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Assignment of Arrival Slots James Schummer Rakesh V. Vohra Kellogg School of Management (MEDS) Northwestern University March 2012 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 1 / 38

Overview Bad weather reduces available landing slots and causes flight cancelations. Initially, scarce resources (slot rationing). Eventually, excess resources (flight cancelations). A (re-)matching problem. Studied from operations perspective; little from mechanism design perspective. FAA/airlines agree on desirable attributes (mechanism design axioms). Our goal: formalize attributes; critique existing mechanism; offer superior alternative. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 2 / 38

Ground Delay Program (part 1 of 2) Rationing a scarce supply of slots to scheduled flights. Slot Flight 1:00 BA027 1:01 UA301 1:02 UA081 1:03 AA111 1:04 AF023 1:05 BA229 1:06 UA123 = Slot 1:00 1:02 1:04 1:06. Flight... U.S. F.A.A. now uses Ration-by-Schedule: first-come first-served, based on position in previous schedule. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 3 / 38

Ground Delay Program (part 1 of 2) Rationing a scarce supply of slots to scheduled flights. Slot Flight 1:00 BA027 1:01 UA301 1:02 UA081 1:03 AA111 1:04 AF023 1:05 BA229 1:06 UA123.. = Slot Flight 1:00 BA027 1:02 UA301 1:04 UA081 1:06 AA111.. U.S. F.A.A. now uses Ration-by-Schedule: first-come first-served, based on position in previous schedule. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 3 / 38

GDP (part 2 of 2): Reassignment Rationing/bad weather/mechanical problems may cause an airline to cancel a flight, leaving excess resources (slots). Part 2 of GDP is to move flights up, making efficiency use of landing capacity. Slot Flight 1:00 BA027 1:02 UA301 1:04 UA081 1:06 AA111 1:08 AF023 1:10 BA229 1:12 UA123.. 1:58 EI022 U.S. FAA now uses the Compression Algorithm (described later). Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 4 / 38

GDP (part 2 of 2): Reassignment Rationing/bad weather/mechanical problems may cause an airline to cancel a flight, leaving excess resources (slots). Part 2 of GDP is to move flights up, making efficiency use of landing capacity. Slot Flight 1:00 1:02 UA301 1:04 1:06 AA111 1:08 AF023 1:10 BA229 1:12 UA123.. 1:58 EI022 U.S. FAA now uses the Compression Algorithm (described later). Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 4 / 38

A matching problem Our objective: study only GDP part 2 (the reassignment problem). We take part 1 s rationing (RBS) as given. Any improvement we offer over the current algorithms becomes more striking, since adapting to RBS is a design constraint. In actuality, RBS is executed just once, while part 2 is repeatedly iterated over time: too complex to make reassignment a function of previous rounds trades. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 5 / 38

Industry Objectives Incentives The FAA and airlines agree on various objectives. If an airline reported a mechanical delay on a flight, the system would re-project its arrival time. If [rationing with Grover Jack were done] at that time, that flight would likely receive an additional delay on top of its mechanical delay. These effects were known as the Double Penalty issue... The airlines would simply not send in information that would [harm themselves]. RBS removes this disincentive." FAA website (http://cdm.fly.faa.gov/ad/rbs.html) That is, the FAA likes strategy-proofness: incentive to report feasible arrival times truthfully. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 6 / 38

Industry Objectives Incentives Once arrival slots have been allocated, the Compression algorithm performs schedule updates by an inter-airline slot exchange, which aims to provide airlines with an incentive to report flight cancelations and delays. Vossen and Ball (2006) Note, two incentive conditions: Incentive to report delays (arrival times). (strategy-proofness) Incentive to report cancelations (infinite arrival time?). No formalization in this trans/ops literature. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 7 / 38

Industry Objectives Incentives If an airline sits on a slot that it is not planning to use, is there any way for [the system] to detect this and to take this slot away from the airline? Should this be done?" US DOT internal memo, 1996. Concern about failure to truthfully report cancelations. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 8 / 38

