Understanding two models of fairness: outcome-based inequity aversion vs. intention-based reciprocity

Why are people fair? Theoretical economics provides two generic models that fits the data. According to the first, inequity aversion, people are inequity-averse: they don't like a situation where one agent is disadvantaged over another. This model is based on consequences. The other model is based on intentions: although the consequences of an action are important, what matters here is the intention that motivates the action. I won't discuss which approach is better (it is an ongoing debates in economics), but I just wanted to share with a extremely clear presentations of the two parties, found in van Winden, F. (2007). Affect and Fairness in Economics. Social Justice Research, 20(1), 35-52., on pages 38-39:

In inequity aversion models (Bolton and Ockenfels, 2000; Fehr and Schmidt, 1999), which focus on the outcomes or payoffs of social interactions, any deviation between an individual's payoff and the equitable payoff (e.g., the mean payoff or the opponent's payoff) is supposed to be negatively valued by that individual. More formally, the crucial difference between an outcome-based inequity aversion model and the homo economicus model is that, in addition to the argument representing the individual's own payoff, a new argument is inserted in the utility function showing the individual's inequity aversion (social preferences), as in the social utility model (see, e.g., Handgraaf et al., 2003; Loewenstein et al., 1989; Messick and Sentis, 1985). The individual is then assumed to maximize this adapted utility function.

In intention-based reciprocity models it is not the outcomes of the interaction as such that matter, but the intentions of the players (Rabin, 1993; see also Falk and Fischbacher, 2006). The idea is that people want to reciprocate perceived (un)kindness with (un)kindness, because this increases their utility. Obviously, beliefs play a crucial role here. More formally, in this case, in addition to an individual's own payoff a new argument is inserted in the utility function incorporating the assumed reciprocity motive. As a consequence, if someone is perceived as being kind it increases the individual's utility to reciprocate with being kind to this other person. Similarly, if the other is believed to be unkind, the individual is better off by being unkind as well, because this adds to her or his utility. Again, this adapted utility function is assumed to be maximized by the individual.