## Collective Action

Collective action occurs when a group of people work together to achieve a common goal. For example, citizens living under the oppressive rule of a despot share a common interest, namely, to replace the autocrat with a democratic government. In order to advance toward this goal, they need to work together to organize an effective opposition movement. It has long been recognized that having a common goal does not automatically mean that it will be pursued. In other words, collective action may fail to be effective. The reason for this is that each individual may have an incentive to take a free ride: “Let others face the risk of challenging the despot. I will stay home, safe and sound, and then enjoy the benefits of a democratic government if my fellow citizens succeed in their attempt.”

In this post we will briefly summarize the two historical main strategies in modelling collective action, namely, that of Olson and Schelling, respectively. Then, we review a novel and unifying approach devised by Medina and present experimental evidence that supports its key theoretical predictions.

Collective action problems were popularized by the American political economist Mancur Olson (Olson, 1965), who thought that coercion or selective payments to those who contribute to a cause would have to be employed in order to induce a group of individuals to act in a group’s common interest. Olson’s view that, in the absence of external inducements, rational, self-seeking individuals would systematically fail to work in coordination to advance toward a common goal, became the received conventional wisdom. The first crucial departure from the Olsonian framework was the analysis of “tipping games” developed by Thomas Schelling (Schelling, 1978). These games are notorious because, contrary to the Olsonian prediction, they can generate high levels of cooperation. The crucial difference is that, in the model studied by Olson, individuals always prefer to get a free ride whereas, in the model studied by Schelling, the incentives for cooperation depend on the proportion of cooperators in the group. From the standpoint of game theory, the key distinction is the number of Nash equilibria in each game. While the Olsonian game has a unique equilibrium, tipping games have multiple equilibria.

Both approaches capture important features of collective action. However, in some sense, they both fall short of providing a comprehensive explanation for collective action phenomena. As Olson eloquently argued, the incentives for free riding cannot be ignored. Still, we observe instances in which large groups find a way to overcome this problem and cooperate closely with one another. This should not happen if the unique Nash equilibrium is always no cooperation. In principle, Schelling’s approach seems immune to part of this criticism. But how should we deal with the multiplicity of Nash equilibria in a tipping game? The theory does not help us much. None and full cooperation, as well as each person cooperating with a specific positive probability, are Nash equilibria, but the model does not provide us any clue as to which equilibrium we should expect to emerge.

Fortunately, there is a novel approach that solves many of these problems. Medina (2007) has developed a unifying framework that covers both paradigms and produces new and different comparative statics predictions about the effects of the parameters of the game on the probability of successful collective action. In games with a unique equilibrium, the payoff structure determines the outcome of the game. Thus, if a person knows the payoffs, that person can predict what the players will do. In games with multiple equilibria, there is an added element of contingency: the outcome of the game depends on the beliefs that players have about which equilibrium will be played. The new framework relies on the notion of stability sets in order to deal with multiple equilibria. The crucial advantage of the stability-sets method is that it provides an assessment of the likelihood of different equilibria occurring as a function of the payoffs of the game and the distribution of prior beliefs. The key theoretical prediction of the new framework is that the probability of successful collective action should increase in line with the benefit accruing to all players involved, including those who do not contribute if collective action is successful, as well as in line with the extra benefit obtained by those who do contribute.

Every new theory requires empirical corroboration. Our work (Anauati et al., 2016) tests the main empirical implications of the stability-sets approach to collective action using a controlled randomized laboratory experiment. Subjects were randomly assigned to different groups and asked to play a simple game. At the beginning, each subject has 1 point and must decide whether to invest it or not. The probability that the investment is successful depends on the share of subjects who contribute their point. If the investment is successful, all players obtain *B* points and those who contributed obtain *s* extra points. Depending on the values of *B* and *s,* the game has one Nash equilibrium in which nobody contributes, or three Nash equilibria: one in which nobody contributes, another in which all contribute and a third one in which each player contributes with a positive probability (the same for all players). We consider four possible treatments. Treatment 1 is the baseline free-rider Olsonian model with one Nash equilibrium in which nobody contributes. In treatments 2 to 4, we gradually increase *B* and/or *s*, inducing multiple equilibria. Furthermore, the probability of successful collective action as predicted by the stability-sets method is 0 in treatment 1 and increases to 0.25, 0.50 and 0.75 in treatments 2, 3 and 4, respectively (assuming initial beliefs about the expected share of cooperators are uniformly distributed).

We find robust support for the key comparative static predictions of the theory. As we increase the payoff of successful collective action accruing to all players (*B*) and only to those who contribute (*s*), the share of cooperators and payoffs both increase. Overall, the experiment indicates that the stability-sets method could be a very useful tool for studying games with multiple equilibria.

As in many other laboratory experiments, we find that subjects behave more cooperatively than is predicted by theory. But we also show that the gap between theoretical predictions and observed behavior narrows significantly when we refine the theory by allowing for a distribution of prior beliefs that varies with the parameters of the model. To analyze this, we first assume that subjects’ prior beliefs about the share of cooperators have a uniform distribution over the interval [0,1] for all treatments. Second, in some randomly selected sessions, before subjects started playing, we asked them to report their prior beliefs as to the share of cooperators in each treatment. We find that subjects’ prior beliefs are not uniformly distributed and vary among treatments: as the benefit of cooperation increases, subjects upgrade their assessments concerning the expected share of cooperators. Thus, using reported prior beliefs to compute the predictions regarding the probability of successful collective action reduces the gap between the model predictions and observed behavior.

Finally, taking into account the fact that prior beliefs vary across treatments, we decompose the total effect on the probability of successful collective action into two analytically different effects: a “belief effect” and a “range of cooperation effect”. We find evidence of the presence of both.

Understanding the logic of collective action is crucial from a political economy standpoint. Explicitly or implicitly, collective action is a core component of many models of political influence, political representation and coalition formation. A new approach to collective action can produce significant impacts in terms of the way that we approach those topics. To illustrate this point, consider the following example. In the standard common agency model of lobbying (Dixit et al., 1997, and Grossman and Helpman, 2000), it is assumed that groups are either organized (meaning that the group has solved the collective action problem and can lobby to advance its members’ common interests) or unorganized. The stability-sets approach can serve as the basis for an assessment of the likelihood that a group is organized as a function of structural parameters that characterize the collective action problem of group organization. Thus, by combining the common agency model of lobbying with the stability-sets approach to collective action, we can build a more accurate theory of political influence.

**References:**

Anauati, M. V., B. Feld, S. Galiani and G. Torrens (2016). “Collective action: Experimental evidence” (forthcoming in *Games and Economic Behavior*). Available at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2557620.

Dixit, A., G. Grossman and E. Helpman (1997). “Common agency and coordination: General theory and application to government policy making”, *Journal of Political Economy*, vol. 105, pp. 752-769.

Grossman, G., and E. Helpman (2000). *Special Interest Politics*, Cambridge, Massachusetts and London, UK: MIT Press.

Medina, L. F. (2007). *A Unified Theory of Collective Action and Social Change,* Ann Arbor: University of Michigan Press.

Olson, M. (1965).* The Logic of Collective Action: Public Goods and the Theory of Groups, *Cambridge, Massachusetts: Harvard University Press.

Schelling, T. C. (1978). *Micromotives and Macrobehavior*. New York: W. W. Norton.