Coerced participation or the impossibility of self-sorting is a standard Milgramian practice in experimental procedures and in mechanism-market design. This implicit assumption --that a violation of the participation constraint has no impact -- questions the validity of common measurement and recommendations. Laboratory experiments about public goods found that subjects' contributions are initially higher than the Nash prediction, but lower than the efficient level. Experimental studies search for institutional designs that foster such prosocial behaviors, e.g. social image, but hardly take the participation constraint seriously.

In his historical study of the incorporation of seemingly unselfish behaviors into modern economics, Fontaine (2007) finds that the main motivations of prosocial behaviors may have been discovered at the beginning of the 1990's. If he can find early traces of invocations of image motivations being a driver for prosocial behavior, we see as a third generation the literature based on image-motivation that only recently emerged since the 2000's as a collective investigation. Among others, Bénabou & Tirole (2006) appears as the prominent theoretical contribution to the standard image-motivation literature. They add a third type of motivation - an image one - being lineary added to intrinsic and monetary incentives. The social-image version of their model is the one that experienced the most experimental studies that unanimously lead to an increase in prosocial beahviors, especially in public-good settings.

To date, it is not clear how far experimental economics can go to tackle this self-sorting threat (Al-Ubaydi & List, 2017). Based on a previous study that document the (absence of) pure effect of voluntary participation in the polar case of non-excludable public good where one cannot avoid consumption, we enrich our investigation with a study of an interaction between an explicit outside option and a design feature that is meant to increase seemingly unselfish behaviors: social image.Combining theoretical and empirical evidence, the standard literature identifies two underlying motives that can be at play: either quest-for-honor or avoiding-stigma.

Based on a previous experiment, we implement the same opting-out procedure where it is pay-off equivalent not to participate, and to participate to free-ride. We propose an experiment made of three treatments. The Baseline is a standard linear VCM with social-image. The Baseline is a benchmark for the two treatments with the outside option we implemented. The only difference between the two is that in Treatment 1, a subject that does not participate will have her photograph displayed to others whereas in Treatment 2, her photograph is not displayed. By this design variation, we aim at controlling for a potential fly-to-anonymity, a concern based on our previous work.

Our preliminary results. First, we observe a high level of contribution in an environment with social-image incentives when participation is coerced. Second, one-shot exit rates range from 7\% in Treatment 1 to 14\% in Treatment 2. Self-sorting is significant with respect to baseline, but the difference across treatments is just above conventional significance levels, even if facially it gives weight to the fly-to-anonymity argument. Third, contrary to an anonymous environment, offering an outside option does have a negative impact on mean contribution levels as well as in public-good provision.

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