Belief-updating rule and sequential reciprocity

We revisit Dufwenberg and Kirchsteiger's (2004) model of reciprocity in sequential games. One important assumption they make is that players' perception of their opponents' kindness depends on their most updated beliefs at their decision nodes along the game. We argue that this is not always the case. We propose a modified belief-updating rule that categorizes beliefs by whether perceived kindness is calculated using their most updated forms. We use a simple example to demonstrate how equilibrium predictions differ for the new rule compared to the original one.