Characterizing Welfare-egalitarian Mechanisms with Solidarity When Valuations are Private Information

Abstract

In the problem of assigning indivisible goods and monetary transfers, we characterize welfareegalitarian mechanisms (that are decision-efficient and incentive compatible) with an axiom of solidarity under preference changes and a fair ranking axiom of order preservation. This result is in line with characterizations of egalitarian rules with solidarity in other economic models. We also show that we can replace order-preservation with egalitarian-equivalence or no-envy (on the subadditive domain) and still characterize the welfare-egalitarian class. However, if we weaken order preservation to symmetry, mechanisms that are not welfare-egalitarian exist. We also study upper bounds on deficit and welfare lower bounds that characterize subclasses of the welfare-egalitarian class. JEL Classifications: C79, D61, D63.

No-envy and egalitarian-equivalence under multi-object-demand for heterogeneous objects

“…(d) By Proposition 2b in Yengin (2012a), a Groves mechanism G h,τ satisfies order preservation and solidarity if and only if G h,τ ∈ E. The rest of the proof is as in part (c). (e) Follows from Proposition 4b in Yengin (2012a).…”

“…On the other hand, Yengin (2012a) shows that the mechanisms in E γ generate the minimum deficit among all Groves mechanisms satisfying the following welfare lower bounds that are analogous to weak social participation constraints: for each N ∈ N , no agent is worse off than the case where she is assigned all the tasks and compensated by an amount of money γ (N )(γ -compensation-lower-bound, γ -CLB). In particular, the mechanisms in E γ T are the only Groves mechanisms satisfying Tbounded-deficit and compensate each agent an equal share of the upper bound on deficit, T .…”

“…By Theorem 1 in Yengin (2012a), if a Groves mechanism is egalitarian-equivalent, then for economies with different populations, different reference set of tasks can be chosen; but for economies with the same population N , the same reference set of tasks R(N ) must work. Moreover, by Yengin (2012a), a Groves mechanism is egalitarianequivalent if and only if for each N ∈ N , there are a real number γ (N ) ∈ R and a reference set R(N ) ∈ 2 A such that for each i ∈ N ,…”

“…Yengin (2012a) shows that on the additive or the subadditive domain, E is the class of all envy-free Groves mechanisms that satisfy solidarity. Hence, on these domains, E γ T is the Pareto-dominant subclass in the class of all envy-free Groves mechanisms that satisfy solidarity and T-bounded-deficit (Theorem 2c).…”

“…In only few papers (Pápai 2003;Yengin 2012aYengin , b, 2013a, the more complex problem of allocating heterogeneous objects when each agent can be assigned any number of objects (multi-object-demand model) is studied. It is to this strand of literature on the Groves mechanisms that our paper belongs to.…”