6

Conclusions

This final chapter roughly consists of three parts. First, we look back at the efforts in previous chapters and summarize the main arguments and findings. Second, we take a step back and evaluate the general approach to research in this book, characterized by a combination of formal modeling, computer simulation, and various empirical strategies, from a broader perspective. Lastly, we conclude the chapter by looking at some possibilities for further research.

6.1 Summary of the findings

It is well established in sociology that social networks influence many social and economic outcomes. Networks play an important role in, for instance, the diffusion of opinions and innovations and can under certain conditions foster cooperation. The majority of past research has considered social networks as exogenously fixed and has studied the consequences of network embeddedness for individual behavior. However, it is increasingly recognized that social networks are dynamic and are often the results of individual decisions about relationships. Thus, the question how networks evolve becomes salient. It is likely that individual decisions on relationships are related to the same individual traits that are also influenced by social networks. This implies that social networks and the traits of individuals within these networks develop interdependently or co-evolve. For instance, we may be influenced by our close friends with regard to our political views, but our political views may also (partly) determine whom we pick as our friends. It is not trivial to predict what network structures would emerge from such a process and what the emerging distribution of behavior would be.

The research presented here fits into this general theme but focuses on a specific type of behavior, namely, behavior in social dilemmas. We focus on two types of social dilemmas in particular: coordination problems and cooperation problems. Coordination problems emerge when actors face individual incentives to align their behavior but are at risk of ending up in Pareto-suboptimal conventions. Cooperation problems emerge when actors have incentives to take advantage of each other even though they could jointly gain more by cooperation (as in the Prisoner's Dilemma). Past research has shown that social networks influence behavior in these two dilemmas. This dissertation extends this research by relaxing the assumption that networks are fixed and by assuming that social networks and behavior are interdependent. We study how social networks and behavior in social dilemmas co-evolve and under which conditions optimal or suboptimal outcomes are more or less likely.

These questions are addressed in four chapters, each from a different angle. Three chapters are concerned with coordination problems, while one chapter studies cooperation problems. The core assumption of the theoretical approach is that both social networks and outcomes of social dilemmas are driven by individual goal-directed action. Hypotheses are derived through formal modeling of the interaction process, using both analytical methods and computer simulation. Empirically, we use two different strategies: laboratory experiments and field research.

Chapter 2 presents a theoretical study on how the emergence of different conventions in coordination games in dynamic networks depends on initial conditions in terms of behavior and social network structures. First, we specify a formal theoretical model for this co-evolution process. We then analytically characterize stable states of the process induced by the model. Because a multitude of stable states are possible, including efficient states, inefficient states, and states with multiple conventions, we use computer simulations to study which of these stable states is more or less likely to occur, given the initial conditions of the process. We focus on two features of stable states: heterogeneity and efficiency of emerging conventions. Emerging network structures turn out to be completely determined by the constellation of behavioral choices in the coordination game. The results of the simulations show that although heterogeneous states are possible, they are unlikely to occur in a dynamic process. Moreover, we show that the initial density of the network strongly catalyzes the initial tendency of the process, while centralization has the opposite effect. When starting from a very heterogeneous situation, a higher density of the initial network makes coordination on the risk-dominant convention more likely, while higher centralization makes coordination on the risk-dominated convention more likely.

Chapter 3 studies cooperation problems, here conceptualized as two-person Prisoner's Dilemmas played in a co-evolving network. We develop a theoretical model in which actors play repeated Prisoner's Dilemmas and learn about their interaction partners using information from third parties (i.e., reputation). At the same time actors can choose with whom they interact, thus changing the network endogenously. The model builds upon previous research that shows that cooperation is facilitated by cohesive networks. The model extends this research by relaxing the assumption that networks are fixed exogenously. We analyze this model using analytical methods and computer simulations. The analytical results show that in both fixed and dynamic networks reputation effects allow for a broader range of stable states as compared with isolated encounters. However, cooperation levels in stable states are not necessarily higher with stronger reputation effects. The analytical results on dynamic networks show that stronger reputation effects lead to more homogeneous network structures.

