The Future of Social Experimenting (Full Story)

Dirk Helbing^*a, Attila Szolnoki^b, Matjaz Perc^c, Gyorgy Szabo^b, and Wenjian Yu^a

^aETH Zurich, Chair of Sociology, in particular of Modeling and Simulation, Clausiusstr. 50, 8092 Zurich, Switzerland,^bResearch Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary, and ^cFaculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia

Recent lab experiments by Traulsen et al. (1) for the spatial prisoner's dilemma suggest that exploratory behavior of human subjects prevents cooperation through neighborhood interactions over experimentally accessible time spans. This indicates that new theoretical and experimental efforts are needed to explore the mechanisms offering fascinating explanations for a number of famous puzzles in the social sciences.

When Nowak and May published their computational study of spatial games in 1992, it soon became a scientific milestone (2). They showed that altruistic ("cooperative'') behavior would be able to survive through spatial clustering. This finding, also called "network reciprocity'' (3), is enormously important, as cooperation is the essence that keeps societies together. It is the basis of solidarity and social order. When humans stop cooperating, this implies a war of everybody against everybody.

Understanding why and under what conditions humans cooperate is one of the grand challenges of science (4), particularly in social dilemma situations (where collective cooperation is beneficial, but individual free-riding is even more profitable). How should humans otherwise be able to create public goods (such as a shared culture or a public infrastructure), build up functioning social benefit systems, or fight global warming collectively in the future? From a theoretical point of view, Nowak and May's work demonstrates that the representative agent paradigm of economics (according to which interactions with others can be represented by the interaction with average individuals) can be quite misleading. This paradigm predicts that cooperation should completely disappear in social dilemma situations, leading to a "tragedy of the commons''. If the world was really like this, social systems would not work.

However, when the same interactions take place in a spatial setting, they can cause correlations between the behaviors of neighboring individuals, which can dramatically change the outcome of the system (as long as the interactions are local rather than global). The effect is even more pronounced, when a success-driven kind of mobility is considered in the model (5). Spatio-temporal pattern formation facilitates a co-evolution of the behaviors and the spatial organization of individuals, creating a "social milieu'' that can encourage cooperative behavior. In fact, some long-standing puzzles in the social sciences find a natural solution, when spatial interactions (and mobility) are taken into account. This includes the higher-than-expected level of cooperation in social dilemma situations and the spreading of costly punishment (the eventual disappearance of defectors and "second-order free-riders'', i.e. cooperators who abstain from the punishment of non-cooperative behaviors), see Fig. 1.

Despite the importance of these topics, it took 18 years until somebody made an effort to test the effect of spatial game- theoretical interactions in laboratory experiments. The recent study of Traulsen et al. (1) reports experiments of a spatial prisoner's dilemma game for the original setting of Nowak and May, while the size of the spatial grid, the number of interaction partners and the payoff parameters were modified for experimental reasons. According to their results, spatial interactions have no significant effect on the level of cooperation. This is, because their experimental subjects did not show an unconditional imitation of neighbors with a higher payoff, as it is assumed in many game- theoretical models.

In fact, it is known that certain game-theoretical results are sensitive to details of the model such as the number of interaction partners, the inclusion of self-interactions or not, or significant levels of randomness (see videos 1-4). Moreover, people have proposed a considerable number of different strategy update rules, which matter as well. Besides unconditional imitation, these include the best response rule (6), multi-stage strategies such as tit for tat (7), win-stay-lose-shift rules (8) and aspiration-dependent rules (9), furthermore probabilistic rules such as the proportional imitation rule (9), the Fermi rule (11), and the unconditional imitation rule with a superimposed randomness ("noise'') (5). In addition, there are voter (12) and opinion dynamics models (13) of various kinds, which assume social influence. According to these, individuals would imitate behavioral strategies, which are more frequent in their neighborhood. So, how do individuals really update their behavioral strategies?

Video 1: Computer simulation of the spatial prisoner's dilemma without self-interactions, illustrating the representative dynamics of strategy updating on a 49x49 lattice. Here, we assume an unconditional imitation of the best performing direct neighbor (given his/her payoff was higher). Blue sites correspond to cooperative individuals, red sites to defecting ones. The payoffs in the underlying prisoner's dilemma were assumed as in the paper by Traulsen et al. (1). It is visible that the level of cooperation decays quickly, and defectors prevail after a short time. Since the simulation assumes no randomness in the strategy updates, the spatial configuration "freezes" quickly, i.e. it does not change anymore after a few iterations.

