I found there are a couple versions of reciprocity theory.
One is Newcomb's from a perspective of social psychology, talking about interpersonal attractiveness.
Newcomb, T. (1979). Reciprocity of Interpersonal Attraction: A Nonconfirmation of a Plausible Hypothesis. Social Psychology Quarterly, 42(4), 299-306. Retrieved from http://www.jstor.org.proxy.library.cornell.edu/stable/3033801
Altman talks about revealing informaiton and feelings to each other.
Altman, I. (1973). Reciprocity of Interpersonal Exchange 1. Journal for the Theory of Social Behaviour, 3(2), 249-261.
In Building a successful community, they present three studies that show newcomers who receive comments, feedback, even negative ratings engage with the community more. Even though they did not mention reciprocity theory, it can be explained in this way.
I started searching CSCW paper and this one has some theoretical explanation of reciprocity:
Qian Zhao, Zihong Huang, F. Maxwell Harper, Loren Terveen, and Joseph A. Konstan. 2016. Precision CrowdSourcing: Closing the Loop to Turn Information Consumers into Information Contributors. In Proceedings of the 19th ACM Conference on Computer-Supported Cooperative Work & Social Computing (CSCW '16). ACM, New York, NY, USA, 1615-1625. DOI: https://doi.org/10.1145/2818048.2819957
It cited a bunch of paper, such of Cosley's paper. It defines reciprocity:
Reciprocity: people make or withhold contributions to others based on how others treat them (Rabin 1993).
It also works in economics and game theory. This paper is cited by Cosley. It talks about some social phenomenon and proved by math. But the word reciprocity only appears once, in Reference.
Rabin, M. 1993. Incorporating fairness into game theory and economics. Am. Econ. Review 83(5):1281–1302.
So the paper in the reference of Rabin's is:
Goranson, R. E., & Berkowitz, L. (1966). Reciprocity and responsibility reactions to prior help. Journal of Personality and Social Psychology, 3(2), 227.
Zhao et al.(2016) cites Falk et al. (2006)'s paper:
People are reciprocal if they reward kind actions and punish unkind ones.
Their theory takes into account that "people evaluate the kindness ofan action not only by its consequences but also by its underlying intention".
Falk, A., & Fischbacher, U. (2006). A theory of reciprocity. Games and economic behavior, 54(2), 293-315.
They also cites Gouldner's work, reciprocity is analyzed as a social norm: the social norm of doing for others because they (either specifically or generally) have done or will do for you.
Gouldner, A. (1960). The Norm of Reciprocity: A Preliminary Statement. American Sociological Review, 25(2), 161-178. Retrieved from http://www.jstor.org/stable/2092623