Computer simulations of this model confirm the analytical results and highlight that reputation effects in dense networks do not foster cooperation under all conditions. In fixed networks reputation effects make both high and low cooperation rates more likely. In dynamic networks stronger reputation effects lead to a higher variance in outcomes but lead to lower cooperation on average. Lastly, the simulation results indicate that cohesive networks are not likely to emerge without a preexisting tendency for cooperation.

In Chapter 4 a laboratory experiment on coordination in dynamic networks is presented. The experiments test predictions derived from the model developed in Chapter 2 on the effects of initial network density on efficiency and heterogeneity of conventions. In addition we develop and test new hypotheses on the effect of information availability on the emergence of different conventions. Two information conditions are compared. Under global information, actors are informed about the actions of all other actors in the population. Under local information, actors are informed only about the actions of their direct neighbors. To model how actors choose new relations under local information, we assume that actors use the average behavior of current neighbors as an approximation of the expected behavior of a potential (unobserved) neighbor. The main theoretical result is that limiting information on behavior of others makes it less likely that a population will develop into subgroups supporting different conventions, because limited information makes it more difficult to avoid others who support a different convention.

In order to derive informative predictions for the experiment, we conduct new computer simulations that closely mimic the experimental conditions in terms of payoffs, initial networks, and information availability. We find only limited support for the hypotheses on emerging conventions at the macro-level. In particular, we find no significant effects of the initial network structure or information availability on emergent conventions. However, if we examine individual behavior of the subjects, we find that the micro-foundations of the model are largely supported. That is, we find clear indications that subjects’ behaviors resemble myopic best-reply play against direct neighbors. The way subjects choose new partners when they have limited information, however, differs from what we assumed in the model. The results are more consistent with a model in which actors assume that potential neighbors are likely to behave differently than their current neighbors.

Chapter 5 tests hypotheses on coordination in dynamic networks again but in a “real-world” setting rather than in the laboratory. We analyze alcohol use among adolescents as a coordination game, arguing that using alcohol can be modeled as risk-dominant but inefficient behavior in a coordination game, given that adolescents face incentives to align their behavior with that of their friends. We test predictions from the model developed in previous chapters using data on alcohol use and friendships in Dutch high schools. Whereas most previous research on this topic studied only effects of personal networks of adolescents, our theoretical approach allows for predictions of effects of the macro-level social network structure in a class on average alcohol use.

In the empirical analysis we are able to replicate the “catalyzing” effect of initial network density on the development of alcohol use—the denser the initial network, the more likely the process will move further in the direction of the initial tendency. This confirmation, which we did not firmly establish in the experiment of Chapter 4, adds further support to the theoretical model. However, the predicted opposing effect of centralization could not be confirmed.

6.2 Theory, computer simulation, and empirical tests

Aside from the substantive problem of understanding co-evolution of networks and behavior in various contexts, a major theme in this book has been the combination of formal modeling, computer simulations, and empirical research.

Formal models formed the backbone of our theoretical approach and were used most explicitly in Chapters 2 and 3, where we formulated models for the co-evolution of networks and coordination and cooperation, respectively. Formalization of these processes allowed us to use the analytical tools of game theory to derive general statements about possible outcomes of these processes, something that would have been impossible by just verbal reasoning. For both types of interaction we came up with characterizations of stable states of the co-evolution process, as depending on the parameters of the game.

However, we also found that while these characterizations provided important insights, they left many questions unanswered as well. In particular, the theorems of Chapters 2 and 3 allow for many different constellations of networks and behaviors to be stable. To be able to test these models empirically, we would like to have predictions that are somewhat more precise. For that purpose, we used computer simulation, in various ways. In Chapters 2 and 3 we used simulation to explore the outcomes of the models under a wide range of parameter combinations and initial conditions. The aim there was to understand the behavior of the model in a general sense, and we therefore varied parameter combinations and initial conditions as much as possible. For example, in Chapter 2, we included all isomorphic networks possible with eight actors.

This broad selection of parameters and initial conditions subsequently allowed us to test hypotheses based on the coordination model in Chapter 5. There, the regression analysis results of Chapter 2, which can be interpreted as general statements about the behavior of the model under different circumstances, served as hypotheses about expected outcomes, given the equally varied initial conditions in the data.

