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Title: Preference%20Elicitation%20in%20Combinatorial%20Auctions


1
Preference Elicitation in Combinatorial Auctions
  • Tuomas Sandholm
  • Carnegie Mellon University
  • Computer Science Department
  • (papers on this topic available via
    www.cs.cmu.edu/sandholm)

2
Outline
  • Combinatorial auctions for multi-item auctions
  • The revelation problem
  • Previous approaches
  • Our approach Elicitor agent
  • Topological observations that motivate
    elicitation
  • Different elicitation queries
  • Policy dependent elicitor algorithms
  • General policy independent elicitor framework
    (with data structures assimilation algorithms)
    specific elicitor algorithms
  • Making the elicitor incentive compatible

3
Combinatorial auction
  • Can bid on combinations of items Rassenti,Smith
    Bulfin 82...
  • Bidders perspective
  • Allows bidder to express what she really wants
  • Avoids exposure problems
  • No need for lookahead / counterspeculationing of
    items
  • Auctioneers perspective
  • Automated optimal bundling
  • Binary winner determination problem
  • Label bids as winning or losing so as to maximize
    sum of bid prices
  • Each item can be allocated to at most one bid
  • NP-complete Rothkopf et al 98 using Karp 72
  • Inapproximable Sandholm IJCAI-99, AIJ-02 using
    Hastad 99

4
Another complex problem in combinatorial
auctions Revelation problem
  • In direct-revelation mechanisms (e.g. VCG),
    bidders bid on all 2items combinations
  • Need to compute the valuation for exponentially
    many combination
  • Each valuation computation can be NP-complete
  • For example if a carrier company bids on trucking
    tasks TRACONET Sandholm AAAI-93
  • Need to communicate the bids
  • Need to reveal the bids
  • Loss of privacy strategic info

5
Revelation problem
  • Agents need to decide what to bid on
  • Waste effort on counter-speculation
  • Waste effort making losing bids
  • Fail to make bids that would have won
  • Reduces economic efficiency revenue

6
What info is needed from an agent depends on what
others have revealed
Elicitor
Clearing algorithm
Elicitor decides what to ask next based on
answers it has received so far
Conen S. IJCAI-01 workshop on Econ. Agents,
Models Mechanisms, ACMEC-01
7
Elicitor Conen Sandholm 2001
  • Have auctioneer incrementally elicit information
    from bidders
  • based on the info received from bidders so far

8
Elicitation
  • Goal minimize elicitation
  • Regardless of computational / storage cost
  • (Future work explore tradeoffs across these)
  • Approach
  • At each phase
  • Elicitor decides what to ask (and from which
    bidder)
  • Elicitor asks that and propagates the answer in
    its data structures
  • Elicitor checks whether the auction can already
    be cleared optimally given the information in hand

9
Setting
  • Combinatorial auction m items for sale
  • Private values auction, no allocative
    externalities
  • Each bidder i has value function, vi 2m ? R
  • Unique valuations (to ease presentation)

10
Terminology
  • (X1,...,Xbidders) is a collection
  • Bundle Xi is earmarked for agent i
  • An allocation is a feasible collection (i.e.,
    collection where Xis dont overlap in items)
  • Objectives (1) Find Pareto efficient
    allocation(s) (2) Find social welfare
    maximizing allocation(s)

11
Outline
  • Query policy dependent ( rank lattice based)
    elicitor algorithms
  • Policy independent elicitor algorithms
  • Note Private values model

12
Rank lattice
Bundle Ø A B AB Rank for Agent 1
4 2 3 1 Rank for Agent 2 4 3
2 1
1,1
1,2
2,1
3,1
2,2
1,3
2,3
3,2
1,4
4,1
2,4
3,3
4,2
3,4
4,3
4,4
Infeasible
Feasible
Dominated
13
A search algorithm for the rank lattice
  • Algorithm PAR PAReto optimal
  • OPEN ? (1,...,1)
  • while OPEN ? do
  • Remove(c,OPEN) SUC ? suc(c)
  • if Feasible(c) then
  • PAR ? PAR ? c Remove(SUC,OPEN)
  • else foreach node ? SUC do
  • if node ? OPEN and Undominated(node,PAR)
  • then Append(node,OPEN)
  • Thrm. Finds all feasible Pareto-undominated
    allocations (if bidders utility functions are
    injective)
  • Welfare maximizing solution(s) can be selected as
    a post-processor by evaluating those allocations
  • Call this hybrid algorithm MPAR (for maximizing
    PAR)