Traulsen et al. find that the probability to cooperate increases with the number of cooperative neighbors as expected from the Asch experiment (14). Moreover, the probability of strategy changes increases with the payoff difference in a way that can be approximated by the Fermi rule (11). In the case of two behavioral strategies only, it corresponds to the well-known multi- nomial logit model of decision theory (15). However, there is a discontinuity in the data as the payoff difference turns from positive to negative values, which may be an effect of risk aversion (16). To describe the time-dependent level of cooperation, it is sufficient to assume unconditional imitation with a certain probability and strategy mutations otherwise, where the  mutation rate is surprisingly large in the beginning and exponentially decaying over time.

Video 2: Computer simulation of the spatial prisoner's dilemma without self-interactions, illustrating the representative dynamics of strategy updating according to Eq. [3] of Traulsen et al. (1). The lattice size, payoff parameters, and color coding are the same as in Video 1, but individuals are performing random strategy updates with an exponentially decaying probability, while unconditional imitation occurs only otherwise. Due to the presence of strategy mutations, the spatial configuration keeps changing. Compared to Video 1, the level of cooperation drops further, since metastable configurations are broken up by strategy mutations ("noise").

The most surprising fact is maybe not the high level of randomness, which is quite typical for social systems. While one may expect that a large noise level quickly reduces a high level of cooperation, it actually leads to more cooperation than the unconditional imitation rule predicts (see Fig. 2 of Ref. (1)). This goes along with a significantly higher average payoff than for the unconditional imitation rule (see Supporting Information). In other words, the random component of the strategy update is profitable for the experimental subjects. This suggests that noise in social systems may play a functional role.

Video 3: Computer simulation of the spatial prisoner's dilemma assuming unconditional imitation. Compared to Video 1, we take self- interactions into account, which supports the spreading of cooperators. Since individuals are assumed to imitate unconditionally, there are no strategy mutations. As a consequence, the spatial configuration freezes after a few iterations.

Given that Traulsen et al. do not find effects of spatial interactions, do we have to say good bye to network reciprocity in social systems and to all the nice explanations that it offers? Probably not. The empirically confirmed spreading of obesity, smoking, happiness, and cooperation in social networks (18) suggests that effects of imitating neighbors (also friends or colleagues) are relevant, but probably over longer time periods than 25 interactions. In fact, according to formula [3] of Traulsen et al., one would expect a sudden spreading of cooperation when the mutation rate has decreased to low values (after about 40 iterations), given that self-interactions are taken into account (see Supporting Information). To make the effect observable experimentally, it would be essential to reduce the necessary number of iterations for the occurrence of it and favorable to control the noise level.

Video 4: Computer simulation of the spatial prisoner's dilemma with self-interactions, assuming strategy updates according to Eq. [3] of Traulsen et al. (1). Initially, there is a high probability of strategy mutations, but it decreases exponentially. As a consequence, an interesting effect occurs: While the level of cooperation decays in the beginning, it manages to recover later and becomes almost as high as in the noiseless case displayed in Video 3 (see also Fig. 3).


The particular value of the work by Traulsen et al. is that it facilitates more realistic computer simulations. Therefore, it becomes possible to determine payoff values and other model parameters, which are expected to produce interesting effects (such as spatial correlations) after an experimentally accessible number of iterations. In fact, the "phase diagram'' in Figure 1 illustrates that experimental games can have qualitatively different outcomes, which are hard to predict without extensive computer simulations scanning the parameter space. Such parameter dependencies  could, in fact, explain some of the apparent inconsistencies between empirical observations in different areas of the world (19) (at least when framing effects such as the expected level of reciprocity and their impact on the effective payoffs (3) are taken into account). The progress in the social sciences by understanding such parameter dependencies would be enormous. However, as the effort to determine phase diagrams experimentally is prohibitive, one can only check computationally predicted, parameter- dependent outcomes by targeted samples. The future of social experimenting lies in the combination of computational and experimental approaches, where computer simulations optimize the experimental setting and experiments are used to verify, falsify or improve the underlying model assumptions.

Besides selecting parameter values which maximize the signal-to-noise ratio and minimize the number of iterations after which the expected effect becomes visible, one could try to reduce the level of randomness by experimental noise control. For this, it would be useful to understand the origin and relevance of the observed randomness (see supporting videos and figures). Do the experimental subjects make mistakes and why? Do they try to optimize their behavioral strategies or do they apply simple heuristics (and which ones)? Do they use heterogeneous updating rules? Or do they just show exploratory behavior? (20) Is it useful to work with subjects who have some experience with behavioral experiments (without having a theoretical background in them)? How relevant is the homogeneity of the subject pool? What are potentials and dangers of framing effects? How can effects of the individual histories of experimental subjects be eliminated? Does it make sense to perform the experiment with a mixture of experimental subjects and computer agents (where the noise level can be reduced by implementing deterministic strategy updates of these agents)?