Heuristic Mechanism Design
David C. Parkes
Harvard University
Joint with Florin Constantin, Ben Lubin
and Quang Duong
Cornell CS/Econ Workshop
September 4, 2009
Embracing messiness
• Early development of MD theory focused on
an “in principle” mathematical approach.
• Today, we see great demand for
mechanisms and markets that need to
manage (messy) real world details
– e.g., dynamics, complex preferences, scalability,
transparency, stability, ...
• Krugman, 9/2/09 New York Times
• How did Economists Get it So Wrong?
“...economists, as a group, mistook beauty, clad in
impressive-looking mathematics, for truth. ...
economists will have to learn to live with
messiness.”
Examples of “Messy” systems
• Sponsored search
– dynamic system, massive # of goods, use of
machine learning, bidder tools, asynch. updating
• Medical matching (Roth & Peranson)
– couples have preferences, hospitals may specify
revisions; may be no stable match, empirically
“set of stable matchings is very stable empty”
• HBS draft mechanism (Cantillon & Budish’09)
– Non-SP. But ex ante welfare higher than under
RSD (only anon., SP and and ex post efficient.)
• UK wireless spectrum auction (Cramton)
– use a bidder-optimal core for final stage; not SP
but can avoid other instability of VCG.
Observations
• Most deployed mechanisms and markets are
not strategyproof
– need to develop solutions that are “truthful and
stable enough” given complexities of environ.
– balance SP with other considerations
• Real-world problems are multi-dimensional,
and dynamic. Not isolated events.
– need theory and engineering knowledge to guide
practical design
• Al Roth, 1999 “...if we fail to develop... an
"engineering" literature, we will fail to profit from
design experience in a cumulative way.”
• c.f. Yoav’s comment
One starting point
• Adopt computational approach that would be
desirable without incentive/stability concerns
• Modify decisions, and/or design payments to
make the method truthful and stable enough.
• How to evaluate?
– comparative study of initial algorithm and
modified algorithm
– analysis of strategic properties (through comput.
and/or theoretical approaches)
– identify good and bad cases
Two examples
• Dynamic knapsack auctions
– would use an online stochastic algorithm to solve
– with incentive concerns, adopt a “self-correction”
approach to obtain SP
• CAs and CEs
– would use a branch-and-bound, cutting-plane
approach to solve
– with incentive concerns, adopt a “reference
mechanism” approach to obtain approx-SP
Dynamic knapsack auction
• Input: { (a1, d1, v1, q1), ... (an, dn, vn, qn) }
• Capacity C to sell. Probabilistic arrival model.
• Patience ) no simple characterization of
optimal policies available
– c.f., threshold policies; optimal mechanisms
(Kleywegt & Papastavrou’01, Pai & Vohra’08, Dizdar et
al.’09.)
Online Stochastic
Optimization
(Van Hentenryck and Bent; Mercier; Shapiro’06)
• Multistage stochastic integer program
Q = maxx1 E[ maxx2 E[... maxxT v(x, ») ]]
– where » = (»1, ..., »T) is a stochastic process, »t
observation at time t, (x1..t-1, »1..t) state at time t.
Online Stochastic
Optimization
(Van Hentenryck and Bent; Mercier; Shapiro’06)
• Multistage stochastic integer program
Q = maxx1 E[ maxx2 E[... maxxT v(x, ») ]]
– where » = (»1, ..., »T) is a stochastic process, »t
observation at time t, (x1..t-1, »1..t) state at time t.
• Solve anticipatory relaxation:
maxxt E» [Opt(st, xt, »>t)]
– i.e., construct scenarios »1,..., »w. For each xt,
compute g(xt) = 1/w i Opt(st, xt, »i). Pick best.
– need exogenous uncertainty
Obtaining SP
• Self-correction (P. & Duong’07, Constantin & P.’09):
– check a proposed allocation is consistent with a
monotonic policy, cancel allocation otherwise.
• A local check:
– Fixing reports of other agents, just verify that the
agent is still allocated for higher types.
– i.e., no need to check for other “-i” type profiles
• Combine (a,v,q)-ironing + departure-mon,
obtain SP.
• Make sensitivity analysis tractable.