14
Value-augmented rank lattice
Bundle Ø A B AB Value for Agent 1 0
4 3 8 Value for Agent 2 0 1 6 9
17
1,1
14
13
1,2
2,1
10
12
9
3,1
2,2
1,3
8
9
2,3
3,2
1,4
4,1
2,4
3,3
4,2
3,4
4,3
4,4
15
Search algorithm family for the value-augmented
rank lattice
  • Algorithm EBF Efficient Best First
  • OPEN ? (1,...,1)
  • loop
  • if OPEN 1 then c ? combination in OPEN
  • else
  • M ? k ? OPEN v(k) maxnode ? OPEN v(node)
  • if M ? 1 ? ?node ? M with Feasible(node) then
    return node
  • else choose c ? M such that c is not dominated
    by any node ? M
  • OPEN ? OPEN \ c
  • if Feasible(c) then return c
  • else foreach node ? suc(c) do
  • if node ? OPEN then OPEN ? OPEN ? node
  • From now on, assume quasilinear utility functions
  • Thrm. Any EBF algorithm finds welfare maximizing
    allocations
  • Thrm. VCG payments can be determined from the
    information already elicited

16
Rank lattice based partially-revealing VCG
  • Use EBF to explore rank lattice top-down,
    best-first
  • Elicitors queries (start at rank 1)
  • tell me the bundle at the current rank (bundle
    query),
  • tell me the value of the bundle at the current
    rank (value query), increment rank
  • Natural sequence from good to bad bundles
  • Elicit just the information necessary to find the
    best undominated feasible allocation
  • Thrm. VCG payments can be determined from the
    information already obtained

17
Best worst case elicitation effort
  • Best case rank vector (1,...,1) is feasible
  • One bundle query to each agent, no value queries
  • (VCG payments 0)
  • Thrm. Any EBF algorithm requires at worst
    (2items bidders biddersitems)/2 1 value
    queries
  • Proof idea. Upper part of the lattice is
    infeasible and not less in value than the
    solution
  • Not surprising because worst-case communication
    complexity of the problem is exponential Nisan
    01

18
EBF minimizes feasibility checks
  • Def An algorithm is admissible if it always
    finds a welfare maximizing allocation
  • Def An algorithm is admissibly equipped if it
    only has
  • value queries, and
  • a feasibility function on rank vectors, and
  • a successor function on rank vectors
  • Thrm There is no admissible, admissibly equipped
    algorithm that requires fewer feasibility checks
    (for every problem instance) than any EBF
    algorithm

19
Partial-revelation mechanisms Theoretical results
  • The EBF-based mechaAn extended EBF algorithm,
    RANK, determines an efficient allocation and VCG
    payments with no additional queries
  • A RANK mechanism is incentive-compatible and
    economically efficient
  • Thrm. Let B be the EBF that is used in a specific
    RANK mechanism. Then there does not exist any
    other mechanism based on an admissible,
    admissibly equipped, deterministic algorithm that
    requires fewer checks of the feasibility of nodes
    for all instances of the allocation problem

20
MPAR minimizes value queries
  • Thrm. No admissible, admissibly equipped
    algorithm (that calls the valuation function for
    bundles in feasible rank vectors only) will
    require fewer value queries than MPAR

21
MPAR minimizes value queries
  • Thrm. No admissible, admissibly equipped
    algorithm (that calls the valuation function for
    bundles in feasible rank vectors only) will
    require fewer value queries than MPAR
  • MPAR requires at most biddersitems value queries

22
Differential-revelation
  • Extension of EBF
  • Information elicited differences between
    valuations
  • Hides sensitive value information
  • Motivation max ? vi(Xi) ? min ? vi(r-1(1))
    vi(Xi)
  • Maximizing sum of value ? Minimizing difference
    between value of best ranked bundle and bundle in
    the allocation
  • Thrm. Differences suffice for determining welfare
    maximizing allocations VCG payments
  • 2 low-revelation incremental ex post incentive
    compatible mechanisms ...

