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Dynamic Housing Allocation

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 ).

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Dynamic Housing Allocation

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  1. Dynamic Housing Allocation by Morimitsu Kurino Presented by Malvika Rao and Alice Gao House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  2. Introduction – an Example • 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! House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  3. Introduction • Spot 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 properties • Impact of orderings • Futures mechanism House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  4. Preferences Assumptions • Same # of agents arriving. • Each agent stays for same amount of time. • Same set of houses every period. • Period preferences: (h1, h2) < (h2, h1) • But(h1, h1) ? (h2, h2) • Time-separable preferences. • Time-invariant preferences. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  5. Model • Time starts at t = 1, agents live in houses for T periods • (A, H, R, e) • A: set of agents; A = E + N • H: set of houses • R: set of preference profiles • e: set of endowment profiles • E: existing tenants; N: new tenants • D: endowed agents; U: unendowed agents House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  6. Model Continued • Period t matching µ(t) • Matching plan µ: collection of period t matchings • Set of all matching plans M • Period t static mechanism: (D(t), U(t), H, R(t), e(t)) • Dynamic mechanism π: R M House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  7. Desirable Properties • Acceptability • Each agent is weakly better off as time goes on. • Strategyproofness • History-independent strategy of revealing true period preferences is weakly better than any other HI strategy. • Pareto efficiency • A 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. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  8. Impossibility Result • Theorem 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. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  9. 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)] House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  10. SD Spot Mechanism • Spot mechanism without property rights transfer • Dynamic problem without endowments • Proposition 1: SD Spot Mech. is strategy-proof • Proof: Each SD period mechanism is independent of past assignments. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  11. 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. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  12. 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. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  13. Dynamic Mechanisms under General Preferences House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  14. AS-TTC Static Mechanism • Static serial dictatorship mechanism with squatting rights is not Pareto efficient. • AS-TTC static mechanism (YRMH-IGYT) – • Pareto efficient, individually rational, and strategyproof. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  15. TTC Spot Mechanism • Acceptable? • Pareto efficient? House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  16. TTC Spot Mechanism • Strategy-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. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  17. TTC Spot Mechanism House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  18. TTC Spot Mechanisms • Theorem 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 House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  19. TTC Spot Mechanisms • Theorem 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. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  20. Dynamic Mechanisms under Time-Invariant Preferences Yes* - the spot mechanism is acceptable for ND Yes** - Strategyproof (Pareto efficient) for ND and Strategyproof (Pareto efficient) among all agents except initial existing tenants for WD. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  21. SD Futures Mechanisms • Dynamic 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. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  22. Dynamic Mechanisms under Time-Invariant Preferences Yes* - the spot mechanism is acceptable for ND Yes** - Strategyproof (Pareto efficient) for ND and Strategyproof (Pareto efficient) among all agents except initial existing tenants for WD. House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

  23. Thank you! • Discussion Questions… House Allocation with Overlapping Agents: A Dynamic Mechnism Design Approach

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