House Allocation Problems Research Articles

Applicatoin of TTCC Algorithm in House Reallocation Market in China

In recent years, many low-income families have been suffering house allocation problem. The current welfare house allocation mechanism is of low effiency. Despite Chinese government has been working on improving the current mechanism to solve this proplem, there are still many people which try to cheat in the house allocation market. Most of the people could not even truly express their preference through the current mechanism. It is important to find a more suitable mechanism which can help low-income familes reallocate their welfare housing. This article tries to make anaysis about applying Top Trading Cycles and Chians mechansim (TTCC) in the house reallocation market. This mechanism can lead to a more efficient result. Besides, this article expalins why TTCC is better than the current mechanism by studing the feature of the result from TTCC. The results show that TTCC can be used to in house reallocation market with a strcit ranking among low-come familes and there requires a strcit background investigation organization as well.

Bilevel optimization of a housing allocation and traffic emission problem in a predictive dynamic continuum transportation system

AbstractIn recent decades, the effects of vehicle emissions on urban environments have raised increasing concerns, and it has been recognized that vehicle emissions affect peoples’ choice of housing location. Additionally, housing allocation patterns determine people's travel behavior and thus affect vehicle emissions. This study considers the housing allocation problem by incorporating vehicle emissions in a city with a single central business district (CBD) into a bilevel optimization model. In the lower level subprogram, under a fixed housing allocation, a predictive dynamic continuum user‐optimal (PDUO‐C) model with a combined departure time and route choice is used to study the city's traffic flow. In the upper level subprogram, the health cost is defined and minimized to identify the optimal allocation of additional housing units to update the housing allocation. A simulated annealing algorithm is used to solve the housing allocation problem. The results show that the distribution of additional housing locations is dependent on the distance and direction from the CBD. Sensitivity analyses demonstrate the influences of various factors (e.g., budget and cost of housing supply) on the optimized health cost and travel demand pattern.

A Fine-grained View on Stable Many-to-one Matching Problems with Lower and Upper Quotas

In the NP-hard Hospital Residents problem with lower and upper quotas ( HR-Q L U ), the goal is to find a stable matching of residents to hospitals where the number of residents matched to a hospital is either between its lower and upper quota or zero. We analyze this problem from a parameterized complexity perspective using several natural parameters such as the number of hospitals and the number of residents. Moreover, answering an open question of Biró et al. [TCS 2010], we present an involved polynomial-time algorithm that finds a stable matching (if it exists) on instances with maximum lower quota two. Alongside HR-Q L U , we also consider two closely related models of independent interest, namely, the special case of HR-Q L U where each hospital has only a lower quota but no upper quota and the variation of HR-Q L U where hospitals do not have preferences over residents, which is also known as the House Allocation problem with lower and upper quotas. Last, we investigate the parameterized complexity of these three NP-hard problems when preferences may contain ties.

Allocation Mechanisms without Reduction

We study a simple variant of the house allocation problem (one-sided matching). We demonstrate that agents with recursive preferences may systematically prefer one allocation mechanism to the other, even among mechanisms that are considered to be the same in standard models, in the sense that they induce the same probability distribution over successful matchings. Using this, we propose a new priority groups mechanism and provide conditions under which it is preferred to two popular mechanisms, random top cycle and random serial dictatorship. (JEL C78, D44, D82)

Swap-flexibility in the assignment of houses

A house allocation rule should be 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).

Flexibility in House Allocation and Housing Markets

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).

Random mechanisms for house allocation with existing tenants

We study the house allocation problem with existing tenants: n houses (stand for “indivisible objects”) are to be allocated to n agents; each agent needs exactly one house and has strict preferences; k houses are initially unowned; k agents initially do not own houses; the remaining n−k agents (the so-called “existing tenants”) initially own the remaining n−k houses (each owns one). In this setting, we consider various randomized allocation rules under which voluntary participation of existing tenants is assured and the randomization procedure either treats agents equally or discriminates against some (or all) of the existing tenants. We obtain two equivalence results, which generalize the equivalence results in Abdulkadiroğlu and Sönmez (1999) and Sönmez and Ünver (2005).