23
Differential elicitation ...
  • Questions (start at rank 1)
  • tell me the bundle at the current rank
  • tell me the difference in value of that bundle
    and the best bundle
  • increment rank
  • Natural sequence from good to bad bundles

24
Differential elicitation ...
  • Variation Bitwise decrement mechanism
  • Is the difference in value between the best
    bundle and the bundle at the current rank greater
    than d?
  • if yes increment d, requires min. Increment
  • allows establishing a bit stream (yes/no
    answers)

25
Differential-revelation Algorithm
  • Like EBF algorithms, except in step 3,
    determination of the set of combinations that are
    considered for expansion
  • M k?OPEN Tight(k) ? ?k ?d for all d with
    Tight(d) ? ?k lt ?d for all d with Not(Tight(d))

26
Differential-revelation Theoretical results
  • Any algortihm of the modified EBF family finds a
    welfare-maximizing feasible allocation
  • Given an arbitrary subset of rank lattice nodes,
    the set M is the same whether the original EBF or
    the differential-revelation EBF is used
  • No additional revelation is needed to determine
    the VCG payments
  • The differential-revelation mechanisms are
    incentive compatible and economically efficient

27
Policy independent elicitor algorithms
28
Some of our elicitors query types
  • Order information Which bundle do you prefer, A
    or B?
  • Value information What is your valuation for
    bundle A? (Answer Exact or Bounds)
  • Rank information
  • What is the rank of bundle b?
  • What bundle is at rank x?
  • Given bundle b, what is the next lower (higher)
    ranked bundle?

29
Interrogation An Example
Questions of the Auctioneer Answers of the
Agents
  1. a1,a2 Give me your highest ranking bundle
  2. a1,a2 Give me your next best bundle
  3. a1 Give me your valuation for AB and Aa2 Give
    me your valuation for AB and B
  • a1 AB, a2 AB(not feasible)
  • a1 A, a2 B(feasible)
  • a1 vAB8, vA4a2 vAB9, vB6

30
General Algorithmic Framework for Elicitation
Algorithm Solve(Y,G) while not Done(Y,G) do o
SelectOp(Y,G) ? Choose question I
PerformOp(o,N) ? Ask bidder G Propagate(I,G) ?
Update data structures with answer Y
Candidates(Y,G) ? Curtail set of candidate
allocations
Output Y set of optimal allocations Input Y
set of candidate allocations (some may turn
out infeasible, some suboptimal) G partially
augmented order graph
31
General Task of the Procedures
  • Done checks if the topological structure has
    been sufficiently explored to exclude
    existence of better solutions
  • In SelectOp, a Policy determines which questions
    to ask next
  • PerformOp asks the questions and obtains
    answers
  • Propagate will update the augmented order graph
  • Candidates will determine a new set of potential
    solutions based on the update graph

32
(Partially) Augmented Order Graph
8
8
8
8
8
8
Ø
B
A
AB
Agent1
A
Ø
0
0
0
0
gt
Allocations
B
B
4
0
3
6
2
6
1
9
Ø
A
B
AB
Agent2
1
1
0
0
1
6
1,1
1,2
2,1
Rank
Upper Bound
3,1
2,2
1,3
1
9
2,3
3,2
1,4
1,4
AB
6
2,4
3,3
4,2
3,4
4,3
Lower Bound
4,4
Some interesting procedures for combining
different types of info
33
Storing the answer
  • Interval constraint networks, 1 per agent
  • Nodes store upper/lower bounds on value of
    bundle
  • Edge (b,b) means vi(b) ? vi(b)
  • At start create all nodes, add edges for free
    disposal

34
Constraint Network
111
1 per agent
110
101
011
100
010
001
000
35
Constraint Network
0,?
111
Upper bound
0,?
0,?
0,?
110
101
011
Lower bound
0,?
0,?
0,?
100
010
001
0
000
36
Constraint Propagation
0,?
111
vi(110)5
0,?
0,?
5
110
101
011
0,?
0,?
0,?
100
010
001
0
000
37
Constraint Propagation
0,?
111
vi(110)5
0,?
0,?
5
110
101
011
0,?
0,?
0,?
100
010
001
0
000
38
Constraint Propagation
5,?
111
vi(110)5
0,?
0,?
5
110
101
011
0,5
0,5
0,?
100
010
001
0
000
39
Constraint Propagation
5,?
111
vi(110)5
0,?
0,?
5
110
101
011
0,5
0,5
0,?
100
010
001
0
000
40
Constraint Propagation
5,?
111
vi(110)5
0,?
0,?
5
110
101
011
0,5
0,5
0,?
100
010
001
0 ,5
000
000
Additional edges from order queries
41
Constraint propagation
  • Davis87 shows propagation is
  • complete for assimilation (values for UB, LB are
    as tight as they can be made)
  • incomplete for inference (cannot always use
    values to infer vi(b) ? vi(b))
  • Need to use both values and network topology
    during inference