Industry Objectives Property Rights Under the FAA s Facility Operation and Administration handbook, airlines can rearrange their own portion of the schedule. [An airline] can reassign its flight-slot assignment... It should be emphasized that this notion of slot ownership is one of the main tenets of the CDM paradigm: there is a general consensus among airlines that this is indeed a fair method of rationing arrival capacity." Vossen and Ball (2006) The CDM paradigm results from collaboration between FAA and airlines. We view this as an endorsement of the normative idea that airlines have a degree of property rights associated with some degree of ownership" of the slots assigned to them by the RBS procedure. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 9 / 38

Industry Objectives Money? No. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 10 / 38

Overview of Talk -2 Explanation of GDP -1 Discussion of objectives 0 Overview 1 Model 2 Compression Algorithm characteristics 3 TradeCycle algorithm Connection to previous literature characteristics Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 11 / 38

Model Set of slots S = {1, 2,..., S }. (s, t S) Set of airlines A. (A, B A) Set of flights F. (f, g F A F) earliest arrival time for f : e f S. Landing Schedule Π: F S (feasible). Slot ownership function Φ: S A (consistent with Π). We call (Π, Φ) an assignment. An Instance (or Economy) is I = (S, A, (F A ) A, e, Π, Φ). ( F < S ) A matching function maps I Π. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 12 / 38

Example of an Instance Slot Flight Airline feasible arrival time e f 1 vacant A 2 f 2 B 1 3 f 3 C 1 4 f 4 A 2 Slot 1: vacant and owned by airline A. Slot 2: owned by B, occupied by f 2 F B which could arrive in slot 1. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 13 / 38

Example of an Instance Slot Flight Airline feasible arrival time e f 1 vacant A 2 f 2 B 1 3 f 3 C 1 4 f 4 A 2 5 vacant B 6 f 6 C 5 7 f 7 A 5 8 f 8 B 6 9 vacant C 10 f 10 A 9 11 f 11 B 9 12 f 12 C 10 Slot 1: vacant and owned by airline A. Slot 2: owned by B, occupied by f 2 F B which could arrive in slot 1. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 13 / 38

Formalizing Objectives: preferences We are concerned with matching functions satisfying... Strategy-proofness; Non-manipulability by withholding slots; property rights (via IR, core, etc.). When is an airline better off? A weak" model: An airline gains only if each flight gains. Why use? Airlines already have some ability to make tradeoffs, by swapping flights within their own subschedule. Negative results are stronger. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 14 / 38

Formalizing Objectives We are concerned with matching functions that are... Strategy-proof: no airline can gain by misreporting the arrival times of its flights. Non-manipulable by slot destruction: no airline can gain by withholding (destroying) a vacant slot from the mechanism. (Weak) core selecting: no coalition of airlines could all (strictly) gain by simply trading amongst themselves. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 15 / 38

Basic Literature Our model is similar to housing problems (Shapley-Scarf). Differences are: Airlines can own multiple flights. Vacant slots (houses) belong to airlines. Preferences (of flights) are restricted: e f e f + 1 s 1 e f 1 Nevertheless we will see a connection to previous housing-market generalizations, e.g. Abdulkadiroglu and Sonmez (1999); Papai (2000). Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 16 / 38

Compression Algorithm Compression: If an airline can t use a slot, it trades with the next scheduled flight that can use it. Step 0 Begin with an initial assignment (Π, Φ). Set V = the set of vacant slots. Step 1 If V =, end the algorithm at (Π, Φ). Otherwise make active the earliest vacant slot s V. Step 2 Let A = Φ(s) denote the airline that owns s. If A has a later flight f F A that could feasibly use slot s, move f to s, make f s original slot active, and repeat Step 2. Otherwise go to Step 3. Step 3 If any other airline B has a later flight that could feasibly use slot s, let f be the earliest such flight. Move f to s, assign f s original slot to A, make it active, and return to Step 2. Otherwise delete useless slot s from V and return to Step 1. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 17 / 38

Compression Example Slot Flight Airline feasible arrival time e f 1 vacant A 2 f 2 B 1 3 f 3 C 1 4 f 4 A 2 5 vacant B 6 f 6 C 5 7 f 7 A 5 8 f 8 B 6 9 vacant C 10 f 10 A 9 11 f 11 B 9 12 f 12 C 10 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 18 / 38

