Influence in Private-Goods Allocation

47 Pages Posted: 8 Aug 2018 Last revised: 19 Nov 2020

See all articles by Madhav Raghavan

Madhav Raghavan

Department of Economics, University of Lausanne

Date Written: April 1, 2020


We reinterpret the `bossiness' of a private-goods allocation rule (Satterthwaite and Sonneschein, 1981) as the ability of an agent to `influence' another's welfare with no change to her own welfare. We propose simple conditions on (1) which agents may have influence (`acyclicity' and `preservation'), and (2) the welfare consequences of influence (`positivity' and `oppositeness'). We apply these conditions to three well-known bossy rules: the `Vickrey rule' in single-object auctions (Vickrey, 1961) (acyclic, positive), the `doctor-optimal stable rule' in matching with contracts (Hatfield and Milgrom, 2005) (acyclic, positive, preserving) and `generalised absorbing top-trading cycles (GATTC) rules' in housing markets with indifferences in preferences (Aziz and Keijzer, 2011) (acyclic, opposite, preserving). Under mild restrictions, we show how the nature of influence under a strategy-proof rule determines whether or not it satisfies `weak group-strategy-proofness' (requires acyclicity and either positivity or preservation), `weak Maskin monotonicity' (acyclicity and positivity) and `Pareto-efficiency' (acyclicity and oppositeness). In addition, we propose an influence-related generalisation of the`efficiency-adjusted deferred acceptance mechanism' in school choice (Kesten, 2010), and characterise influence for strategy-proof GATTC rules in housing markets.

Keywords: private-goods allocation, welfare, strategy-proofness, influence, matching, single-object auctions, object-allocation, non-bossiness, Pareto-efficiency, stability

JEL Classification: C78, D71, D78

Suggested Citation

Raghavan, Madhav, Influence in Private-Goods Allocation (April 1, 2020). Journal of Mathematical Economics, Vol. 89, pp. 14-28. , Available at SSRN: or

Madhav Raghavan (Contact Author)

Department of Economics, University of Lausanne ( email )

Quartier UNIL-Chamberonne
Lausanne, Vaud CH-1015

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