Set systems related to a house allocation problem

We are given a set A of buyers, a set B of houses, and for each buyer a preference list, i.e., an ordering of the houses. A house allocation is an injective mapping τ from A to B, and τ is strictly better than another house allocation τ′≠τ if for every buyer i, τ′(i) does not come before τ(i) in the preference list of i. A house allocation is Pareto optimal if there is no strictly better house allocation.Let s(τ) be the image of τ i.e., the set of houses sold in the house allocation τ. We are interested in the largest possible cardinality f(m) of the family of sets s(τ) for Pareto optimal mappings τ taken over all sets of preference lists of m buyers and all sets of houses. This maximum exists since in a Pareto optimal mapping with m buyers, each buyer will always be assigned one of their top m choices. We improve the earlier upper bound on f(m) given by Asinowski et al. (2016), by making a connection between this problem and some problems in extremal set theory.

Envy-freeness in house allocation problems

We consider the house allocation problem, where m houses are to be assigned to n agents so that each agent gets exactly one house. We present a polynomial-time algorithm that determines whether an envy-free assignment exists, and if so, computes one such assignment. We also show that an envy-free assignment exists with high probability if the number of houses exceeds the number of agents by a logarithmic factor.

Local envy-freeness in house allocation problems

We study the fair division problem consisting in allocating one item per agent so as to avoid (or minimize) envy, in a setting where only agents connected in a given social network may experience envy. In a variant of the problem, agents themselves can be located on the network by the central authority. These problems turn out to be difficult even on very simple graph structures, but we identify several tractable cases. We further provide practical algorithms and experimental insights.

Size Versus Truthfulness in the House Allocation Problem

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomised mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomised mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of frac{e}{e-1}. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of frac{18}{13} on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. By using a characterisation result of Bade, we show that any randomised mechanism that is a symmetrisation of a truthful, non-bossy and Pareto optimal mechanism has an improved lower bound of frac{e}{e-1}. Since our new mechanism is a symmetrisation of RSDM for strict preferences, it follows that this lower bound is tight. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomised strategy of the administrator who interviews the applicants.

Strategy-Proofness of Stochastic Assignment Mechanisms

This paper compares two prominent stochastic assignment mechanisms in the laboratory: Random serial dictatorship (RSD) and top trading cycles with random endowments (TTC). In standard theory, both mechanisms are strategy-proof and Pareto-efficient for the house allocation problem without endowments. In the experiment, RSD outperforms TTC. This can be attributed to more dominant strategy play under RSD. The behavioral theory of obvious strategy-proofness can partly explain this difference in dominant strategy play. Generally, subjects with extremely high and low levels of contingent reasoning play their dominant strategies. These results suggest that one strategy-proof mechanism may outperform another one if individuals are boundedly rational.

Endowments-swapping-proof house allocation

We consider house (re)allocation problems (Shapley and Scarf, 1974) with strict preferences. We are concerned with the possibility that a pair of agents may gain by swapping their endowments before the operation of the chosen rule. A rule is called endowments-swapping-proof if it is immune to this kind of manipulation. Our main result is that the top trading cycles rule is the only rule that satisfies individual rationality, strategy-proofness, and endowments-swapping-proofness.

Endowments-Swapping-Proof House Allocation

We consider house (re)allocation problems (Shapley and Scarf, 1974) with strict preferences. We are concerned with the possibility that a pair of agents may gain by swapping their endowments before the operation of the chosen rule. A rule is called endowments-swapping-proof if it is immune to this kind of manipulation. Our main result is that the top trading cycles rule is the only rule that satisfies individual rationality, strategy-proofness, and endowments-swapping-proofness.

Stable and efficient resource allocation under weak priorities

We study the indivisible object allocation problem without monetary transfer, in which each object is endowed with a weak priority ordering over agents. It is well known that stability is generally not compatible with efficiency. We characterize the priority structures for which a stable and efficient assignment always exists, as well as the priority structures that admit a stable, efficient and (group) strategy-proof rule. While house allocation problems and housing markets are two classic families of allocation problems that admit a stable, efficient and group strategy-proof rule, any priority-augmented allocation problem with more than three objects admits such a rule if and only if it is decomposable into a sequence of subproblems, each of which has the structure of a house allocation problem or a housing market.