In Chapter 4 we used simulation in a somewhat different way. In this case, the range of initial conditions for which we needed to generate predictions was rather limited as compared with the field data from Chapter 5, because we largely controlled the initial conditions ourselves in our experimental design. Instead, we chose to run many iterations on this limited set of initial conditions in order to create very precise predictions for these specific conditions. Thus, we might say that our simulation approach in Chapter 4 aimed for “depth” rather than “width,” as we did in Chapter 2.

That computer simulations do not always lead to directly testable predictions is illustrated by Chapter 3. As in Chapter 2, we aimed for a “wide” rather than “deep” approach here, but as the results show, the model still predicts a large range of possible outcomes, especially as reputation effects become stronger. Further research will be necessary to figure out which of these outcomes is more likely to be obtained under given conditions.

Aside from the different ways of using simulation, the analyses in Chapters 4 and 5 are also different from a more philosophical perspective. This difference is best illustrated using Coleman's 1990 well-known scheme for micro–macro explanations (see Figure 6.1). Using this scheme, Coleman argued that sociological explanations of social phenomena should never involve direct macro–macro causal relations but should instead always be formulated through a causal mechanism at the individual level, which are to be explicitly linked to the macro-level. Thus, a good theory ought to specify how social conditions affect individual goals (A → C in Fig. 6.1), how individual goals lead to individual action (C → D), and how actions by many individuals are aggregated to generate social phenomena (D → B).

As we argued in Chapter 1, the general theoretical approach in this book is very much inspired by this template, and we now argue that the different empirical approaches used in the various chapters can be seen as referring to different parts of Coleman's scheme.

In Chapters 2, 4, and 5 we studied the effects of initial network structures and game parameters on efficiency, polarization, and network structure in the context of coordination problems. The strategic structure of the game and initial network conditions coincide with part A in Coleman's scheme (the social conditions), while the outcomes coincide with part B (social phenomena, or collective effects). Our theoretical model, then, specifies how individuals behave under these circumstances and how collective outcomes emerge from their individual actions. In our theoretical approach we made assumptions with regard to all the elements in Coleman's scheme, namely that:

• The social phenomena that we are substantively interested in have the strategic structure of coordination games (A → C);
• This situates individuals in a certain decision situation, and that they respond to the incentive and information given by this situation in a certain way, roughly characterized as “myopic best response” (C → D);
• The individual decisions are combined in a certain way (via dynamic social networks) to produce collective effects (D → B).

The role of Chapter 4 in this ensemble was to test hypotheses related to parts C and D in Coleman's scheme, that is, to focus on the way that individuals react to the strategic structure given to them by the social conditions. In our controlled experimental environment we knew that this strategic structure was a certain type of coordination game played in a dynamic network, because we created this structure ourselves. Thus, assumptions on the strategic structure of the situation were not in question here.1 Consequently, if our hypotheses on the macro-level outcomes of the process were rejected, this could only have been caused by wrong assumptions in the remaining elements of the theory, namely assumptions on individual behavior.

This is a general but often overlooked feature of experiments in sociology and economics and is both a strength and a weakness. On the one hand, because experimentalists create and control the social conditions themselves, they are able to focus very specifically on individual behavior and to scrutinize the micro-level assumptions of their theories. On the other hand, this also means that the assumptions on the nature of the social conditions that play a role in the explanation of a social phenomenon stay out of the reach of empirical testing.

In contrast, the empirical tests of our model in Chapter 5 involved the complete sequence of explaining social outcomes (group-level alcohol use) from social conditions (initial network structure and initial behavior). Here, we did not study individual behavior given a certain coordination game but instead had to assume that social influence in alcohol use among adolescents functions like a coordination game. The success of our predictions, therefore, not only depended on the correctness of our assumptions on individual behavior (as in Chapter 4), but also on this assumption on the strategic structure of this natural social situation. Also, in this study we did not explicitly test hypotheses on individual behavior.