Compression Example Slot Flight Airline feasible arrival time e f 1 f 2 B 1 2 vacant A 3 f 3 C 1 4 f 4 A 2 5 vacant B 6 f 6 C 5 7 f 7 A 5 8 f 8 B 6 9 vacant C 10 f 10 A 9 11 f 11 B 9 12 f 12 C 10 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 18 / 38

Compression Example Slot Flight Airline feasible arrival time e f 1 f 2 B 1 2 f 4 A 2 3 f 3 C 1 4 vacant A 5 vacant B 6 f 6 C 5 7 f 7 A 5 8 f 8 B 6 9 vacant C 10 f 10 A 9 11 f 11 B 9 12 f 12 C 10 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 18 / 38

Compression Example Slot Flight Airline feasible arrival time e f 1 f 2 B 1 2 f 4 A 2 3 f 3 C 1 4 vacant A 5 f 6 C 5 6 vacant B 7 f 7 A 5 8 f 8 B 6 9 vacant C 10 f 10 A 9 11 f 11 B 9 12 f 12 C 10 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 18 / 38

Compression Example Slot Flight Airline feasible arrival time e f 1 f 2 B 1 2 f 4 A 2 3 f 3 C 1 4 vacant A 5 f 6 C 5 6 f 8 B 6 7 f 7 A 5 8 vacant B 9 vacant C 10 f 10 A 9 11 f 11 B 9 12 f 12 C 10 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 18 / 38

Compression Example Slot Flight Airline feasible arrival time e f 1 f 2 B 1 2 f 4 A 2 3 f 3 C 1 4 vacant A 5 f 6 C 5 6 f 8 B 6 7 f 7 A 5 8 vacant B 9 f 10 A 9 10 vacant C 11 f 11 B 9 12 f 12 C 10 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 18 / 38

Compression Example Slot Flight Airline feasible arrival time e f 1 f 2 B 1 2 f 4 A 2 3 f 3 C 1 4 vacant A 5 f 6 C 5 6 f 8 B 6 7 f 7 A 5 8 vacant B 9 f 10 A 9 10 f 12 C 10 11 f 11 B 9 12 vacant C Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 18 / 38

Compression: incentives Theorem The compression algorithm is strategy-proof: it cannot be manipulated by misreporting an arrival time. Proof. Suppose f gets s by reporting e f honestly, but reports e f. If e f < e f s, then the outcome of the algorithm cannot be affected. Whenever f is the flight chosen in Steps 2 or 3 when e f is reported, f would still be chosen when e f is reported, because f never moved into a slot earlier than s. If s < e f, then f would have to end up in a slot strictly worse than s, since the Compression Algorithm never places a flight in a slot earlier than its reported earliest arrival time. If e f < e f, then the only way this misreport can change the outcome is to assign f to a slot earlier than e f, which is infeasible for f. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 19 / 38

Compression: slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 vacant A 2 vacant B 3 vacant A 4 f 4 C 2 5 f 5 B 4 6 f 6 A 4 7 f 7 B 1 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 20 / 38

Compression: slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 f 7 B 1 2 vacant B 3 vacant A 4 f 4 C 2 5 f 5 B 4 6 f 6 A 4 7 vacant A Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 20 / 38

Compression: slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 f 7 B 1 2 f 4 C 2 3 vacant A 4 vacant B 5 f 5 B 4 6 f 6 A 4 7 vacant A Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 20 / 38

Compression: slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 f 7 B 1 2 f 4 C 2 3 vacant A 4 f 5 B 4 5 vacant B 6 f 6 A 4 7 vacant A Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 20 / 38

Compression: slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 f 7 B 1 2 f 4 C 2 3 vacant A 4 f 5 B 4 5 f 6 A 4 6 vacant B 7 vacant A Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 20 / 38

Compression: slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 vacant A 2 f 7 B 1 3 vacant A 4 f 4 C 2 5 f 5 B 4 6 f 6 A 4 7 vacant B Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 20 / 38

