Collective Action, Free Riding And Evolution
Nash equilibrium is the point of departure of most of the standard literature on public goods. This stresses the sub-optimality of voluntary contributions towards the provision of a public good: in game theoretic terms, with unboundedly rational agents, individual best response is no cooperation in the provision of public goods. However, this is not a satisfactory conclusion, as empirical facts show that, to a certain degree, cooperative behavior as well as free riding emerge in collective action: privately provided public goods do in fact exist. This suggests rethinking the behavioral assumptions that support the conclusions of the conventional model and the extreme abilities and requirements that it imposes on economic agents. This is especially true in complex exchange situations such as the voluntary provision of a public good. Within this context, the aim of this paper is to sketch a behavior theory of non-market decision making in which agents choose a level of individual contribution for a public good. To this end, it departs from the concepts of bounded rationality and evolution, which help in explaining the outcomes of social interaction.The modelThe model may be considered as a simultaneous N player's game; its basic features can be briefly sketched as follows:1. Homogeneous agents interact during a finite time horizon. 2. At the beginning of each stage, agents are endowed with an identical income I, that can be expended in a private good or in the provision of a public good. The basic decision an agent takes is the proportion of income that will be devoted to financing the public good. There is a 1:1 technical transformation relation between the public and private good. 3. Agents take their decisions guided by the payoffs they obtain from each stage. In order to do so they follow a behavioral rule F that maps states into actions: F:S->A.Agents are modeled as classifier systems. A classifier system may be understood as a set of rules with an associated fitness. Rules guide the behavior of agents in that each one is related to a level of contribution. The process by which agents take their actions may be briefly described as (...): identification of the environment, selecting the action and updating the classifier. (...)ExperimentsGiven the previous setup, the paper presents the outcomes of different experiments. The experiments were run with the aim of identifying the effect of different variables on the outcomes of the model: Time, Population Size, Discount rate and Imitation rate. (...)ResultsExperiments suggest some conclusions that are worth mention:First, the system dynamic behavior differs significantly for discount rates above a threshold value. Below this value, the system (asymptotically) converges towards an attractor, in a process that shows a decreasing aggregate level of private contributions. The convergence was not to free riding but for extremely small populations (i.e. comprised of 10 individuals), so some (sub-optimal) level of private provision is guaranteed. However for high enough discount values, contributions behaved as a random walk. In fact, testing the series against the unit root hypothesis (augmented Dickey-Fuller and Phillips-Perron) did not rejected the null, which suggests that possibility. In this case the overall level of public good would wander with an unbounded variance and permanently affected by shocks. As the discount rate affects the dynamic behavior of the model, the rest of the results consider discount values below the threshold.Second, the population size definitely affects the provision. But not increasing voluntary contributions for smaller samples as it has been suggested in the standard literature. In fact the lower levels of contributions were achieved for small samples. And conversely, the larger the population the higher levels of contributions. This may sound striking at first, but in a large population free riding may be less detectable than in small communities, which would allow to conclude (or at least conjecture) that some level of cooperation may be easier to hold in the former case.Third, imitation affects the outcomes. For low imitation rates (only the 10 per cent of the population engaged in imitation at each stage) and using the "imitate the best" strategy, agents did tend to free riding. In general it was found that the aggregate level of cooperation tended to decay when imitation was introduced. However increasing the imitation rate produced unexpected results, which included cycling and increase the global contributions.To conclude, modeling agents engaged in non-market decision making by means of ACE techniques may help to get new insights to the problems of collective action, and give more accurate predictions of what happens in real world than the standard economic approach does.
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