42
Are we done yet?
  • Need to stop when enough information has been
    gathered
  • Store list of possible allocations (candidates)
    C
  • After each phase, eliminate allocations that
    cannot be optimal v(c) ? v(c)
  • Stop when C 1

43
We present algorithms that use any combination of
value, order rank queries
  • If value queries are used, all social welfare
    maximizing allocations are guaranteed to be found
  • Otherwise, all Pareto efficient allocation are
    guaranteed to be found
  • We propose several query policies that are geared
    toward reducing the number of queries needed

44
What to query should the elicitor ask (next) ?
  • Simplest answer value query
  • Ask for the value of a bundle vi(b)
  • How to pick b, i?
  • First try Randomly (subject to not asking
    queries whose answer can be inferred from info
    already elicited)

45
Random elicitation with value queries only
  • Thrm. If the full-revelation (direct) mechanism
    makes Q value queries and the best
    value-elicitation policy makes q queries, we
    make value queries
  • Proof idea We have q red balls, and the
    remaining balls are blue how many balls do we
    draw before removing all q red balls?
  • Universal revelation reducer
  • Is it tight? Run experiments

46
Experimental setup for all graphs in this talk
  • Simulations
  • Draw agents valuation functions from a random
    distribution where free disposal is honored
  • Run the auction auctioneer asks queries of
    agents, agents look up answer from a file
  • Each point on plots is average of 10 runs

47
Random elicitation
  • Not much better than theoretical bound

queries
queries
2 agents
4 items
80
1000
60
Full revelation
100
Queries
40
10
20
1
9
2
2
3
4
5
6
3
4
5
6
7
8
10
agents
items
48
Querying random allocatable bundle-agent pairs
only
  • Bundle-agent pair (b,i) is allocatable if some
    yet potentially optimal allocation allocates
    bundle b to agent i
  • How to pick (b,i)?
  • Pick a random allocatable one
  • Asking only allocatable bundles means throwing
    out some queries
  • Thrm. This restriction causes the policy to make
    at worst twice as many expected queries as the
    unrestricted random elicitor. (Tight)
  • Proof idea These ignored queries are either
  • Not useful to ask, or
  • Useful, but we would have had low probability of
    asking it, so no big difference in expectation

49
Querying random allocatable bundle-agent pairs
only
  • Much better
  • Almost (items / 2) fewer queries than
    unrestricted random
  • Vanishingly small fraction of all queries asked !
  • Subexponential number of queries

queries
queries
80
1000
60
Full revelation
100
40
Queries
10
20
1
2
3
4
5
6
3
4
5
6
7
8
9
2
10
agents
items
50
Best value query elicitation policy so far
Focus on allocations that have highest upper
bound. Ask a (b,i) that is part of such an
allocation and among them, pick the one that
affects (via free disposal) the largest number
of bundles in such allocations.
Fraction of values queried before optimal
allocation found proven
Number of items for sale
51
Order queries
  • Order query agent i, is bundle b worth more to
    you than bundle b ?
  • Motivation Often easier to answer than value
    queries
  • Order queries are insufficient for determining
    welfare maximizing allocations
  • How to interleave order, value queries?
  • How to choose i, b, b ?

52
Value and order queries
  • Interleave
  • 1 value query (of random allocatable agent-bundle
    pair)
  • 1 order query (pick arbitrary allocatable i, b,
    b )
  • To evaluate, in the graphs we have
  • value query costs 1
  • order query costs 0.1

53
Value and order queries
  • Elicitation cost reduced compared to value
    queries only
  • Cost reduction depends on relative costs of order
    value queries

54
Rank lattice based elicitation
  • Go down the rank lattice in best-first order (
    EBF)
  • Performance not as good as value-based why?
  • nodes in rank lattice is 2bidders items
  • feasible nodes is only biddersitems

queries
queries
80
1000
Full revelation
60
100
40
Queries
10
20
1
2
3
4
5
6
4
6
8
2
10
12
agents
items
55
Bound-approximation queries
  • Often bidders can determine their valuations more
    precisely by allocating more time to deliberation
    S. AAAI-93, ICMAS-95, ICMAS-96, IJEC-00 Larson
    S. TARK-01, AGENTS-01 workshop, SITE-02 Parkes
    IJCAI workshop-99
  • Get better bounds UBi(b) and LBi(b) with more
    time spent deliberating
  • Idea dont ask for exact info if it is not
    necessary
  • Query agent i, hint spend t time units
    tightening the upper (lower) bound on b
  • How to choose i, b, t, UB or LB ?
  • For simplicity, in the experiment graph, fix t
    0.2 time units (1 unit gives exact)