Compression: slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 vacant A 2 f 7 B 1 3 f 4 C 2 4 vacant A 5 f 5 B 4 6 f 6 A 4 7 vacant B Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 20 / 38

Compression: slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 vacant A 2 f 7 B 1 3 f 4 C 2 4 f 6 A 4 5 f 5 B 4 6 vacant A 7 vacant B Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 20 / 38

The Core Definition An assignment is in the core if no coalition of airlines can strictly gain by simply trading amongst themselves from their original endowments. Loosely speaking, if an outcome is not in the core, then some airlines are not receiving the best slots to which they are entitled, based on their slot endowments. In this sense, the core provides a form of property rights. The Strong Core can be empty. (E.g., airline with a vacant slot and no flights.) Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 21 / 38

Core: Example revisited Slot Flight Airline feasible arrival time e f 1 vacant A 2 f 2 B 1 3 f 3 C 1 The strong core can be empty. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 22 / 38

Core: Example revisited Slot Flight Airline feasible arrival time e f 1 vacant A 2 f 2 B 1 3 f 3 C 1 4 f 4 A 2 Unique (strong) core matching (a là Shapley Scarf). Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 22 / 38

Core: Example revisited Slot Flight Airline feasible arrival time e f 1 vacant A 2 f 2 B 1 3 f 3 C 1 4 f 4 A 2 5 vacant B 6 f 6 C 5 7 f 7 A 5 8 f 8 B 6 9 vacant C 10 f 10 A 9 11 f 11 B 9 12 f 12 C 10 The core can be multi-valued. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 22 / 38

Compression and Core Apply Compression to the following example. Slot Flight Airline feasible arrival time e f 1 vacant A 2 vacant B 3 f 3 C 1 4 f 4 B 1 5 f 5 A 2 f 3 assigned to slot 1. Slot 3 is active; f 5 fills it. Slot 2 is active; f 4 fills it. However, this is not in the core. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 23 / 38

Compression and Core Apply Compression to the following example. Slot Flight Airline feasible arrival time e f 1 f 3 C 1 2 vacant B 3 vacant A 4 f 4 B 1 5 f 5 A 2 f 3 assigned to slot 1. Slot 3 is active; f 5 fills it. Slot 2 is active; f 4 fills it. However, this is not in the core. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 23 / 38

Compression and Core Apply Compression to the following example. Slot Flight Airline feasible arrival time e f 1 f 3 C 1 2 vacant B 3 f 5 A 2 4 f 4 B 1 5 vacant A f 3 assigned to slot 1. Slot 3 is active; f 5 fills it. Slot 2 is active; f 4 fills it. However, this is not in the core. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 23 / 38

Compression and Core Apply Compression to the following example. Slot Flight Airline feasible arrival time e f 1 f 3 C 1 2 f 4 B 1 3 f 5 A 2 4 vacant B 5 vacant A f 3 assigned to slot 1. Slot 3 is active; f 5 fills it. Slot 2 is active; f 4 fills it. However, this is not in the core. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 23 / 38

Top trading cycles Housing markets Each airline has exactly one flight/slot. No vacant slots. However, preferences are arbitrary. Shapley & Scarf describe the top trading cycle algorithm to find the unique core outcome. Each flight points to its favorite slot. Cycles exist, and are cleared. Repeat. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 24 / 38

TradeCycle Algorithm tep 0 Take as input an initial assignment, and declare all slots and flights active." tep 1 If the set of active flights is empty, the algorithm ends. Otherwise, construct a graph as follows. Step 1a Introduce a node for each active slot and each active flight. Step 1b From each flight f, draw a directed edge to the earliest active slot that f can occupy. Step 1c From each occupied slot, draw a directed edge to the flight that occupies it. Step 1c From each vacant slot owned by any airline A, draw a directed edge to (i) the earliest scheduled active flight in F A, if one exists; (ii) the earliest scheduled active flight in F, otherwise. tep 2 Within any (directed) cycle in the graph: Permanently assign each flight to the slot it points to in the cycle; declare the flight and its assigned slot inactive. (Newly vacated slots within a cycle remain active.) Return to Step 1. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 25 / 38

