Incentives in Landing Slot Problems

Transcription

1 Incentives in Landing Slot Problems James Schummer 1 Azar Abizada 2 1 MEDS, Kellogg School of Management Northwestern University 2 School of Business Azerbaijan Diplomatic Academy June 2013 Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

2 Overview The problem: to (re-)assign arriving flights to landing slots at a single airport. Objective: earlier is better. Each flight may have a constraint on earliest feasible time of arrival. In an ideal world, schedules are static. In the real world, disruptions (weather) create shocks that require rescheduling. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

3 Overview Main motivation: Ground Delay Programs Bad weather reduces supply of landing slots (per hour). Rationing step: flights are moved to later arrival times. This disrupts airline planning: flights cancelled, departure times changed. Airlines must report this information to FAA. Compression step: flights rescheduled again to fill vacated slots. (ad hoc looping of Compression.) Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

4 Overview Main motivation: Ground Delay Programs Bad weather reduces supply of landing slots (per hour). Rationing step: flights are moved to later arrival times. This disrupts airline planning: flights cancelled, departure times changed. Airlines must report this information to FAA. Compression step: flights rescheduled again to fill vacated slots. (ad hoc looping of Compression.) Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

5 Overview Main motivation: Ground Delay Programs Bad weather reduces supply of landing slots (per hour). Rationing step: flights are moved to later arrival times. This disrupts airline planning: flights cancelled, departure times changed. Airlines must report this information to FAA. Compression step: flights rescheduled again to fill vacated slots. (ad hoc looping of Compression.) Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

6 GDP Rationing Step Inclement weather reduces landing-slot supply. Slot Flight 1:00 UAL1 1:01 AAL2 1:02 BEL3 1:03 UAL4 1:04 THY5 1:05 AHY6 1:06 JAL7 = Slot 1:00 1:02 1:04 1:06. Flight... F.A.A. uses Ration-by-Schedule: first-come first-served, based on position in original landing schedule. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

7 GDP Rationing Step Inclement weather reduces landing-slot supply. Slot Flight 1:00 UAL1 1:01 AAL2 1:02 BEL3 1:03 UAL4 1:04 THY5 1:05 AHY6 1:06 JAL7.. = Slot Flight 1:00 UAL1 1:02 AAL2 1:04 BEL3 1:06 UAL4.. F.A.A. uses Ration-by-Schedule: first-come first-served, based on position in original landing schedule. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

8 GDP Compression Step Schedule changes/weather/mechanical problems cause airlines to subsequently cancel/delay flights, freeing slots, so... Part 2 of GDP: make use of vacated slots. Slot Flight Slot Flight Slot Flight 1:00 UAL1 1:02 AAL2 1:04 BEL3 1:06 UAL4 1:08 THY5 1:10 AHY6 1:12 JAL7 = 1:00 1:02 AAL2 1:04 1:06 UAL4 1:08 THY5 1:10 AHY6 1:12 JAL7 = 1:00????? 1:02????? 1:04????? 1:06????? 1:08????? 1:10????? 1:12?????.. 1:58 SAS1.. 1:58 SAS1.. 1:58????? Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

9 GDP Compression Step Schedule changes/weather/mechanical problems cause airlines to subsequently cancel/delay flights, freeing slots, so... Part 2 of GDP: make use of vacated slots. Slot Flight Slot Flight Slot Flight 1:00 UAL1 1:02 AAL2 1:04 BEL3 1:06 UAL4 1:08 THY5 1:10 AHY6 1:12 JAL7 = 1:00 1:02 AAL2 1:04 1:06 UAL4 1:08 THY5 1:10 AHY6 1:12 JAL7 = 1:00????? 1:02????? 1:04????? 1:06????? 1:08????? 1:10????? 1:12?????.. 1:58 SAS1.. 1:58 SAS1.. 1:58????? Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

