The way you put the question there must be: Antecedents are "creating or preventing" equity whereas components are part of the construct.
Where the question comes from is likely that there are few such diversely defined constructs as brands and equity in our field. I advise reading up on some of the literature suggested above - and maybe also on literature regarding formative versus reflective indicators, because this may be where your question was coming from:
The Problem of Measurement Model Misspecification in Behavioral and Organizational Research and Some Recommended Solutions.
MacKenzie, Scott B.; Podsakoff, Philip M.; Jarvis, Cheryl Burke
Journal of Applied Psychology, Vol 90(4), Jul 2005, 710-730. http://dx.doi.org/10.1037/0021-9010.90.4.710
Higly recomend you to read Feldwick's paper: Feldwick, P. (1996). What is brand equity anyway, and how do you measure it?. Journal of the Market Research Society, 38(2), 85-105.
There is a research line in which the competiveness of the brand in the market is analyzed through game theory. The name of this line of work is “competitive marketing behavior”. Here, the marketing mix is used as the information to which the competitors reacts before each other (Ramaswamy et al., 1994). I have some works in this area, also in brand equity. In this case I am not sure that the problem of antecedents and outcomes of brand equity is approachable through game theory. I cannot see how. In literature, common antecedents of BE are product involvement, consumer personal characteristics and brand engagement. Typical outcomes of BE are satisfaction, loyalty and perceived value. In other words, brand equity is more approached as a consumer perceptual issue.
Kotler and Keller (2012:277) identify two basic approaches to measuring brand equity. An indirect approach—assesses potential sources of brand equity by identifying and tracking consumer brand knowledge structures.
A direct approach—assesses the actual impact of brand knowledge on consumer response to different aspects of the marketing. The two general approaches are complementary and marketers can employ both.