Upload
eshana
View
53
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Dynamic Housing Allocation. by Morimitsu Kurino Presented by Malvika Rao and Alice Gao. Introduction – an Example. Two available houses h 1 and h 2 . Each agent prefers h 1 to h 2 in each period. Each agent prefers (h 2 ,h 1 ) to (h 1 ,h 2 ). - PowerPoint PPT Presentation
Citation preview
by Morimitsu Kurino
Presented by Malvika Rao and Alice Gao
Dynamic Housing Allocation
1House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Introduction – an Example
2House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
•Two available houses h1 and h2.•Each agent prefers h1 to h2 in each period.•Each agent prefers (h2,h1) to (h1,h2).
Static allocation is not dynamically Pareto efficient!
IntroductionSpot mechanism
W/o property rights transfer – for problems w/o endowments
With property rights transfer – for problems with and w/o endowments
SD versus TTC
Mechanism propertiesImpact of orderingsFutures mechanism
3House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Preferences
Same # of agents arriving. Each agent stays for same amount of time.Same set of houses every period.
4House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Assumptions
Period preferences: (h1, h2) < (h2, h1)But (h1, h1) ? (h2, h2)
Time-separable preferences.Time-invariant preferences.
ModelTime starts at t = 1, agents live in houses
for T periods
(A, H, R, e)A: set of agents; A = E + NH: set of housesR: set of preference profilese: set of endowment profiles
E: existing tenants; N: new tenantsD: endowed agents; U: unendowed agents
5House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Model ContinuedPeriod t matching µ(t)Matching plan µ: collection of period t
matchingsSet of all matching plans M
Period t static mechanism: (D(t), U(t), H, R(t), e(t))
Dynamic mechanism π: R M
6House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Desirable PropertiesAcceptability
Each agent is weakly better off as time goes on.
StrategyproofnessHistory-independent strategy of revealing true
period preferences is weakly better than any other HI strategy.
Pareto efficiencyA matching plan is PE if there exists no other
matching plan that makes all agents weakly better off and at least one agent strictly better off.
7House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Impossibility ResultTheorem 1: For a dynamic problem with or
without endowments, there is no dynamic mechanism that is Pareto efficient and acceptable, if there are at least 2 newcomers in each period who live for at least 3 periods.
8House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
A different notion of acceptability?Acceptability (their version):
τ = t+1, …, t+T-1: µ(τ) Ra(τ) µ(τ-1)
Acceptability (different version):
τ = t+1, …, t+T-1: [µ(τ), …, µ(t+T-1)] Ra [µ(τ-1), …, µ(τ-1)]
9House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
SD Spot MechanismSpot mechanism without property rights
transferDynamic problem without endowments
Proposition 1: SD Spot Mech. is strategy-proofProof: Each SD period mechanism is
independent of past assignments.
10House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
SD Spot Mech. – Pareto efficient ?What period orderings can induce Pareto
efficient SD Spot mechanisms?
Theorem 2: Without endowments, constant SD Spot Mech. favoring existing tenants is Pareto efficient.
11House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
When is SD Spot Mech. undesirable?Pareto efficiency depends on the ordering
structure
Theorem 3: SD spot mech. favoring newcomers under time-invariant preferences is NOT Pareto efficient.
12House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Dynamic Mechanisms under General Preferences
Acceptable Strategy-proof
Pareto efficient
General SD Spot Yes (Prop 1)
Constant SD Spot Favoring E
Yes Yes (Thm 2)
SD Spot Favoring N Yes No (Thm 3)
TTC Spot Yes
SD Futures Yes Yes
13House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
AS-TTC Static MechanismStatic serial dictatorship mechanism with
squatting rights is not Pareto efficient.
AS-TTC static mechanism (YRMH-IGYT) – Pareto efficient, individually rational, and
strategyproof.
14House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
TTC Spot MechanismAcceptable?
Pareto efficient?
15House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
TTC Spot MechanismStrategy-proof?
Theorem 5: For WD and time-invariant preferences, a constant TTC spot mechanism favoring existing tenants is strategy-proof among all agents except initial existing tenants.
16House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
TTC Spot Mechanism
17House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
TTC Spot MechanismsTheorem 6: For WD or ND and time-
invariant preferences, TTC spot mechanism favoring newcomers is NOT strategy-proof among all agents except initial existing agents
18House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
TTC Spot MechanismsTheorem 7: For WD and time-invariant
preferences, a constant TTC spot mechanism favoring existing tenants is Pareto efficient among all agents except initial existing tenants, but not Pareto efficient for all agents.
Theorem 8: For WD or ND and time-invariant preferences, a TTC spot mechanism favoring newcomers is NOT Pareto efficient among all agents except initial existing tenants, if there are at least 2 newcomers in each period.
19House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Dynamic Mechanisms under Time-Invariant Preferences
Acceptable Strategy-proof
Pareto efficient
General SD Spot Yes
Constant SD Spot Favoring E
Yes* Yes Yes
SD Spot Favoring N Yes
General TTC Spot Yes (Thm 4)
TTC Spot Favoring E Yes Yes** (Thm 5) Yes** (Thm 7)
TTC Spot Favoring N Yes No (Thm 6) No (Thm 8)
SD Futures Yes (Thm 9) Yes (Thm 9)
Yes* - the spot mechanism is acceptable for NDYes** - Strategyproof (Pareto efficient) for ND and Strategyproof (Pareto efficient) among all agents except initial existing tenants for WD.
20House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
SD Futures MechanismsDynamic problem without endowments
Agents report preferences over “assignments” during the period when he is in the market, and are given “assignments” of houses
Theorem 9: For ND, a SD futures mechanism is strategy-proof and Pareto efficient but not acceptable under same assumptions as the Impossibility Theorem.
21House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Dynamic Mechanisms under Time-Invariant Preferences
Acceptable Strategy-proof
Pareto efficient
General SD Spot Yes
Constant SD Spot Favoring E
Yes* Yes Yes
SD Spot Favoring N Yes
General TTC Spot Yes (Thm 4)
TTC Spot Favoring E Yes Yes** (Thm 5) Yes** (Thm 7)
TTC Spot Favoring N Yes No (Thm 6) No (Thm 8)
SD Futures Yes (Thm 9) Yes (Thm 9)
Yes* - the spot mechanism is acceptable for NDYes** - Strategyproof (Pareto efficient) for ND and Strategyproof (Pareto efficient) among all agents except initial existing tenants for WD.
22House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
Thank you!
House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach
23
Discussion Questions…