Reallocation with priorities and minimal envy mechanisms

We investigate the problem of reallocation with priorities where one has to assign objects or positions individuals. Agents can have an initial ownership over object. Each object a priority ordering agents. In this framework, there is no mechanism that both individually rational (IR) and stable, i.e. blocking pairs. Given impossibility, alternative approach compare mechanisms based on pairs they generate. A minimal envy within set if other in always leads included former mechanism. Our main result shows modified Deferred Acceptance (Guillen Kesten Int Econ Rev 53(3):1027–1046, 2012), IR strategy-proof mechanisms. also show extension Top Trading Cycle (Karakaya et al. J Theory 184:104948, 2019) IR, Pareto-efficient These two results extend existing ones school choice.