The Reciprocity Set

We study procedures that embed clauses granting agents the right to oppose actions that are not in their interest, retract actions that face opposition, and punish harmful actions. Our analyses show that coalitional strategic behaviors under these procedures lead to reciprocal actions. We then introduce a solution concept--the reciprocity set--to predict stable outcomes for effectivity function games. We find that under mild conditions, the reciprocity set (1) is always non-empty; (2) only selects efficient outcomes; (3) strategically protects minority interests; and (4) is compatible with classical notions of fairness and Rawlsian justice in distributive problems