Example Apply TC to this example. Slot Flight Airline feasible arrival time e f 1 vacant A 2 vacant B 3 f 3 C 1 4 f 4 B 1 5 f 5 A 2 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 26 / 38

Link to past work Proposition TradeCycle is algorithmically equivalent to a fixed endowment hierarchical exchange rule (Pápai 2000) where 1 flights are treated as individual agents, and 2 each slot has an inheritance structure that prioritizes flights in the following order: 1 the flight that occupies it (if any), 2 other flights of the same airline, by ETA (if any), 3 flights of other airlines, by ETA. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 32 / 38

Incentives Theorem TradeCycle is strategy-proof: it cannot be manipulated by misreporting an arrival time. Proof. From Pápai 2000, FEHE rules for assignment problems are group strategy-proof even when arbitrary preferences over slots are permitted. Here, an airline is a coalition of flights, and (flight) preferences are restricted (e f e f + 1, etc.). Since group strategy-proofness is preserved under domain reduction, the result follows. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 33 / 38

Main Point Theorem TradeCycle returns an assignment in the weak core. Proof. Suppose B blocks the assignment via Π B. If B flights point to Π B, assignment stays same (gsp). Consider first round in which B loses a slot to B c. A cycle is formed where a flight in B c is pointed to by a vacant slot from B. Its owner must already be fully assigned, receiving its favorite slot for each airline, not strictly better off at Π B, contradiction. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 34 / 38

Tradecycle: slot destruction Proposition TradeCycle is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 vacant C 2 f 2 A 1 3 vacant A 4 vacant D 5 f 5 B 3 6 f 6 C 5 7 f 7 A 5 8 f 8 D 7 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 35 / 38

Tradecycle: slot destruction Proposition TradeCycle is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 f 2 A 1 2 vacant A 3 f 5 B 3 4 vacant D 5 f 6 C 5 6 vacant C 7 f 7 A 5 8 f 8 D 7 Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 35 / 38

Tradecycle: slot destruction Proposition TradeCycle is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 f 2 A 1 2 vacant A 3 f 5 B 3 4 vacant D 5 f 6 C 5 6 f 7 A 5 7 f 8 D 7 8 vacant C Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 35 / 38

Tradecycle: slot destruction Proposition TradeCycle is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 vacant C 2 f 2 A 1 3 vacant A 4 f 5 B 3 5 f 7 A 5 6 f 6 C 5 7 f 8 D 7 8 vacant D Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 35 / 38

Tradecycle: slot destruction Proposition TradeCycle is manipulable by slot destruction. Proof. Slot Flight Airline feasible arrival time e f 1 f 2 A 1 2 vacant C 3 vacant A 4 f 5 B 3 5 f 7 A 5 6 f 6 C 5 7 f 8 D 7 8 vacant D Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 35 / 38

Slot Destruction" in other matching models Theorem (Atlamaz and Klaus, 2007) Using our terminology, suppose airlines have arbitrary preferences over all subsets of slots. Then [Efficient + Individually Rational] [Manipulable by Endowment Destruction] No implication to our model, due to our preference restriction. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 36 / 38

Wrap-up Application of matching theory to another real world problem: reassignment of landing slots. FAA s current algorithm may fall outside of weak core. Our algorithm has the same incentives properties, and selects from the core. Our motivation for core rests more on property rights than on stability (e.g. unraveling in doctor/hospital markets). Strategy-proofness: obtainable (weak definition of prefs.) Core: obtainable. Airline incentive to keep useless slot. (proof of concept; is it widespread?) Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 37 / 38

Work in progress (with Azer Abizade) We suppose airlines can evaluate tradeoffs between flights. An airline may prefer moving one flight earlier at the cost of moving another flight later. This requires more preference information. Responsive? Separable? Linear? Preliminary results Any mechanism that does not solicit full preference information is manipulable. Strategy-proofness conflicts with Pareto-optimality. Schummer & Vohra (Northwestern Univ.) Assignment of Arrival Slots March 2012 38 / 38