for other team endeavors. First, we map the different stages of technological development to the prevailing level of complexity of technological architecture as measured by the number of interdependencies between innovation factors. 29 In order to do so, we use NK landscapes. NK landscapes provide control over complexity with a minimal number of parameters required for definition namely N, the spatial dimensions, and K, the degree of dependencies of each dimension, and an interdependency relational matrix. 30,31 We characterize each phase of the life-cycle by a certain level of complexity (viz., low or high) modeled by changing the level of dependencies, K, of each of the dimensions in an N-dimensional solution landscape such that each generated landscape, in turn, gives us a snapshot of environmental complexity of technology at a certain stage of technological maturity. Agents on an NK landscape search for solutions associated with better scores and higher locations on the landscape. We then generate different possible configurations of innovator communities operating at different stages of technological maturity and use computational agent-based simulations to look for the configuration that produces the best performance at each respective stage of technological development. In particular, we consider that innovating agents within the community can adopt either one of two roles: exploiters or explorers. The former prefer communicating with other agents and adopting the best available solution among their contacts. The latter, on the other hand, favor individual and autonomous exploration of the landscape to locate better solutions. Neither type acts in a deterministic way, rather, each type has a certain probability of taking their preferred action. The higher the probability that a certain agent takes their preferred action, the more specialized their strategy is. Besides specialization and proportion of types, we also consider communication density, which is a measure of the likelihood of agents meeting other agents within the community or, alternatively, the expected proportion of community interactions for an individual agent in a time step.
We study this problem from the perspective of an optimum-seeking team designer, who can decide the overall proportion of exploiters and explorers within the team. Intuitively, there are several other dimensions of import: the complexity of product architecture, the interconnectedness among community members, and the prevailing level of specialization for each type of agent. However, it seems reasonable to assume that these other factors are not directly under the designer's control, and thus, we take them as given throughout the course of the analysis. In order to identify the best-performing configuration, we plot the average score trajectory of each innovator community as a whole across time steps and analyze relative performance improvements across varying community configurations and complexity levels. Ceteris paribus, best-performing communities are those that reach a higher average score and/or do so faster than other communities.
In general, we find that performance in low complexities and in the short term is driven by the relative proportion of exploiters in the community, whereas success in high complexities and over the long term requires a larger relative proportion of explorers. Indeed, explorers are able to catch up with exploiters in low complexities if given enough time, and benefit from more frequent knowledge exchange. Finally, we F I G U R E 1 Schematic drawing of AU model in Ref. 8 AU, Abernathy-Utterback. find that a measure of how stark the division of tasks between explorers and exploiter is within a community, which we call specialization, contributes to generating better performances for all teams, especially in higher complexities.
The rest of this paper is organized as follows. Section 2 lays out the theoretical motivation and modeling framework, Section 3 details the computational method, Section 4 presents the results obtained and underlying discussion, and finally section 5 covers the conclusion and recommendations.