10 GDP Compression Step Schedule changes/weather/mechanical problems cause airlines to subsequently cancel/delay flights, freeing slots, so... Part 2 of GDP: make use of vacated slots. Slot Flight Slot Flight Slot Flight 1:00 UAL1 1:02 AAL2 1:04 BEL3 1:06 UAL4 1:08 THY5 1:10 AHY6 1:12 JAL7 = 1:00 1:02 AAL2 1:04 1:06 UAL4 1:08 THY5 1:10 AHY6 1:12 JAL7 = 1:00????? 1:02????? 1:04????? 1:06????? 1:08????? 1:10????? 1:12?????.. 1:58 SAS1.. 1:58 SAS1.. 1:58????? FAA uses the Compression Algorithm (described later). Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

11 General Rescheduling Problem Jobs to be processed sequentially. Each agent owns a subset of jobs. Each job has an earliest-processing-time. There is an arbitrary, pre-existing schedule which may not be feasible. Two special cases: FAA rationing step: additional constraint that each even-numbered slot be vacant. (Typically move everyone down. ) FAA Compression step: pre-existing schedule is feasible, but may contain vacancies. (Typically move everyone up. ) Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

12 GDP Literature Operations/Transportation Economics Optimization: Vossen and Ball (2006a, 2006b): optimization; interpret FCC mechanism as a barter mechanism (implicitly assuming truthful behavior). Generalized optimization models: Niznik (2001) (downstream effects); Hoffman and Ball (2007) (connections constraints); Ball, Dahl, and Vossen (2009) (endogenous cancelations); etc. Equity considerations: Vossen and Ball (2006a) (Lorenz domination result!); Manley and Sherry (2010) (performance and equity measures for various other methods of rationing slots). Matching: Balakrishnan (2007) (flights as agents/ttc). Incentives Schummer and Vohra (2013) (weak incentives/weak core). Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

13 Illustration of Model: A (Simple) Instance (FAA) Slot Flight Airline earliest (e f ) 1 A 2 f 2 B 1 3 f 3 C 1 4 f 4 A 2 5 B 6 f 6 C 5 7 f 7 A 5 8 f 8 B 6 9 C 10 f 10 A 9 11 f 11 B 9 12 f 12 C 10 Slots 1,5,9 have been vacated (e.g. by cancelled flights). From a mechanism design perspective, what is missing? Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

14 Illustration of Model: A (Simple) Instance (FAA) Slot Flight Airline earliest (e f ) 1 A 2 f 2 B 1 3 f 3 C 1 4 f 4 A 2 5 B 6 f 6 C 5 7 f 7 A 5 8 f 8 B 6 9 C 10 f 10 A 9 11 f 11 B 9 12 f 12 C 10 Slots 1,5,9 have been vacated (e.g. by cancelled flights). From a mechanism design perspective, what is missing? Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

15 Preferences The parameters of a Simple Instance do not indicate an airline s relative preference for improving one flight at the expense of another. Possible reasons for this: Complexity and cost: Such preferences would have to be determined on short notice, for each unique situation. There does exist a protocol (SCS) in the real world, in which pairs of airlines can submit requests to trade specific slots. Robyn (2007) argues that this system is unwieldy. Airlines make independent requests; only coincident requests are executed. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

16 What is the preference domain? Earlier is better. How much better? Why would an airline prioritize one flight over another? Variable costs (fuel, labor). Fixed costs (crew timing out, passengers making connections) To simplify initial analysis, we assume that only (constant) variable costs are relevant: each flight has its own linear delay cost. Results are robust to larger domains of preferences. Negative results generalize trivially. Positive results can be shown to extend to reasonably larger domains. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

17 What is the preference domain? Earlier is better. How much better? Why would an airline prioritize one flight over another? Variable costs (fuel, labor). Fixed costs (crew timing out, passengers making connections) To simplify initial analysis, we assume that only (constant) variable costs are relevant: each flight has its own linear delay cost. Results are robust to larger domains of preferences. Negative results generalize trivially. Positive results can be shown to extend to reasonably larger domains. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

18 Example of a (General) Instance Each flight, f, has a weight, w f, reflecting its cost of delay. Slot Flight Airline e f weight 1 vacant A 2 f 2 B f 3 A f 4 A 1 1 Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

