Parking Space Assignment Problem: A Matching Mechanism ... Parking Space Assignment Problem: A Matching

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  • Parking Space Assignment Problem: A Matching Mechanism Design Approach

    Jinyong Jeong

    Boston College ITEA 2017, Barcelona

    June 23, 2017

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 1 / 43

  • Motivation

    Cruising for parking is drivers’ behavior that circle around an area for a parking space.

    While cruising, drivers waste fuel and time, as well as contribute to the traffic congestion and air pollution.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 2 / 43

  • Evidences from the Literature1

    Year Location % of traffic cruising Ave. cruising time (min.) 1927 Detroit 19 1927 Detroit 34 1960 New Haven 17 1965 London 6.1 1965 London 3.5 1965 London 3.6 1977 Freiburg 74 1984 Jerusalem 9.0 1985 Cambridge 30 11.5 1993 New York 8 7.9 1993 New York 10.2 1993 New York 13.9 1997 San Francisco 6.5

    1Source: Shoup (2005), Arnott (2005) Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 3 / 43

  • Overview

    Difficult to find a parking space → Centralized system to assign spaces to drivers

    Wasted residents’ spaces → Include residents’ spaces into system

    Price gap between off-street parking and on-street parking → Endogenous price in the mechanism

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 4 / 43

  • Overview

    Cruising game

    Parking problem as matching

    Mechanism design

    Policy suggestions

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 5 / 43

  • Figure: I’m talking about this,

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 6 / 43

  • Figure: Not this.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 7 / 43

  • Literature: parking related

    Ayala et al. (2011), Parking space assignment games. Xu et al. (2016), Private parking space sharing.

    Shoup (2005), The high cost of free parking. Arnott (2005), Alleviating urban traffic congestion.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 8 / 43

  • Literature: matching

    Ergin and Sönmez (2006), Games of school choice under the Boston mechanism

    Hatfield and Milgrom (2005), Matching with contracts Hatfield and Kojima (2010), Substitutes and stability for matching with contracts

    Sönmez (2013), Bidding for Army Career Specialties

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 9 / 43

  • The Model

    A setup of the parking space assignment problem is:

    I = {i1, · · · , in} : a set of drivers with unit demand, S = {s1, · · · , sm} : a set of available parking spaces, �I = (�i1 , · · · ,�in ) : a list of individuals’ strict preferences. D =(d11, · · · ,dnm) : a list of distances from each driver to each

    space.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 10 / 43

  • Cruising game

    In a decentralized parking market, drivers are facing a game situation, namely a cruising game, where

    the players are the drivers, I, each driver’s strategy is σi ∈ S, strategies of all drivers are denoted by σ, and the outcome is an assignment A(σ; I,S) : I → S.

    A driver chooses a space to go, and park there if it remains empty when he arrives.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 11 / 43

  • Cruising game

    In a decentralized parking market, drivers are facing a game situation, namely a cruising game, where

    the players are the drivers, I, each driver’s strategy is σi ∈ S, strategies of all drivers are denoted by σ, and the outcome is an assignment A(σ; I,S) : I → S.

    A driver chooses a space to go, and park there if it remains empty when he arrives.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 11 / 43

  • Cruising game

    In a decentralized parking market, drivers are facing a game situation, namely a cruising game, where

    the players are the drivers, I, each driver’s strategy is σi ∈ S, strategies of all drivers are denoted by σ, and the outcome is an assignment A(σ; I,S) : I → S.

    A driver chooses a space to go, and park there if it remains empty when he arrives.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 11 / 43

  • Cruising game

    A driver i will be assigned a space s if

    σi = s and, dis < djs for all j with σj = s.

    In words,

    i chooses to go to the space s, and i is closer to any driver who goes to s.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 12 / 43

  • Cruising game

    A driver i will be assigned a space s if

    σi = s and, dis < djs for all j with σj = s.

    In words,

    i chooses to go to the space s, and i is closer to any driver who goes to s.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 12 / 43

  • Cruising game

    Let Ai (σ) be a space assigned to driver i when drivers’ strategy is σ.

    Definition (Nash Equilibrium) A strategy profile σ∗ = {σ∗1, · · · , σ∗n} is a Nash equilibrium of the cruising game if for all i and σi ,

    Ai (σ∗) �i Ai (σi , σ∗−i )

    where σ∗−i denotes the strategy that all drivers except i follows the equilibrium strategy.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 13 / 43

  • Example

    s2 �1 s1 s1 �2 s2

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 14 / 43

  • Example: Nash equilibrium

    s2 �1 s1 s1 �2 s2

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 15 / 43

  • Example: Nash equilibrium

    s2 �1 s1 s1 �2 s2

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 16 / 43

  • Matching

    In a (one-sided) matching problem, there are

    I = {i1, · · · , in} : a set of agents with unit demand, S = {s1, · · · , sm} : a set of resources to be assigned, �I = (�i1 , · · · ,�in ) : a list of agents’ strict preferences over S ∪ ∅, �S =(�s1 , · · · ,�sm ) : a list of priorities at each s over agents.

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 17 / 43

  • Matching

    Priority �s is a binary relation that determines who has a higher claim at the space s. An agent i has higher claim than j at space s, if i �s j .

    Priority structure reflects various ”values”, e.g., senior priority, first-come-first-served, affirmative action, random lottery number, etc.

    In the parking problem, we first consider distance priority.

    i �s j iff dis < djs

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 18 / 43

  • Matching

    Priority �s is a binary relation that determines who has a higher claim at the space s. An agent i has higher claim than j at space s, if i �s j .

    Priority structure reflects various ”values”, e.g., senior priority, first-come-first-served, affirmative action, random lottery number, etc.

    In the parking problem, we first consider distance priority.

    i �s j iff dis < djs

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJune 23, 2017 18 / 43

  • Matching

    Priority �s is a binary relation that determines who has a higher claim at the space s. An agent i has higher claim than j at space s, if i �s j .

    Priority structure reflects various ”values”, e.g., senior priority, first-come-first-served, affirmative action, random lottery number, etc.

    In the parking problem, we first consider distance priority.

    i �s j iff dis < djs

    Jinyong Jeong (Boston College ITEA 2017, Barcelona)Parking Space Assignment Problem: A Matching Mechanism Design ApproachJun