Analyzing the relationship between innovation and complexity
Our discussion on innovation across technological life cycle is motivated by the literature on the Abernathy-Utterback (AU) model, [7][8][9] shown in Figure 1, which studies the rate of innovation at various stages of maturity for both product and process development and how the underlying innovation structure matures over time. In the early stage of product development, innovation is motivated by the high expected demand for some new and advanced breakthrough technology. Uncertainty is high as the technology itself is still in its infancy stage, but over time, it decreases once the focus shifts to multiple dimensions of innovation (e.g., generating alternative variants, local specialization of technology and others) and then to standardization.
The keystone of the AU model is the concept of dominant design, which is the first stable configuration of the product that becomes industry standard and around which further improvements are designed. In contrast, process development is characterized by gradual, less intensive innovation with frequent competitive improvements until innovation becomes systematic and increasingly less flexible. Even though the AU model envisions different discrete stages of maturity for product and process innovation, it nevertheless models technology development as continuous processes. Likewise, even though there is a reference to the prevailing level of uncertainty, the latter is never explicitly modeled as an indicator of complexity.
Instead, the proposed link between maturity and modularity finds its motivation in Baldwin and Clark, 10 which posits that as a certain technology moves across its lifecycle, from its infancy stage to dominant design, stakeholders involved with innovation acquire know-how and learn to prioritize the most important drivers of performance, while environmental uncertainty decreases over time. Thus, maturity stages could be characterized as levels of complexity. Baldwin makes this connection explicit, characterizing these stages of maturity as a shift from a less modular to a more modular innovation structure as technologies advance. With maturity in technological development, the type of interdependency changes gradually so that different innovation factors are organized into modules. Even though aggregate dependency is unchanged, there is higher dependency within modules and less dependency between modules. An evolving innovation structure naturally identifies the dependencies in the architecture of the product between various innovation factors, encapsulating them within separate systems or clusters. 32 The connection between modularity and complexity has been suggested, among others, by Ethiraj et al. 11 and Potts et al. 34 . They argue that it is not straightforward, and hence difficult, to change the number of interdependencies among innovation factors, because this option may be unavailable depending on the inherent workings of the underlying system. Rather, changing the distribution of interdependencies within the system is often more feasible. However, when evaluating heterogeneous technologies that are modular in different ways, their modeling framework adopts a static perspective, comparing technologies that are intrinsically different in nature rather than in states of maturity.
In contrast, when studying how a technology matures as described in the AU model, it makes sense to consider how the number of interdependencies changes across its lifecycle. One of the key postulates of the AU model is that, over time, uncertainty clears or diminishes.
We relate this to the process of identifying interdependencies between factors, elucidating the way in which they are connected. In the previous paragraph, we argued that modularity increases with maturity as various innovation factors become clustered together. This leads us to conclude that complexity decreases, at least in terms of the distribution of interdependencies. This clustering of factors within well-defined groups would not be possible if their relationships had not been first clearly understood by innovation structures, who then move on to plan innovation in such a way that changes in inputs yield a change in output that is as predictable as possible. The link between modularity and the AU model's predicted clearing of uncertainty seems natural, then.

Modeling framework of innovation complexity with NK landscapes
In the absence of clarity regarding the best way forward, innovation often focuses on a number of factors in hopes of revealing critical dependencies and it takes time for an outcome's performance to be apparent. Although causality between factors is evident, since each innovation is affected by a number of factors that interact with one another, predicting the final performance of the outcome is difficult.
Our research uses NK landscapes to model these innovation dynamics resulting from interdependencies such that innovation problems containing high degrees of interdependence are represented as complex landscapes of recombinant search.
Rugged landscapes like NK are standard testing bed for simulating complex search performances. 35 Originally employed in evolutionary biology, where Kauffman in his book Origin of Order (1993) 36 used it to model the interaction of size and interdependence in adaptive systems, NK landscapes were adopted into research in complex systems by many interdisciplinary fields like management science and organizational science. It has been used abundantly since to simulate and study the complex relationship between various organizational forms interaction with environmental selection, 30 simulate search processes that are forward-looking, and backward-learning, 37 and many others in multiple interdisciplinary research. 38 Theoretically NK-landscapes can be tuned to represent extreme complexity comparable to real life experimental search spaces, and integrating simulation into similar studies is widely accepted across the literature. 39 A NK landscape is modeled as an N-dimensional space, in which each dimension corresponds to an innovation factor taking on a binary value, resulting in 2 N positions in the landscape. Each position in the landscape is represented by a vector of N decision variable reflecting the levels of different innovation factors involved in certain technology, commonly referred jointly as solution. Payoff obtained based on the solution represents the score or fitness associated with the position in the landscape. The computation of payoff is a key aspect that realizes the characteristics feature of complex landscapes. Another way to think of or visualize NK landscapes is suggested by Csaszar, 31 who suggests that they may also be thought of as hyper-cubes such that a link exists between two different positions (nodes) if they differ by a single element. In the same vein, the landscape could also be thought of as a q-regular graph with q = K.
The score is calculated as the average of contributions from all N bits. The "contribution" from each decision (bit) variable is a function of its own value and functions of the value of K other bits, as outlined in the interdependency matrix. Figure 2  For simplicity, we call these the functions as components. For each decision, the total contribution by each bit is computed by summing the relevant components. For instance, the contribution of decision 1 is given by the sum of f 11 (b 1 ) and f 13 (b 3 ). More in general, the contribution for each decision i is given by, ∑ j f ij (b j )-the sum of the components. Contributions are normalized to be between 0 and 1, following a F I G U R E 2 Score computation in NK landscape.
right-skewed distribution. Given that the score is simply the average of contributions, this means that the score itself is also normalized, which allows us to compare performances across different landscapes.
To allow for the necessary level of control over the environment to run a battery of experiments of interest, the model is not calibrated against real data. In light of this, we also believed it would be prudent to normalize scores and other parameters to better capture our insights in terms of the relative performance of agents and communities, given a problem space.
What makes NK landscapes appealing is their inherent parsimony.
Indeed, they provide control over complexity with a minimal number of parameters, namely N (the spatial dimension of decision), and K (the degree of dependencies of each dimension). NK landscapes can easily conceptualize recombinant search where each location within the landscape represents a combination of factors of innovation. 35,40 N represents the number of innovation factors, K represents degree of dependencies between the factors. In the context of this paper, K represents the number of dependent factors that innovators must consider prior to changing contribution from the one innovation factor before generating a feasible outcome and eventually computing its score. Without loss of generality, the score is a function of the solution, and the solution of an agent determines their location on the landscape.
The score represents the quality of innovation in the context of product development. In particular, tuning the K parameter changes the spatial distribution of the score-the ruggedness of the landscape, creating peaks (resp. valleys) where scores are higher (resp. lower), as shown in The affinity between firms, industries, and design teams for each of the extreme strategies is observed naturally 42   To conduct our analysis, we turn to simulations using agent-based modeling. 47,48 In each simulation, we generate 10 clones of a commu- reaping the benefits of shared effort, and reaching the peaks faster than explorers. However, in higher complexity, higher peaks are sparse, the landscape more rugged, and therefore shared search and imitation leads to convergence to local optima. This makes exploiter-majority teams ill-equipped to aspire to higher global optima, in turn making imitation and sharing potentially self-destructive. Explorers, on the other hand, rely on independent search to navigate complexity in multiple directions, and together with their reduced imitation propensity their strategy helps them achieve near global optimum at higher complexity. It is generally expected that a higher p exp will only accelerate the convergence in both the scenarios.

