Revealed reciprocity

We propose and characterize the General Reciprocity Model in a framework of context-dependent choice. In the model, the second mover can establish their own rules regarding when or why to reciprocate. The model disentangles the baseline social preference from reciprocity: reciprocity occurs when people deviate from their baseline preference due to the context in which the first mover's choice is made. Our model provides a condition to reveal reciprocity, which aligns with the standard model-free criterion commonly used to identify reciprocity in experimental settings. Thus, it enables us to examine the behavioral foundation of this criterion through the lens of our model. Moreover, in some situations where the standard criterion cannot be applied due to imperfect data, our model offers an additional condition to reveal reciprocity by imposing assumptions about the second mover's psychological processes. Finally, we apply the model to several past experiments, demonstrating how it identifies reciprocity.