Double implementation in a market for indivisible goods with a price constraint

Abstract

I consider the problem of assigning agents to objects where each agent must pay the price of the object he gets and prices must sum to a given number. The objective is to select an assignment-price pair that is envyfree with respect to the true preferences. I prove that the proposed mechanism will implement both in Nash and strong Nash the set of envy-free allocations. The distinguishing feature of the mechanism is that it treats the announced preferences as the true ones and selects an envy-free allocation with respect to the announced preferences.Journal of Economic Literature classification numbers: C78, C71, D78

Sincere and sophisticated players in an equal-income market

“…As a byproduct of our main contribution, we determine the extent to which previous results are robust to the limit Nash equilibrium prediction. References [13,[15][16][17][18] uniformly concluded, for different non-cooperative predictions than ours, that when all agents are strategic and manipulate an eic-scf, they coordinate on the set of eic allocations for true preferences. This is even so when preferences are not quasi-linear [15,17,18].…”

“…Thus, z is the best allocation in W e (u) for agent i. Thus, for each j ∈ N \ {i}, j ¤ (u, z)i [17,18]. By Lemma 2, there is j ∈ N \ {i}, such that i ¤ (u, z)j .…”

“…If the arbitrator explicitly breaks the ties, the non-cooperative prediction may be empty. In order to bypass this problem, [17,31] enlarge agents' strategy space in the direct revelation game associated with an scc and provide explicit actions that allow agents to endogenously break ties when the scc is multivalued for the profile of reports. This manipulation model is inadequate for our purposes, for it is not clear what a truthful report is in an action space different from an agent's admissible domain of preferences.…”

“…Consider the allocation obtained from z ε , without reshuffling objects, by extracting from each agent in N \ N an amount of money t |N | n and distributing the collected t |N\N ||N | n in equal parts 11 The binary relation ¤(u, z) was introduced, in its equivalent form for the set of objects, by [32]. The use of this binary relation for the study of the manipulation of eic-scfs was pioneered by [17]. Following this approach, [14,18,33] characterize the situations in which an agent is able to manipulate any eic-scf.…”

“…Several papers have studied the non-cooperative outcomes of the direct revelation mechanisms associated with eic-scfs [13,[15][16][17][18]. We depart from this literature in two ways.…”