Is there any comprehensive theoretical studies on how third-party certification adoption may affect industrial performance/dynamics of an industry?
This is also a big theme in agriculturaland environmental economics given the amount of nutritional, healthy, organic and other labels that we see on food these days.
Here are a few references to start:
Hamilton, Stephen F., and David Zilberman. "Green markets, eco-certification, and equilibrium fraud." Journal of Environmental Economics and Management 52.3 (2006): 627-644.
Zilberman, David, Scott Kaplan, and Ben Gordon. "The political economy of labeling." Food Policy (2018).
Ibanez, Lisette, and Gilles Grolleau. "Can ecolabeling schemes preserve the environment?." Environmental and Resource Economics 40.2 (2008): 233-249.
For models of the informational role/effects of third-party certifiers on an industry, you might like to look at
Lizzeri, Alessandro (1999). “Information Revelation and Certification Intermediaries”. RAND Journal of Economics 30.2, pp. 214–231.
Albano, Gian Luigi and Alessandro Lizzeri (2001). “Strategic Certification and Provision of Quality”. International Economic Review 42.1, pp. 267–283.