RESULTS AND DISCUSSION
In order to identify optimal configurations for innovation structures, we study the effect of different proportions and specialization levels of agents. Since the dynamics of the agent-based model are such that all scores increase over time, we report the difference in aver-age scores over time instead. This helps identifying whose average scores are growing faster, and thus, which communities are more efficient. For added clarity, we still report raw average scores over time in Appendix B. When looking at innovators within a given community, we can define specialization as the probability for each type of choosing their preferred action. Thus, communities that display a higher p exp also display higher levels of specialization. By way of example, consider a community with p exp equal to 0.6. This means that explorers within the community have a propensity to explore equal to 0.6, whereas this propensity is 0.4 for exploiters. Consider now another community with p exp = 0.9, meaning that explorers and exploiters explore with probability 0.9 and 0.1, respectively. Even though the aggregate level of exploration propensity (as measured by the weighted average probability of exploring for the agents of a community) might be the same in both the aforementioned communities, we say that the level of specialization of the second one is higher than that of the first one. In other words, even though innovators do not act in a deterministic way, the more radical the innovation search strategy, the more specialized are the agents and, in turn, the community. In real world terms, spe- In order to study the effect of specialization in isolation, we created communities with equal proportions of exploring and exploiting agents and then look for differences in performance between radically specialized communities and moderately specialized communities. For instance, p exp of explorers is 0.9 in the former and 0.6 in the latter, keeping the aggregate exploration propensity of both communities at 0.5.
We observe that even though both communities have identical aggregate exploration propensity (0.5), radically specialized communities perform better in higher complexity in comparison to moderately specialized communities. Such a difference in performance is not recorded at lower complexities, meaning that specialization is more significant in higher complexity as shown in Figure 6.
We explain this observation in terms of the interplay between the two mechanisms for score improvement that have been previously defined. Since explorers are responsible for independently querying the landscape for better locations and exploiters help by efficiently diffusing realized scores across the community, more specialized communities benefit from agents who more reliably take on their preferred role. Therefore, explorers explore almost exclusively, whereas exploiters are almost solely concerned with diffusing and adopting superior scores. In the rare cases in which explorers decide to exploit, they can capitalize on high-quality information coming from exploiters. This can allow them to relocate away from local peaks and closer to trajectories of global optima, where their searching capabilities can be put to use. As a result of better division of labor, radically specialized communities outperform moderately specialized communities. Moreover, since we know that the symbiotic effect of both phenomena becomes more critical in higher complexities, we observe a more pronounced effect of specialization only as the complexity of solution landscape increases.

F I G U R E 5
Relative search performance of innovation communities with varying p exp across time steps in landscapes of various complexities. Innovation communities are homogeneous, and contain only one types of agents with probability of exploration p exp mentioned in labels. Base innovation community, represented by the red line, has agents exploring at p exp − .18. We observe that "exploiting" communities perform better in low complexities in comparison to "exploring" communities. Whereas "exploring" communities out play others in higher complexities.