For this reason, experiments and field studies can complement each other in important ways, and the studies in this book serve to illustrate that point. Given a theory of a social phenomenon, experiments can provide some confidence that individual actors behave as they are assumed to behave, given the social conditions assumed in the theory. Field studies can then be used to show that the social conditions present in the real-life phenomena that we are interested in actually resemble those assumed in the theory, given that we already know how individuals behave under such conditions.

A critical reader might complain at this point that our demonstration of this strategy in Chapters 4 and 5 did not follow the recipe to the letter. We did study individual behavior in coordination games in our experiment, and we found that although the micro-level predictions of the model were by and large supported, there were also some deviations from the model. Nevertheless, we proceeded to test macro-level predictions in Chapter 5 without adapting our model to better account for these deviations. Also, one might argue that it is not straightforward that the results of our experiments, conducted with university students, also apply to the population of our field study (adolescents). We would have to agree with our critical reader here and leave it to future research to improve upon our efforts.

6.3 Suggestions for further research

In each of the chapters, limitations and possible extensions are discussed that are specific to the research presented there. In this final section, we will not go again into the details of each study but instead discuss a number of wider implications for further research that emerge from the collection of studies presented in this book. We first discuss theoretical extensions, then proceed with suggestions for empirical research.

6.3.1 Theoretical extensions

Alternative actor models

We developed theoretical models for coordination problems in dynamic networks in Chapters 2 and 4 and for cooperation problems in Chapter 3. While the models share a common theoretical approach, an important difference exists in the way actors are modeled at the micro-level. In the models for coordination, actors are modeled as simple myopic optimizers—they play a best response to what their interaction partners played in the round before.

In the model for cooperation problems of Chapter 3, the actor model is considerably more complex—actors are assumed to use the complete history of play with each interaction partner to form beliefs about these partners, to combine these beliefs with information from third parties, and to translate these beliefs into strategies for a repeated game as well as into linking decisions.

The reason for this difference, or discrepancy if you want, is relatively straightforward. Because defection is the dominant strategy in the Prisoner's Dilemma, myopic best-reply behavior would immediately lead to full defection by all actors. Thus, if we want to explain the variation in cooperation levels that we observe in real life, we need to use different decision models. The learning model that we used in Chapter 3 is a still relatively simple solution to this problem. The results from the experiments on coordination (Chapter 4) also suggest that the myopic best-reply model is an oversimplification. Subjects seem to use more complex strategies, such as strategies that are to some extent forward-looking.

In principle, of course, it would be desirable to have one consistent actor model that can be used to model behavior in various social dilemmas. After all, it seems hard to defend that people would behave according to simple best-reply rules when confronted with coordination problems and switch to higher levels of rationality when facing cooperation problems as the models presented in this dissertation suggest. Rather, we would like to be able to explain behavior in different strategic situations using the same, preferably parsimonious, micro-level model.

Concerns about consistency are precisely one of the main reasons why many economists insist on assuming perfect rationality, even when it is clear that this assumption is unrealistic. In the context of network dynamics, however, we see two reasons to deviate from this principle. First, the complexity inherent in large-population network processes makes it extremely implausible that people are capable of determining the optimal choice in every situation. Second, the same complexity also makes the models that assume perfect rationality too complex for the modeler. Using relatively simple micro-level models, then, can be a way to reduce complexity at the micro-level in order to derive macro-level predictions.

Thus, we see a tension between, on the one hand, the desire to arrive at a model that is complex enough to be applied in various strategic situations and, on the other hand, reasons to keep actor models relatively simple. A major task for future research is therefore to investigate the implications of different micro-level assumptions for macro-level consequences in network formation processes. Building upon the models developed in this dissertation, one direction could be to apply learning models as in Chapter 3 to coordination problems. That is, actors would use the experiences of past actions of other actors to form beliefs about their typical behavior and optimize their own behavior accordingly. Corbae and Duffy (2008) develop ideas along these lines.