56
Bound-approx query policy
This slide is hidden later, it should replace
the next slide.
  • For simplicity, fix t 0.2 units (1 unit gives
    exact)
  • Can choose randomly.
  • More complicated policy does slightly better
  • Choose query that will change the bounds on
    allocatable bundles the most
  • Dont know how much bounds will change
  • Will try 3 policies
  • Compute expectation (assume uniform distribution)
  • Be optimistic assume most possible change
  • Be pessimistic assume least possible change

57
Bound-approximation query policy
  • Could choose the query randomly
  • More sophisticated policy does slightly better
  • Choose query that will change the bounds on
    allocatable bundles the most
  • Dont know exactly how much bounds will change
  • Assume all legal answers equiprobable, sample to
    get expectation

58
Bound-approximation queries
  • This policy does quite well
  • Future work try other related policies

queries
queries
160
1000
Full revelation
120
100
Query cost
80
10
40
1
9
2
2
3
4
5
6
3
4
5
6
7
8
10
agents
items
59
Bound-approximation a note
  • To choose which query to ask, we calculated the
    expected change it makes
  • But what is change from ? ?
  • Policy actually is ask everyone for an UB on the
    grand bundle first
  • After that, we neednt worry about ?
  • Thrm. Upper bound on value of grand bundle is
    needed for all but one agent
  • Thrm. With more than one bidder, eliciting the
    grand bundle from every agent cannot increase the
    length of the shortest elicitation certificate

60
Supplementing bound-approximation queries with
order queries
  • Integrated as before
  • Computationally more expensive

queries
queries
160
1000
Full revelation
120
Total cost
100
80
Order cost
10
Value cost
40
1
2
3
4
5
6
3
4
5
6
7
8
9
2
10
agents
items
61
A potentially better policy
  • Assume auctioneer has an oracle that says which
    allocation is optimal. How to verify?
  • To prove optimality, need to
  • Prove sufficiently tight LB on optimal
  • Prove sufficiently tight UB on all others
  • Indicates a strategy when oracle is missing
  • Usually ask queries that reduce UB
  • But, need to sometimes raise LB

62
Incentive compatibility
  • Elicitors questions leak information about
    others preferences
  • Can be made ex post incentive compatible
  • Ask enough questions to determine VCG prices
  • Worst approach bidders1 elicitors
  • Could interleave these extra questions with
    real questions
  • To avoid lazyness Not necessary from an
    incentive perspective
  • Agents dont have to answer the questions may
    answer questions that were not asked
  • Unlike in price feedback (tatonnement)
    mechanisms Bikhchandani-Ostroy, Parkes-Ungar,
    Wurman-Wellman, Ausubel-Milgrom,
    Bikhchandani-deVries-Schummer-Vohra,
  • Push-pull mechanism

63
Universal revelation reducers
64
Universal revelation reducer
  • Def. A universal revelation reducer is an
    elicitor that will ask less than everything
    whenever the shortest certificate includes less
    than all queries
  • Thrm Hudson Sandholm 03 No determionistic
    universal revelation reducer exists
  • A randomized one exists
  • (E.g., the one that asks random unknown value
    queries)

65
Elicitation where worst-case number of queries is
polynomial in items
66
Read-once valuations
  • Thrm. If an agent has a read-once valuation
    function, the number of queries needed to elicit
    the function is polynomial in items
  • Thrm. If an agents valuation function is
    approximable by a read-once function (with only
    MAX and PLUS nodes), elicitor finds an
    approximation in a polynomial number of queries

Zinkevich, Blum, Sandholm ACMEC-03
67
Toolbox valuations
  • Items are viewed as tools
  • Agent can accomplish multiple goals
  • Each goal has a value requires some subset of
    tools
  • Agents valuation for a package of items is the
    sum of the values of the goals that those tools
    allow the agent to accomplish
  • E.g. items medical patents, goals medicines
  • Thrm. If an agent has a toolbox valuation
    function, it can be elicited in O(items ?
    goals) queries

68
2-wise dependent valuations
  • Thrm. If an agent has a 2-wise dependent
    valuation function, elicitor finds it in n(n1)/2
    queries
  • Thrm. If an agents valuation function is
    approximately 2-wise dependent, elicitor finds an
    approximation in n(n1)/2 queries
  • Thrm. Every super-additive valuation function is
    approximately 2-wise dependent
  • Thrm. These results generalize to k-wise
    dependent valuations

