Swap-Flexibility in the Assignment of Houses

28 Pages Posted: 3 Mar 2019 Last revised: 19 Nov 2020

See all articles by Madhav Raghavan

Madhav Raghavan

Department of Economics, University of Lausanne

Date Written: July 20, 2020


A desirable house allocation rule is flexible in its response to changes in agents' preferences. We propose a specific notion of this flexibility. An agent is said to be `swap-sovereign' over a pair of houses at a profile of preferences if the rule assigns her one of the houses at that profile and assigns her the other house when she instead reports preferences that simply swap the positions of the two houses. A pair of agents is said to be `mutually swap-sovereign' over their assignments at a profile if the rule exchanges their assignments when they together report such `swap preferences'. An allocation rule is `individually swap-flexible' if any pair of houses has a swap-sovereign agent, and is `mutually swap-flexible' if any pair of houses has either a swap-sovereign agent or mutually swap-sovereign agents. We show for housing markets that the top-trading-cycles rule is the unique strategy-proof, individually rational and mutually swap-flexible rule. In house allocation problems, we show that queue-based priority rules are uniquely strategy-proof, individually swap-flexible and envy non-bossy. Varying the strength of non-bossiness, we characterise the important subclasses of sequential priority rules (additionally non-bossy) and serial priority rules (additionally pair-non-bossy and pair-sovereign).

Keywords: House allocation, housing markets, strategy-proofness, non-bossiness, top-trading-cycles, dictatorial rules, flexibility, Pareto-efficiency

JEL Classification: C78, D71

Suggested Citation

Raghavan, Madhav, Swap-Flexibility in the Assignment of Houses (July 20, 2020). Journal of Mathematical Economics, Vol. 91, pp. 1-10, 2020. , Available at SSRN: https://ssrn.com/abstract=3333260 or http://dx.doi.org/10.2139/ssrn.3333260

Madhav Raghavan (Contact Author)

Department of Economics, University of Lausanne ( email )

Quartier UNIL-Chamberonne
Lausanne, Vaud CH-1015

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