Double Implementation in a Market for Indivisible Goods with a Price Constraint

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 envy-free 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.Indivisible Goods, Envy-Freeness, Implementation, Strong Nash Equilibrium

Generalized Rental Harmony

Rental Harmony is the problem of assigning rooms in a rented house to tenants with different preferences, and simultaneously splitting the rent among them, such that no tenant envies the bundle (room+price) given to another tenant. Different papers have studied this problem under two incompatible assumptions: the miserly tenants assumption is that each tenant prefers a free room to a non-free room; the quasilinear tenants assumption is that each tenant attributes a monetary value to each room, and prefers a room of which the difference between value and price is maximum. This note shows how to adapt the main technique used for rental harmony with miserly tenants, using Sperner's lemma, to a much more general class of preferences, that contains both miserly and quasilinear tenants as special cases. This implies that some recent results derived for miserly tenants apply to this more general preference class too.Comment: Generalized all results to "compensable tenants" - a class that contains both miserly and quasilinear tenant

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

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 envy-free 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

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

I consider the problem of assigning agents to indivisible objects, in which each agent pays a price for his object and all prices sum to a given constant. The objective is to select an assignment-price pair that is envy- free with respect to the agents' true preferences. I propose a simple mechanism whereby agents announce valuations for all objects and an envy-free allocation is selected with respect to these announced preferences. I prove that the proposed mechanism implements both in Nash and strong Nash equilibrium the set of true envy-free allocations

Competitive Envy-Free Division

リサーチレポート（北陸先端科学技術大学院大学情報科学研究科）本文は図書館に配架されています。 / This material is stored in the JAIST library

Competitive envy-free division

We are concerned with a fair division problem in which the indivisible “goods” to be distributed among a finite number of individuals have divisible “bads” associated with them. The problem is formulated and analyzed in terms of the housemates problem. We present an efficient procedure that decides whether an envy-free solution exists, and if so, finds one of them; otherwise finds a solution such that each envious housemate is assigned a room whose rent is zero. Copyright Springer-Verlag 2004