# Patterned Interactions in Complex Systems: Implications for Exploration

## Summary (2 min read)

### 1. Introduction

- In the context of organizational, technical, and social systems, however, recent empirical work has shown that interactions are often very patterned.
- Section 5 explains in an intuitive way the link between different interaction patterns and the number of local optima they create.
- 23) points out, “The random network theory of Erdős and Rényi has dominated scientific thinking about networks since its introduction in 1959, also known as As Barabási (2002.

### 2. Types of influence matrices

- Following a long tradition in the organization literature (e.g., Learned, et al. 1961) that has gained energy recently from empirical, prescriptive, and computational studies (e.g., Siggelkow 2002; Porter 1996; Levinthal 1997), the authors conceptualize firms as systems of interdependent choices.
- A number of these decisions interact with each other.
- Influence matrices can differ, however, in the total number of off-diagonal x’s, i.e., in the number of interactions among the decisions, and in the patterns of these interactions.
- One method of creating networks that contain elements that are more central than others has been provided by Barabási and Albert (1999).
- Starting with x’s along the main diagonal, this matrix is created by randomly adding x’s below the diagonal until the matrix contains a total of N*(K+1) interactions.

### 3. Creation of performance landscapes and firms that search on them

- Firms are assumed to make N binary decisions about how to configure their activities.
- Hence, an N- digit string of zeroes and ones summarizes all the decisions a firm makes that affect its performance.
- Once a particular influence matrix is chosen, the computer generates a performance landscape based on this influence matrix.
- In the decentralized firm, decisions are split between two managers, A and B. Manager A is responsible for the first N/2 decisions, while manager B is responsible for the remaining N/2 decisions.
- After evaluating alternatives, each manager implements the alternative that she finds best (or maintains the status quo if no evaluated alternative has higher performance).

### 4. Landscape characterization

- The authors use each of the ten different influence matrices to generate performance landscapes and determine a number of topological characteristics of the resulting landscapes.
- As a result, since the authors are interested in comparisons across influence matrices, they do not investigate values larger than K = 6. 13 that landscapes based on the same number of total interactions but different interaction patterns can contain dramatically different numbers of local peaks.
- On K = 2 landscapes, the number of local peaks ranges from 3.4 for landscapes based on centralized influence matrices to 129.0 for landscapes based on dependent influence matrices.
- One immediate consequence of the different number of local peaks is that firms are much more likely to find the global peak in landscapes with centralized interaction patterns than in landscapes that have dependent interaction patterns.

### 5. Intuition

- Even if the total number of interactions among decisions is held constant, performance landscapes can differ markedly in the number of local peaks they contain.
- For each of these two, the authors describe the shapes of the resulting landscapes as well as the underlying intuition for the number of local peaks that arise.
- Because decisions 4-12 are uninfluential, the alteration of each does not affect the contributions of the other decisions, and this simple procedure produces the greatest possible performance conditional on decisions 1-3.
- This is especially likely when many decisions are uninfluenced, causing all configurations to have a similar underlying level of performance and permitting small differences to create numerous local optima.
- If the authors fill one row of this influence matrix with x’s, i.e., make one decision’s contribution dependent on all other decisions, the number of local peaks increases sharply to 58.

### 6. Performance consequences

- In prior sections, the authors have asserted that the proliferation of local peaks increases the value of, and need for, broad exploration.
- In each firm, managers evaluate two alternatives per period.
- The column labeled “random” replicates the finding of Rivkin and Siggelkow (2003), which used random influence matrices.
- For low levels of K, the hierarchical firm significantly outperforms the decentralized firm, while for high levels of K, the decentralized firm significantly outperforms the hierarchical firm.

### 7. Discussion and Conclusion

- In management science, the study of complex systems has recently gained momentum as simulation tools, originally developed in biology and physics, have been applied to organizational, social, and technological settings.
- Many simulation models in this field of inquiry have two parts: a problem space (a performance landscape, an environment, etc.) and entities that search (or move, or live) in the problem space.
- The interaction patterns that produce very few local peaks are marked by a handful of highly influential decisions and a large number of uninfluential decisions.
- These patterns produce landscapes that are easy to search: once the handful of core decisions are made, other choices fall into place naturally.
- Patterns of interaction, however, may affect not only the power of exploration across discrete modules, but also the ability of managers to explore possibilities within each module.

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...…thus carries important implications for the organizational design literature by providing not only insight into the workings of design elements but also a way to conceptualize how such elements will affect future organizational change efforts (Grandori & Furnari, 2008; Rivkin & Siggelkow, 2007)....

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...This section lays the groundwork of my theory in the form of a set of basic definitions....

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...They, together with Ethiraj and Levinthal (2004) and Rivkin and Siggelkow (2007), then investigated the impact of different modular decompositions on simulated searches in so-called “rugged landscapes.”...

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...This practice was pioneered by Porter (1996) and has been utilized by Rivkin (2000), Siggelkow (2001), Ethiraj and Levinthal (2004), and Rivkin and Siggelkow (2007).2 On the one hand, one can think of the task network representation as a way of “zooming in” on the sequence of stages in prior models…...

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...The organizational implications of this feature have been discussed by Levinthal (1997), Rivkin (2000), and others....

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...2003), memberships in underwriting syndicates (Baum et al. 2003), firmalliance networks (Schilling and Phelps 2004), career networks of artists (Uzzi and Spiro 2005, Guimera et al. 2005), and collaboration networks of scientists (Newman 2001). Following the algorithm by Watts and Strogatz (1998), we create small-world influence matrices in two steps....

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##### Frequently Asked Questions (2)

###### Q2. What are the future works mentioned in the paper "Patterned interactions in complex systems: implications for exploration" ?

This is a speculation that deserves investigation in future research. An exciting question for future research is, what interaction patterns will prevail over time ? Patterns of interaction, however, may affect not only the power of exploration across discrete modules, but also the ability of managers to explore possibilities within each module. Because optimization of high-dimensional systems with many interdependencies is usually a difficult task, it may be very helpful to design a system in a way that smoothes performance landscapes and facilitates the search for good solutions.