19 Example of a (General) Instance Each flight, f, has a weight, w f, reflecting its cost of delay. Slot Flight Airline e f weight 1 vacant A 2 f 2 B f 3 A f 4 A 1 1 Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

20 Model An Instance I consists of... S set of slots; A set of airlines; F A set of flights for each A A; e earliest feasible arrival e f for each f F; w weight w f for each f F; (Π 0, Φ 0 ) initial assignment. For each instance I, a rule ϕ determines a landing schedule ϕ(i). (The domain of instances: results are robust to the specification of the domain. E.g. all of our counterexamples use initial assignments that are feasible.) Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

21 Basic objectives Property rights: forcibly taking slots from an airline is disruptive to its planning, and hence is costly. Note that in Rationing step, bad weather forces the FAA to do this; it is unavoidable. In the Compression step it is feasible to make every airline no worse off, so we require (weak) individual rationality: no airline strictly prefers the initial landing schedule. Efficiency: The FAA s primary objective is to feasibly reschedule flights to improve efficiency. Nonwasteful: no vacant slot is desired by a later flight. Self-optimized (discuss later in talk). Pareto-efficient: requires weights! Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

22 Basic objectives Property rights: forcibly taking slots from an airline is disruptive to its planning, and hence is costly. Note that in Rationing step, bad weather forces the FAA to do this; it is unavoidable. In the Compression step it is feasible to make every airline no worse off, so we require (weak) individual rationality: no airline strictly prefers the initial landing schedule. Efficiency: The FAA s primary objective is to feasibly reschedule flights to improve efficiency. Nonwasteful: no vacant slot is desired by a later flight. Self-optimized (discuss later in talk). Pareto-efficient: requires weights! Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

23 Incentives: reporting arrival times Definition Rule ϕ is manipulable by intentional flight delay if there is airline A A, flight f F A, and (false) e f > e f such that A gains from delaying f to e f : ϕ(i ) w A ϕ(i). Two interpretations (relevant for other applications). e f s are private information and can be misreported without detection. In this case we are defining a weak (one-direction) strategyproofness condition. e f s are observable, but an airline can first take some private action that commits itself to e f > e f (e.g. simply report that. In this case only e f > e f is a feasible misreport. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

24 Incentives: reporting arrival times Definition Rule ϕ is manipulable by intentional flight delay if there is airline A A, flight f F A, and (false) e f > e f such that A gains from delaying f to e f : ϕ(i ) w A ϕ(i). Two interpretations (relevant for other applications). e f s are private information and can be misreported without detection. In this case we are defining a weak (one-direction) strategyproofness condition. e f s are observable, but an airline can first take some private action that commits itself to e f > e f (e.g. simply report that. In this case only e f > e f is a feasible misreport. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

25 Pareto efficiency & flight delay Theorem If a rule is Pareto-efficient and individually rational, then it is manipulable by intentional flight delay. Proof. Slot Flight Airline e f weight 1 b 1 B a 2 A a 3 A b 4 B a 5 A b 6 B There are only two efficient, IR schedules. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

26 Pareto efficiency & flight delay Theorem If a rule is Pareto-efficient and individually rational, then it is manipulable by intentional flight delay. Proof. Slot Flight Airline e f weight 1 b 1 B a 2 A a 3 A b 4 B a 5 A b 6 B There are only two efficient, IR schedules. If ϕ favors B, then A can benefit by delaying a 2. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

27 Pareto efficiency & flight delay Theorem If a rule is Pareto-efficient and individually rational, then it is manipulable by intentional flight delay. Proof. Slot Flight Airline e f weight 1 b 1 B a 2 A a 3 A b 4 B a 5 A b 6 B There are only two efficient, IR schedules. If ϕ favors A, then B can benefit by delaying b 4. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