69
Towards a broad polytime elicitor
  • Thrm. If agents valuation function is in
  • Read-once valuations (with SUM and MAX gates
    only)
  • Toolbox valuations
  • 2-wise dependent valuations
  • then elicitor can learn the function using
  • O(items2 items ? goals) queries

?
?
70
Combining polynomially elicitable classes
  • Thrm. Conitzer, Sandholm, Santi 03 If Class C1
    is elicitable in polytime and class C2 is
    elicitable in polytime, then C1 U C2 is
    elicitable in polytime

71
Power of multi-agent elicitation
  • Thrm. For some classes of valuation functions,
  • eliciting the function requires an exponential
    number of queries,
  • but a polynomial number of queries suffices for
    allocating the items optimally among the agents

72
Ascending combinatorial auctions
73
Demand queries
  • If these were the prices, which bundle would you
    buy?
  • A value query can be simulated by a polynomial
    number of demand queries
  • A demand query cannot be simulated in a
    polynomial number of value queries Nisan

74
Ascending combinatorial auctions
  • Increase prices until each item is demanded only
    once
  • Item prices vs. bundle prices
  • E.g. where there exist no appropriate item prices
  • Discriminatory vs. nondiscriminatory prices

Bundle Bidder 1s valuation Bidder 2s valuation
1 0 2
2 0 2
1,2 3 2
75
Competitive equilibrium
  • Def. Competitive equilibrium (CE)
  • For each bidder, payoff max vi(S) pi(S), 0
  • Sellers payoff maxS ? Feasibles ?i pi(S)
  • Prices can be on bundles and discriminatory
  • Thrm. Allocation S is supported in CE iff it is
    an efficient allocation
  • Thrm Parkes 02 NisanSegal 03. In a
    combinatorial auction, the information implied by
    best-responses to some set of CE prices is
    necessary and sufficient as a certificate for the
    optimal allocation

76
Communication complexity of ascending auctions
  • Exponential in items in the general case
  • (like any other preference elicitation scheme)
  • If items are substitutes (for each agent), then a
    Walrasian equilibrium exists,
  • i.e., nondiscriminatory per-item prices suffice
    for agents to self-select the right items
  • Number of queries needed to find such prices is
    polynomial in items Nisan Segal 03

77
Conclusions on preference elicitation in
combinatorial auctions
  • Combinatorial auctions are desirable winner
    determination algorithms now scale to the large
  • Another problem The Revelation Problem
  • Valuation computation / revelation /
    communication
  • Introduced an elicitor that focuses revelation
  • Provably finds the welfare maximizing (or Pareto
    efficient) allocations
  • Policy dependent search algorithms for
    elicitation
  • Based on topological observations
  • Optimally effective among admissibly equipped
    elicitors
  • Eliciting value differences suffices
  • Policy independent general elicitation framework
  • Uses value, order rank queries (etc)
  • Bound-approximation queries takes incremental
    revelation further
  • Several algorithms, data structures query
    policies in the paper
  • Only elicits a vanishingly small fraction of the
    valuations
  • Presented a way to make the elicitor incentive
    compatible
  • Yields a push-pull partial-revelation mechanism

78
Conclusions on ascending combinatorial auctions
  • Demand queries (exponentially more powerful than
    value queries)
  • Per-item prices vs. bundle prices
  • Discriminatory vs. nondiscriminatory prices
  • Exponential communication complexity, but
    polynomial in special classes (e.g., when items
    are substitutes)
  • To allocate optimally, enough info has to be
    elicited to determine the minimal competitive
    equilibrium prices
  • Could also use descending prices

79
Future research on multiagent preference
elicitation
  • Scalable general elicitors (in queries, CPU, RAM)
  • Current run-time exp in items, poly in agents
  • Current space exp in items, linear in agents
  • More powerful queries, e.g. side constraints
  • New query policies
  • New polynomially elicitable valuation classes
  • Using models of how costly it is to answer
    different queries Hudson S. AMEC-02
  • Decision-theoretic elicitation using priors
  • Elicitors for markets beyond combinatorial
    auctions
  • (Combinatorial) reverse auctions exchanges
  • (Combinatorial) markets with side constraints
  • (Combinatorial) markets with multiattribute
    features
  • Other applications (e.g. voting Conitzer S.
    AAAI-02)
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