Another important extension is to consider forward-looking behavior. A limitation of the models we developed is that actors are assumed to be mostly backward looking, in the sense that they base their decisions on what happened in past interactions, but do not—or to a limited extent—consider the long-term consequences of their decisions. In Chapters 2 through 5, actors are myopic—they simply try to maximize their payoff in the present period by choosing a best–reply to the choices of interaction partners in the previous period. Actors do not anticipate reactions by their partners on these actions. In Chapter 3, actors are assumed to be somewhat more sophisticated and take into account that their interaction partners react to their actions in the next round. However, they do not anticipate reactions by third parties, who might sanction by defection or ostracism. Taking into account that actors anticipate reactions by other actors allows for studying control effects of reputation on cooperation, in addition to the learning effects studied in Chapter 3. Moreover, a model based on forward-looking behavior might also offer better explanations for the results of the experiments on coordination. At present, however, forward-looking behavior in the context of network formation is an area that is hardly explored. Some possible directions that might be taken by such research are sketched by Jackson (2008, Chapter 11). However, for the reasons sketched above, assuming that actors can perfectly anticipate all possible reactions by other actors is not desirable either. A model that considers forward-looking behavior in a network formation context without assuming perfect rationality is discussed by Berninghaus et al. (2008).

Other social dilemmas

We discussed two social dilemmas: cooperation and coordination problems. A natural extension of this research is to broaden the analysis to other social dilemmas, such as the Chicken Game, or multi-person public good games. Some other dilemmas have been studied in the networks literature; see, for example, Bramoullé et al. (2004) on anti-coordination games and Ule (2005) on multi-person Prisoner's Dilemmas. These models, however, are rather heterogeneous in terms of assumptions and analytical methods. Developing a more general theoretical framework that can explain behavior in various social dilemmas with co-evolving networks remains a major task for future research.

Heterogeneity

A simplifying assumption throughout the dissertation is that actors are homogeneous in terms of abilities, action alternatives, and payoffs associated with these alternatives. Differences between actors exist only as arbitrary initial conditions in a dynamic process (e.g., initial network positions, initial behavior, or initial beliefs) or emerge endogenously as a result of this process (e.g., different behaviors in a stable state). While clearly unrealistic, the homogeneity assumption was used with the aim to investigate to what extent individual differences can be explained as the result of a social process, without assuming differences a priori.

It is, however, possible that in reality, structural individual differences (as opposed to endogenous differences) exist that impact network evolution processes. For instance, it is likely that people differ in sociability, that is, the ability to maintain social relations. In terms of the models developed here, such differences would be expressed as individual differences in costs of ties. A first intuition is that such variances would cause a “natural” tendency towards centralization of the network, because some actors can more easily form ties than others. The results on centralization in Chapter 2 suggest that this, in turn, would influence the outcomes of co-evolution processes.

Another form of heterogeneity is that actors differ in terms of preferences for certain outcomes. For instance, in the context of coordination problems, some actors may prefer one convention while other actors prefer another. This approach is explored by Bojanowski and Buskens (2008), who show that such heterogeneity may lead to rather different network structures as compared with the homogeneous model studied in Chapter 2 (also see Bojanowski 2012).

Differentiation of actions

Another difference between the models of Chapters 2 through 5, on the one hand, and Chapter 3, on the other hand, is that the models on coordination assume that actors can only choose one action against all their interaction partners, while in the models on cooperation actors play dyadic games in which they can cooperate with one partner and defect with another.

This difference in itself is not problematic, as the models can be considered as different answers to different types of problems. In many situations, differentiating behavior between interaction partners is simply impossible; the models of Chapters 2 through 5 apply to those situations, at least. In other situations, differentiating behavior is possible but costly, for example, in choosing languages or computer operating systems. For such situations, our models might be considered as reasonable simplifications.

It would, however, be interesting to study the conditions under which people would be willing to differentiate their behavior between different interaction partners, even if this comes at a price. Under what conditions, for example, would people be willing to invest in learning an additional language, rather than adapt to their social environment or to change their relations?

6.3.2 Suggestions for empirical studies

With the studies in Chapters 4 and 5, we hope to have made some contributions to the empirical validation of theories on network dynamics. Much more empirical work is needed, however. Research on network dynamics is currently dominated by theoretical studies. This is not necessarily a problem, as the complexity of the problem requires that the theoretical implications of different assumptions and modeling approaches are carefully explored. However, without systematic empirical tests of the implications of theoretical models, it is difficult to judge which assumptions might be problematic and to decide on how future theoretical research should be developed. In this final section, we sketch the outlines of two empirical studies that follow more or less directly from the research presented in the dissertation. Finally, we discuss some more general directions that empirical research on network dynamics might take.