Results: Knapsack auction
• 10 items; 5 periods; 2 arrivals/period; U[1,5]
demand; U[1,5] patience. Efficiency:
Regular
Results: Knapsack auction
• 10 items; 5 periods; 2 arrivals/period; U[1,5]
demand; U[1,5] patience. Efficiency:
Regular
Results: Knapsack auction
• 10 items; 5 periods; 2 arrivals/period; U[1,5]
demand; U[1,5] patience. Efficiency:
Regular
strategyproof
(via output-ironing)
consensus
algorithm
Results: Knapsack auction
• 10 items; 5 periods; 2 arrivals/period; U[1,5]
demand; U[1,5] patience. Efficiency:
Regular
strategyproof
(via output-ironing)
consensus
algorithm
• Typical: IgnoDep <5% NowWait <5% OSCO
• w/ VVs; as much as 35% rev. improvement
CAs and CEs
• NP-hard WD, but generally solvable on
(current!) problems of practical importance.
• But, VCG mechanism not desirable:
– outside core for CAs
– budget deficit for CEs
) can’t obtain SP together with desired
computational approach.
• How should we set prices, to achieve “almost
SP” and stability?
Possible Answers
• Example: (A,$10), (B,$10), (AB,$15)
• “It doesn’t matter”
– Just use first price, and in any NE agents will
have an efficient outcome with core payoffs
– E.g., outcome (A,$6) (B,$9) (AB,$15)
Possible Answers
• Example: (A,$10), (B,$10), (AB,$15)
• “It doesn’t matter”
– Just use first price, and in any NE agents will
have an efficient outcome with core payoffs
– E.g., outcome (A,$6) (B,$9) (AB,$15)
• “At least minimize distance to VCG”
– respecting no-deficit in CEs (Parkes et al.’01)
– respecting core in CAs (Day & Milgrom ‘07)
– E.g., outcome (A,$7.50) (B,$7.50)
Example: Threshold rule
(Parkes et al.’01)
• pvcg,i = bid - ¢vcg,i
¢vcg,1
...
¢1
...
1
2
3
¢vcg,4 = b4 – pvcg,4
4
• Agent can always extract profit ¢vcg,i
• Regret = ¢vcg,i - ¢i
Example: Threshold rule
(Parkes et al.’01)
• pvcg,i = bid - ¢vcg,i
¢vcg,1
¢i
...
...
1
•
•
•
•
2
3
¢vcg,4 = b4 – pvcg,4
4
Agent can always extract profit ¢vcg,i
Regret = ¢vcg,i - ¢i
Threshold rule minimizes max regret
“²-SP” for minimal ². “Truthful most often,” for
costly manipulation C.
A Surprise!
• Single-minded. Computing approx. BNE
– c.f., Reeves & Wellman’04, Vorobeychik &
Wellman ‘08, Rabinovich et al, ‘09
Small Rule
• max Count(¢i = 0)
1
2
3
4
• maximizes # of agents with nothing to gain
• ... also maximizes worst-case regret!
A Bayesian viewpoint
• Agent with type vi responds to distribution on
strategic environments induced by F(b-i)
• Maximize expected utility: faces uncertainty
– e.g., consider Eb-i [ |¼i (vi, b-i)/vi| ]
– set prices to minimize expected marginal gain
(c.f., Erdil & Klemperer’09)
• Sensitivity of bid price in distr., not regret.
A Bayesian viewpoint
• Agent with type vi responds to distribution on
strategic environments induced by F(b-i)
• Maximize expected utility: faces uncertainty
– e.g., consider Eb-i [ |¼i (vi, b-i)/vi| ]
– set prices to minimize expected marginal gain
(c.f., Erdil & Klemperer’09)
• Sensitivity of bid price in distr., not regret.
• SP mechanisms provide a reference ) try to
“best conform” to payments in distribution!
Distributional analysis
• z = (p1, b1,... bn) instance
• H*(z), Hm(z): if ||H*(z), Hm(z)|| small then
payments in m almost always = reference.
Distributional analysis
• z = (p1, b1,... bn) instance
• H*(z), Hm(z): if ||H*(z), Hm(z)|| small then
payments in m almost always = reference.
• Simplify, obtain univariate distribution:
(p1, v1, ..., vn)
(¼1, v1, ..., vn)
(¼i, V)
(¼i / V)
where V is total value for allocation.
average ||H*, Hm ||
over all environments
• 3 equilibrium x 3
environments x 6 rules
• 54 data points {(eff,metric)
(shaving,metric)}
• corr(KL,eff) = -0.381;
corr(KL,shave)=+0.379,
both at 0.05 signif. level.
average ||H*, Hm ||
over all environments
discount in VCG
discount in VCG
discount in m
Threshold
discount in m
Small
Summary: Heuristic approach
• Start with good, cooperative algorithm
• Modify it, or associate payments with it,
to achieve “good enough” SP, stability.
– output ironing; reference mechanism
fitting.
• Still need theory 
– in which problems can “local correction”
work in achieving SP?
– a theory for “approximate SP”,
“approximate stability” and so forth,
– alt. models of behavior
Thank you!