F I G U R E 6
Comparison of relative search performance across of different types of innovation communities across two types of complexity landscapes (K = 1 and K = 8). Both innovation communities contain two types of agents (Explorer and Exploiters) in equal proportion, each exploring at respective exploring propensities (viz probability of exploration for explorers p exp ) and (1 − p exp for exploiters). Base score of innovation community, is represented by the red line, has all its agents exploring at p exp − .5 and Blue line represents moderately specialized innovative communities with p exp − .7 for explorers, while green line represents radically specialized innovative communities with p exp − .9 for explorers. We observe that radically specialized innovative communities perform better than moderately specialized innovative communities and nonspecialized innovative communities in higher complexities. The effect of specialization is not significant in lower complexity.
Last, we test all our claims with various range of simulation parameters for robustness validation. We notice that, all things equal, denser communities perform better at higher complexities when explorers are the majority, whereas no noticeable improvement occurs for exploitermajority groups. We believe that these results are driven by the fact that, when density increases, agents have access to a wider range of information. This can help both explorers and exploiters escape local optima faster. When given control over the proportion of agent types, designers should prefer explorers for high levels of complexity, and exploiters for low levels of complexity. Exploiters also tend to do better in the early rounds regardless of the level of complexity, so they are to be preferred when time is of the essence. Finally, the effects of specialization are particularly appreciable when complexity is higher.
When possible, team designers should prefer more heavily specialized teams in the early stages of the life cycle of a technology, that is, when complexity is higher. Summarizing broadly, system managers and product design teams can benefit from the insights presented in this paper. Managers should form their teams based on two dimensions: the complexity of the design space and the timeline for development. Although innovators of different types are needed in all cases, we can use these heuristics to identify the relative ratio of innovators of different types: In general, when the interdependencies among design decisions are low-either because the design space is intrinsically simple or, more commonly, because these interdependencies have already been reduced by using modular architectures-the managers need to include more exploiting team members who build on each other's work, rather than those who in independent innovation. The opposite is true when complexity is high, that is when decision variables are highly interdependent, the team benefits from having an increased number of independent innovators (explorers). It is often the case that high complexity is associated with the early stages of a system's lifecycle when the architecture of the system is not fully developed and the benefits of modularity have not yet been realized. In addition, external changes in the environment such as the emergence of new technologies, disruption of the market by new competitors, or regulatory and policy changes may cause a shift from low to high complexity.
In addition, the system design timeline (the second dimension) can moderate complexity effects. When the team of innovators is given enough time, a majority-exploiter team can eventually achieve the same performance as a majority-explorer team, although the breakeven point occurs later, as complexity increases. Therefore, as time pressure increases (because of competition, or the agile nature of system/product development), the appropriate composition of innovation teams (with even moderate complexity level) becomes closer to that of high-complexity environments, calling for including more independent innovators in the team composition.
Finally, our findings highlight the importance and the added benefit of clearly dividing and defining the roles among innovators within the same team. Regardless of complexity, explorers and exploiters can work in a synergistic way to generate better outcomes, especially when information can be shared efficiently among large groups of colleagues.

CONCLUSION
Throughout the course of the paper, we have set out to find criteria to employ to build optimally performing teams for technological innovation tasks. Agents within teams explore solution spaces that we render as NK landscapes of varying levels of ruggedness, relating to the prevailing level of complexity in the environment and eventually to the maturity of the technology. Despite the fact that complexity can be measured in many ways, 34,52 and that it is difficult to map dynamically changing complexity at various stages of technologylife cycle precisely, we choose the degree of interdependence between innovation factors as a basic framework to define the notion of complexity. This allows us to give different recommendations depending on the stage of the technology's life cycle. We have characterized agents as being either explorers or exploiters, and we have characterized communities as possessing a certain level of specialization, which governs the propensity with which each agent takes their preferred action (i.e., exploring for explorers and exploiting for exploiters). We also tune the level of density of the community, which governs how wide the network of contacts of each agent is.
Our analysis offers two main findings. First of all, in accordance with existing literature, we find that teams with a higher proportion of explorers perform better in higher complexities, which correspond to the early stages of the life cycle in our characterization. In contrast, teams with a higher proportion of exploiters do better in the early rounds at low complexities, but teams with relatively more explorers are eventually capable to catch up with them.
Our main assumption has been that team designers can observe the type of agent, and for this reason, we give recommendations mostly