28 Incentives: reporting weights Definition Rule ϕ is manipulable via weights if there is airline A A, flight f F A, and (false) weight w f such that A gains from reporting w f : ϕ(i ) w A ϕ(i). Trivially, the FAA s current rule is not manipulable in this way (because no such information is solicited). Is this condition relevant? Fuel cost/aircraft size are observable. However other things are not: crew time-outs, passenger connections, flight occupancy, etc. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

29 Pareto efficiency & weight reports Theorem If a rule is Pareto-efficient and individually rational, then it is manipulable by misreporting weights. Proof. Slot Flight Airline e f weight 1 b 1 B a 2 A a 3 A a 4 A b 5 B 4 3 There are only two efficient, IR schedules. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

30 Pareto efficiency & weight reports Theorem If a rule is Pareto-efficient and individually rational, then it is manipulable by misreporting weights. Proof. Slot Flight Airline e f weight 1 b 1 B a 2 A a 3 A a 4 A b 5 B 4 3 There are only two efficient, IR schedules. B can overweight b 1 to ensure B s favorite outcome. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

31 Pareto efficiency & weight reports Theorem If a rule is Pareto-efficient and individually rational, then it is manipulable by misreporting weights. Proof. Slot Flight Airline e f weight 1 b 1 B a 2 A a 3 A a 4 A b 5 B 4 3 There are only two efficient, IR schedules. A can underweight a 2 to ensure A s favorite outcome. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

32 Incentives: timely report of cancellations If an airline sits on a slot that it is not planning to use, is there any way for ATMS to detect this and to take this slot away from the airline? Should this be done? D.O.T. memo, Definition Rule ϕ is manipulable via slot destruction at instance I if there is airline A A and slot s S such that (i) A initially owns s; (ii) s is initially vacant; (iii) A is better off at ϕ( I \ s ). But, what ultimately happens to the destroyed slot? Hide" slot s by postponing cancellation; run ϕ on I \ s ; Release s by announcing cancellation;??? by law, owner has first rights to s before rerunning ϕ Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

33 Incentives: timely report of cancellations If an airline sits on a slot that it is not planning to use, is there any way for ATMS to detect this and to take this slot away from the airline? Should this be done? D.O.T. memo, Definition Rule ϕ is manipulable via slot destruction at instance I if there is airline A A and slot s S such that (i) A initially owns s; (ii) s is initially vacant; (iii) A is better off at ϕ( I \ s ). But, what ultimately happens to the destroyed slot? Hide" slot s by postponing cancellation; run ϕ on I \ s ; Release s by announcing cancellation;??? by law, owner has first rights to s before rerunning ϕ Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

34 Incentives: timely report of cancellations If an airline sits on a slot that it is not planning to use, is there any way for ATMS to detect this and to take this slot away from the airline? Should this be done? D.O.T. memo, Definition Rule ϕ is manipulable via slot destruction at instance I if there is airline A A and slot s S such that (i) A initially owns s; (ii) s is initially vacant; (iii) A is better off at ϕ( I \ s ). But, what ultimately happens to the destroyed slot? Hide" slot s by postponing cancellation; run ϕ on I \ s ; Release s by announcing cancellation;??? by law, owner has first rights to s before rerunning ϕ Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

35 Incentives: timely report of cancellations If an airline sits on a slot that it is not planning to use, is there any way for ATMS to detect this and to take this slot away from the airline? Should this be done? D.O.T. memo, Definition Rule ϕ is manipulable via slot destruction at instance I if there is airline A A and slot s S such that (i) A initially owns s; (ii) s is initially vacant; (iii) A is better off at ϕ( I \ s ). But, what ultimately happens to the destroyed slot? Hide" slot s by postponing cancellation; run ϕ on I \ s ; Release s by announcing cancellation;??? by law, owner has first rights to s before rerunning ϕ Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

36 Incentives: timely report of cancellations A more realistic definition: Definition Rule ϕ is manipulable by postponing a flight cancelation at instance I if there is airline A A and slot s S such that (i) A initially owns s; (ii) s is initially vacant; (iii) A is better off when allowed to assign its flights to any slots in {s} ϕ( I \ s ). Analogous to the endowment hiding" incentive conditions in the literature. One might even consider rerunning ϕ after A unhides" s. When ϕ is individually rational, this is a stronger condition than ours. Our results would continue to hold using this condition. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