Most attention in this dissertation went to coordination problems (three chapters), and less to cooperation problems (one chapter). Moreover, the chapter on cooperation problems does not include empirical work. Thus, an obvious way to proceed with this line of research would be to “complete the picture” and conduct experimental studies as well as field research on cooperation problems in dynamic networks. As with coordination problems, experiments could be used as a first test of the predictions of the model of Chapter 3 and to examine to what extent individual behavior deviates from what is assumed in the model. Of particular interest for experimental studies on cooperation is the question that whether a model that assumes only learning—and no control—can sufficiently explain individual choices in cooperation problems in dynamic networks.

Another interesting issue that can be addressed in experimental studies is the interplay of various sanctioning mechanisms. If cooperation problems are embedded in networks, reputation effects can lead to sanctioning of defectors by third parties. In dynamic networks defectors may also be sanctioned by ostracism. These mechanisms are not necessarily compatible. The use of ostracism might prevent the formation of dense networks that facilitate the emergence of reputation. Experiments can be designed that manipulate the environment such that these mechanisms can be compared. Such an experiment might, for instance, compare cooperation rates in four conditions in a two-by-two setup—conditions with and without reputation effects, and with fixed and dynamic networks.

Next to experimental research, theory on co-evolution of cooperation and networks should be tested in field research. An interesting application is inter-firm relations. Strategic alliances, in particular, can be analyzed as dyadic cooperation problems. In these alliances, firms undertake collaborative R&D projects, in which both partners can benefit from the sharing of knowledge. However, firms also face incentives to act opportunistically and take advantage of the efforts of their partner. In this sense, strategic alliances share features of the Prisoner's Dilemma (Kogut 1989; Parkhe 1993). Economic sociologists have long emphasized the important role of networks in the success of inter-firm relations (Granovetter 1985; Powell 1990). Empirically, records of such collaborations can be used to reconstruct inter-organizational networks in a longitudinal fashion (e.g., Powell et al. 2005).

A possible cause of the relative lack of “real-life” empirical research on network dynamics is the shortage of suitable data. To test hypotheses on network dynamics, one typically needs detailed measurements of all relevant relations in a population, measured at various points in time. In order to study co-evolution of behavior and networks, one needs, in addition, longitudinal measures of behavior. Collecting such data takes considerable time and effort, and consequently, datasets that meet these requirements are rare, although some datasets exist (e.g., the data analyzed in Chapter 5, see Knecht 2004).

Of course, data do not always need to be collected in the field. Sometimes, existing data sources can be used, as exemplified by the research on strategic alliances mentioned above. Another potentially interesting source of data is presented by the recent emergence of so-called “online social networks;” web-based services that allow users to maintain social relations. In the last decade, these services have become immensely popular (Boyd and Ellison 2007). The fact that relations via these services are mediated by technology allows for detailed longitudinal observations of networks and certain types of behavior. Although data collection using these services will have to deal with concerns over privacy, first steps in this direction (Corten 2012; Lewis et al. 2008) prove this to be a promising development. Of particular interest are online environments in which trust plays an important role, such as online markets or “sharing economy” websites (Parigi et al. 2013).

Data from such administrative data sources, however, are necessarily limited, because the researcher has little control over the measurements and can often not choose the specific variables needed to test particular hypotheses. Moreover, for many topics (e.g., alcohol use among adolescents as studied in Chapter 5) data records are simply not available. Therefore, own data collection in the field remains indispensable. To advance research on social network dynamics, it is essential that future research efforts and funds focus on the collection of new longitudinal network data, which can be used to test hypotheses from existing theoretical models and can suggest new research problems.

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1. There is one caveat here, namely, that we need to assume that the monetary incentives we provided in the experiment, map to utility in a straightforward way. Theoretically, subjects may have utility functions that translate the monetary payoffs into a different type of strategic situation.