APPENDIX A: A ROBUSTNESS TESTS
In order to validate our findings on specialization, we run a series of experiments by altering the value of simulation parameters that may conceal the real mechanism that causes specialized teams to succeed.
Since our original robustness test is run in a community that is equally split between explorers and exploiters, running additional tests should help us verify whether that was a corner case or a general rule. It bears restating that specialization is parametrized by p exp , the probability of exploring for explorers (resp., the probability of exploiting for exploiters). The higher it, the higher we say specialization is in a team.
For clarity of exposition, we define the weighted average propensity of exploration as where N l is the number of explorers and N t is the number of exploiters in the community, respectively.
In our first test, we create two communities populated only with explorers. The first community has p exp equal to 0.8, whereas it is 0.7 for the second. We run this test as a basic control, to make sure everything is working as intended. As expected, we find that the first community outperforms the second in support of our first result.
For our second test, we again use the second community from our previous test. This time we compare it to a community that is 90% made up of explorers, and whose p exp is equal to 0.75. Notice that both communities in this test have an A p of 0.7. We run this experiment because we wish to understand if the relative number of explorers matters more than specialization, per se. We find that, as expected, the more specialized community performs better than the less specialized one.
In the same spirit, we compare a community that is 90% made up of explorers to one that is 80% made up of explorers. We choose the p exp parameter for each community to be 0.75 and 0.834, respectively, so that A p is equal to 0.7. In line with the previous test, we see that the community with higher p exp achieves better results over time.
For our next set of experiments, we relax the assumption that the probability of exploring for exploiters is equal to 1 − p exp . This allows us to widen the range of simulations we can run, while also disentangling our findings from one of our simplifying modeling choices. Notice that now p exp is no longer sufficient to characterize the degree of specialization within the community, since probability of exploration for explorers and the probability of exploration for exploiters are no longer complementary of the other. Thus, we measure specialization simply as the probability for each agent to take their preferred action.
We consider again two communities made up of 90% explorers, and where the probability of exploration for exploiters is .3. In the first community, however, the probability of exploration for explorers is .8, whereas it is .75 in the second. The reason we run this experiment is to try and identify if specialization matters only on the exploiter side, or if it matters for explorers too. All things equal, if our findings are correct, we would expect the first community to do better. This is, in fact, confirmed by the outcome of the experiment, which clearly shows the first community performing better.
In the same vein, we compare two communities, both made up of 80% explorers. The probability of exploration for explorers is the same for both and equal to .8, whereas the probability of exploring for exploiters is .3 in the first community and .4 in the second community.
Notice that in this case, the first community is more specialized, as the probability of exploiters to take their preferred action is higher. Our motivation for running this experiment is perfectly complementary to that of our previous one, namely, wanting to see if specialization matters only for the explorers side, or if it matters for exploiters too. In line with all our findings so far, we observe that the community with more exploiting exploiters performs better.
Finally, we compare three communities made up of 80% explorers.
All these communities will have the same A p of 0.7, but different probabilities of exploration for explorers and for exploiters. Respectively, they will be equal to 0.834 and 0.167 in the first community, 0.8 and 0.3 in the second community, and 0.75 and 0.5 in the third community. Notice how in the first community probability of exploration for explorers and probability of exploration for exploiters are still complementary to each other, but that is not the case for the second and third community. The purpose of this experiment is thus to verify whether or not complementarity matters to our results. In this case too, we observe that the first community, which is the most specialized, performs the best. This is in line with our results so far, in that the symbiotic mechanism strengthens as the level of specialization (measured as the distance between p exp and 1 − p exp ) increases.
Observing the results from these experiments, we conclude that higher performance by more specialized communities is not driven by any other factor outside of specialization itself.

COMPUTATION
In Figure A1, we show the evolution of absolute scores at different complexities for communities with different average p exp and the corresponding evolution of relative scores. Interestingly, whereas we observe a converge in scores for no to low complexity, the same does not happen for medium and high complexity, where teams with a higher propensity to explore have a definite edge.

12:
if agent chooses to Mutate then 13: vary a subset of the N binary variables (determined by distance). Update their solution if the resulting score shows an improvement.

14:
else agent chooses to Communicate and Adopt scores (Continues) 15: if Randomly select a group of community members and adopt score of best-performing agent in the selected group if selected agent's score is higher than their own then 16: copy the solution of their best-performing agent in the selected group 17