Pre-Exchange-Proof House Allocation

We consider house allocation problems (Shapley and Scarf, 1974) with strict preferences. We introduce a new axiom called pre-exchange-proofness, which states that no pair of agents gain by exchanging their endowments with each other prior to the operation of the chosen rule. We establish that a rule is individually rational, strategy-proof, and pre-exchange-proof if and only if it is the top trading cycles rule. However, with regard to a strict version of pre-exchange-proofness, we obtain the following impossibility result: no individually rational rule satisfies strict pre-exchange-proofness if there are three or more agents.

A Brief Survey of the House Allocation Problems

The objective of this paper is to briefly review house allocation problems. We first give the definition and the aim of the mechanism design theory. Next we discuss its applications to markets with no monetary transfer, such as house allocation, kidney exchange and school choice. We review the literature for (i) house allocation problems, (ii) house allocation problems with existing tenants, and (iii) house allocation problems with existing tenants and newcomers.

Passively-Strictly Strong Nash Equilibrium in a Preference Revelation Game under the Student-Optimal Deferred Acceptance Algorithm

We revisit a college admission market and a related preference revelation game under the student-optimal deferred acceptance algorithm (SODA). Previous research has demonstrated the existence of a strictly strong Nash equilibrium (SSN) based on either an iterative deferred acceptance algorithm (DA-SSN) or the core of a corresponding house allocation problem (Core-SSN). We propose a new equilibrium concept called passively-strictly strong Nash equilibrium (P-SSN). It rules out a kind of deviation called passively weak deviation which includes students who were threatened to deviate. Then we show two preliminary existence results about P-SSN. (i) If the DA-SSN and the Core-SSN are not equivalent, then neither of them is a P-SSN. (ii) If the matching determined by the DA-SSN satisfies a property called irrelevance of low-tier agents, then the DA-SSN is also a P-SSN.

Counting houses of Pareto optimal matchings in the house allocation problem

In an instance of the house allocation problem, two sets A and B are given. The set A is referred to as applicants and the set B is referred to as houses. We denote by m and n the size of A and B, respectively. In the house allocation problem, we assume that every applicanta∈A has a preference list over the set of houses B. We call an injective mapping τ from A to B a matching. A blocking coalition of τ is a non-empty subset A′ of A such that there exists a matching τ′ that differs from τ only on elements of A′, and every element of A′ improves in τ′, compared to τ, according to its preference list. If there exists no blocking coalition, we call the matching τ a Pareto optimal matching (POM).A house b∈B is reachable if there exists a Pareto optimal matching using b. The set of all reachable houses is denoted by E∗. We show |E∗|≤∑i=1,…,m⌊mi⌋=Θ(mlogm). This is asymptotically tight. A set E⊆B is reachable (respectively exactly reachable) if there exists a Pareto optimal matching τ whose image contains E as a subset (respectively equals E). We give bounds for the number of exactly reachable sets. We find that our results hold in the more general setting of multi-matchings, when each applicant a of A is matched with ℓa elements of B instead of just one. Furthermore, we give complexity results and algorithms for corresponding algorithmic questions. Finally, we characterize unavoidable houses, i.e., houses that are used by all POMs. We obtain efficient algorithms to determine all unavoidable elements.

Object allocation via deferred-acceptance: Strategy-proofness and comparative statics

We study the problem of assigning indivisible and heterogeneous objects to agents. Each agent receives at most one object and monetary compensations are not possible. We consider mechanisms satisfying a set of basic properties (unavailable-type-invariance, individual-rationality, weak non-wastefulness, or truncation-invariance).In the house allocation problem, deferred-acceptance (DA)-mechanisms allocate objects based on exogenously fixed priorities over agents. We show that DA-mechanisms are characterized by our basic properties and (i) strategy-proofness and population-monotonicity or (ii) strategy-proofness and resource-monotonicity.Once we allow for multiple identical copies of objects, on the one hand the first characterization breaks down and there are unstable mechanisms satisfying our basic properties and (i) strategy-proofness and population-monotonicity. On the other hand, our basic properties and (ii) strategy-proofness and resource-monotonicity characterize (the most general) class of DA-mechanisms based on objects' fixed choice functions that are acceptant, monotonic, substitutable, and consistent.