37 Pareto efficiency and flight cancelations Theorem If a rule is Pareto-efficient and individually rational, then it is manipulable by slot destruction (and hence by postponing a flight cancellation). Idea behind the instance used in proof: Efficiency requires a three way trade between airlines A, B, C; IR requires a payment to C from A and/or B; Either payer (A, B) can make payment appear too costly by destroying a vacant slot. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

38 (Instance used in previous proof.) Slot Flight Airline e f weight 1 a 1 A b 2 B b 3 B c 4 C c 5 C a 6 A a 7 A d 8 D 8 9 d 9 D 9 10 vacant A 11 c 11 C b 12 B d 13 D d 14 D vacant B 16 c 16 C Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

39 Dropping Pareto-efficiency The first three results tell us that non-manipulability conflicts with Pareto-efficiency. This is a (partial!) justification for the FAA s approach: not to solicit weights (i.e. preference information) at all. Next step: analyze rules in which the planner does not solicit weights. Weaken Pareto-efficiency to non-wastefulness. Definition (Soon to be obsolete.) A rule is weight-invariant if it is constant with respect to weights. But there is a problem with this definition. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

40 Dropping Pareto-efficiency The first three results tell us that non-manipulability conflicts with Pareto-efficiency. This is a (partial!) justification for the FAA s approach: not to solicit weights (i.e. preference information) at all. Next step: analyze rules in which the planner does not solicit weights. Weaken Pareto-efficiency to non-wastefulness. Definition (Soon to be obsolete.) A rule is weight-invariant if it is constant with respect to weights. But there is a problem with this definition. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

41 Self-optimizing From the FAA s Facility Operation and Administration Handbook, Section c: Users are permitted to exchange and substitute Controlled Times of Arrival (CTA) congruent with CDM agreements concerning substitutions. Translation: by rule, an airline can trade with itself. Regardless of what a rule prescribes, an airline will self-optimize its own portion of the landing schedule. Thus a revelation-principle argument restricts us to: Definition A rule is self-optimized if no airline can gain by trading with itself (swapping flights within its own portion of the schedule). Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

42 Self-optimizing From the FAA s Facility Operation and Administration Handbook, Section c: Users are permitted to exchange and substitute Controlled Times of Arrival (CTA) congruent with CDM agreements concerning substitutions. Translation: by rule, an airline can trade with itself. Regardless of what a rule prescribes, an airline will self-optimize its own portion of the landing schedule. Thus a revelation-principle argument restricts us to: Definition A rule is self-optimized if no airline can gain by trading with itself (swapping flights within its own portion of the schedule). Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

43 Self-optimizing examples Not self-optimized: Slot Flight Airline e f weight 1 vacant B 2 a 2 A a 3 A 2 4 Self-optimized: Slot Flight Airline e f weight 1 vacant B 2 a 3 A a 2 A 1 2 Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

44 FAA-conforming All of this motivates our restriction to the following class of rules. Definition A rule is FAA-conforming if it is non-wasteful; self-optimizing; simple (weak w-invariant): the set of slots allocated to an airline is invariant to the reports of weights. Trivially, FAA-conforming implies non-manipulable by misreporting weights. The FAA s current rule (the Compression Algorithm) is FAA-conforming (assuming airlines actually perform self-optimization themselves). Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

45 FAA-conforming - Manipulable by flight delay Theorem If a rule is individually rational and FAA-conforming (simple, nonwasteful, self-optimized), then it is manipulable by intentional flight delay. Proof. Slot Flight Airline e f w w Uses: 1 A 2 A 3 b 3 B c 4 C b 5 B c 6 C b 7 B Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

46 FAA-conforming rules and slot destruction Previous examples of FAA-conforming rules are also manipulable by slot destruction. Proposition (Schummer Vohra) Both the Compression Algorithm Rule and the TTC-variant of Schummer Vohra are (strongly) manipulable by slot destruction. (Strongly manipulable: an airline could make all of its flights better off through manipulation.) On the other hand we now provide a rule that is very robust to such manipulation. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

47 Deferred Acceptance with Self Optimization (Simplified description. See paper for more.) For any slot s S, let s be a strict order of the airlines, with the owner of s at the top of s. The DASO rule for ( s ) S yields the outcome of this algorithm (deferred acceptance plus a flight-specific assignment): Step 1: Each slot s proposes to the top airline in s. Each airline A tentatively accepts proposals from its favorite set of slots from those that proposed to A. Step k: Each rejected slot s proposes to the best airline in s that has not yet rejected s. Each airline A tentatively accepts proposals from its favorite set of slots from those that have ever proposed to A. Self-optimization step: Once no slots are rejected, each airline A assigns flights to its slots as it wishes. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

48 Simplified algorithm (exploiting structure of model) Step 1: Temporarily assign to slot 1 any f F A, where A is the highest-ranked airline in 1 that can feasibly use slot 1. Remove f from the list of flights. (If no such flight, slot 1 permanently vacant.) Step 2: Temporarily assign to slot 2 any g F B such that, subject to the removal of f, B is the highest-ranked airline in 2 that can feasibly use slot 2. Remove g from the list of flights. (If no such flight, slot 2 is vacant.) Step k: Continue such assigning to each slot k, until no more flights. Self-optimization step: self-optimize the temporary landing schedule. We thank Utku Ünver for pointing out this description. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

49 DASO: properties DASO rules satisfy the following. FAA-conforming (non-wasteful, simple, self optimized); individually rational; non-manipulable by misreporting weights; is manipulable by intentional flight delay (previous thm.). However, weakly non-manipulable by flight delay à la Schummer/Vohra. and... Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

50 DASO: reporting cancelations DASO rules are not only immune to slot destruction, but satisfy our stronger property. Theorem Each DASO rule is non-manipulable by postponing flight cancellations. In fact if an airline hides a slot, then all airlines are made (weakly) worse off. (Crawford (1991) implies non-manipulable by slot destruction.) Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

51 Weak incentives Definition (Schummer/Vohra) A rule has a strong manipulation by flight delay if airline A A can misreport e f and improve each of its flights (weakly, with at least one strictly). It is weakly non-manipulable by flight delay if there is never a strong manipulation. Motivation: A strong manipulation would be profitable for any weight profile. Hence an airline need not think about weights to detect profitable deviations. Proposition Any DASO rule is weakly non-manipulable by intentional flight delay. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

52 Weak incentives Definition (Schummer/Vohra) A rule has a strong manipulation by flight delay if airline A A can misreport e f and improve each of its flights (weakly, with at least one strictly). It is weakly non-manipulable by flight delay if there is never a strong manipulation. Motivation: A strong manipulation would be profitable for any weight profile. Hence an airline need not think about weights to detect profitable deviations. Proposition Any DASO rule is weakly non-manipulable by intentional flight delay. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

53 Weak incentives Schummer Vohra consider only strong manipulations (where each flight improves). Because weights w f are not present in their model, they also do not explicitly model self-optimization of landing schedules. Proposition (Schummer-Vohra) The FAA s Compression Algorithm (without self-optimization) is weakly non-manipulable by intentional flight delay. The TTC-variant of S V (without self-optimization) is weakly non-manipulable by intentional flight delay. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

54 Weak incentives and self-optimization Adding weights and self-optimization to Schummer Vohra s model, we show that their result is robust as follows: Proposition Consider a rule that first self-optimizes the initial landing schedule, and then runs the Compression Algorithm (or the TTC-variant). This rule is weakly non-manipulable by intentional flight delay. (The output is also self-optimized.) Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

55 Weak incentives and self-optimization A subtlety: Proposition Consider a rule that first runs the Compression Algorithm (resp. TTC-variant), and then self-optimizes the output. This rule is not weakly non-manipulable by intentional flight delay (i.e. it is strongly manipulable). This reveals an important design consideration in this environment: it is important to know whether the agents have the right to use their allocated objects as they wish. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

56 Weak incentives and self-optimization (Illustration of previous Proposition.) A Compress-then-self-optimize rule can be strongly manipulated. Slot Flight Airline e f weight 1 vacant C 2 a 2 A b 3 B a 4 A By misreporting e a 2 = 1 (and self-optimizing later).... By swapping the positions of a 2 and a 4 before Compression is executed. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

57 Weak incentives and self-optimization Compression can be manipulated by de-self-optimizing the initial schedule. Slot Flight Airline e f weight 1 C 4 d 4 D 5 a 5 A b 6 B a 7 A 1 1 A can (suboptimally) swap a 5 and a 7 which, initially, makes A worse off. DASO rules are invariant to changes in the specific assignment of A s flights to A s initial slots; hence non-manipulable by such behavior. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

58 Summary We considered two general classes of methods for reassigning landing slots. Pareto-efficient methods. All are manipulable by misreporting... flight delays (arrival time). full preference information (weights). cancellations (slot destruction). FAA-conforming methods (ignore weights, except to self-optimize). Manipulable by intentional flight delays. Trivially non-manipulable by misreporting weights. DASO rules... non-manipulable by postponing flight cancellations (slot-hiding); weakly non-manipulable by intentional delays. Weak incentives Three rules satisfy; only DASO robust to order/decentralization of self-optimization. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

59 Main punchlines Main points: DASO rules dominate other simple rules in terms of incentive properties. Robust non-manipulability to postponing flight cancelations. DASO weak non-manipulability to flight delay is robust to timing of self-optimization (important since airlines handle this part of the implementation in a decentralized way). Simple Rule Non-manipulable by... Compression TC DASO flight delay (weakly) Y* Y* Y slot destruction (weakly) Y slot destruction Y postpone flight cancelation Y selects from weak core Y Y*: weak incentives may not be robust to self-optimization. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

60 Main punchlines Main points: DASO rules dominate other simple rules in terms of incentive properties. Robust non-manipulability to postponing flight cancelations. DASO weak non-manipulability to flight delay is robust to timing of self-optimization (important since airlines handle this part of the implementation in a decentralized way). Simple Rule Non-manipulable by... Compression TC DASO flight delay (weakly) Y* Y* Y slot destruction (weakly) Y slot destruction Y postpone flight cancelation Y selects from weak core Y Y*: weak incentives may not be robust to self-optimization. Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

61 Appendix Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

62 Appendix: Compression Example Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

63 Appendix: Compression Example Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

64 Appendix: Compression Example Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

65 Appendix: Compression Example Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

66 Appendix: Compression Example Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

67 Appendix: Compression Example Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

68 Appendix: Compression Example Slot Flight Airline e f (earliest feas.) 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 f 11 B 9 12 vacant C Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

69 Appendix: Compression and incentives Good news (weak incentive compatibility): Theorem Under Compression, if an airline misreports a flight s arrival time, that flight is weakly worse off (gets an infeasible slot or a later slot). Bad news (fails a stronger form): Slot (s) Flight (f ) Airline e f weight 1 vacant A 2 f 2 B 1-3 f 3 A f 4 A 1 1 Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

70 Appendix: Compression and incentives Good news (weak incentive compatibility): Theorem Under Compression, if an airline misreports a flight s arrival time, that flight is weakly worse off (gets an infeasible slot or a later slot). Bad news (fails a stronger form): Slot (s) Flight (f ) Airline e f weight 1 vacant A 2 f 2 B 1-3 f 3 A f 4 A 1 1 Schummer/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

71 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

72 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

73 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

74 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

75 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

76 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

77 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

78 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

79 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43

80 Appendix: Compression and slot destruction Proposition The Compression Algorithm is manipulable by slot destruction. Proof. Slot Flight Airline e f (earliest feas.) 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/Abizada (Northwestern/A.D.A.) Incentives in Landing Slot Problems June / 43