AUCTIONSWITHDYNAMICPOPULATIONS: EFFICIENCYANDREVENUEMAXIMIZATION MaherSaid November2012 · 2020. 6. 27. · EXAMPLE:EBAY ConsiderabuyersearchingforaproductoneBay. Buyerarrivesonthemarket

AUCTIONS WITH DYNAMIC POPULATIONS:EFFICIENCY AND REVENUE MAXIMIZATION

Maher Said

November 2012

MOTIVATION

Many real-world markets are asynchronous.▶ Not all buyers and sellers available at same time.▶ Arrive at the market at different times.▶ Transactions occur at different times.

This introduces dynamic trade-offs:▶ Competition in future can be higher or lower.▶ Opportunities to trade in future may be greater or fewer.▶ Transact now, or wait until future?

Said (2012): Auctions with Dynamic Populations

MOTIVATION

Additional strategic element: competition across time.▶ May face same competitors repeatedly.▶ Individuals may want to learn about others.▶ May also be concerned about others’ use of information.

How do population dynamics affect competition, price determination, efficiency, revenue?

How should markets and institutions be designed to account for dynamics and its effects?


EXAMPLE: EBAY

Consider a buyer searching for a product on eBay.▶ Buyer arrives on the market.▶ Can choose to participate in an auction immediately.▶ May choose to “wait and see” instead.

Willingness to pay depends on expectations about future.

Future supply random, as is future competition:▶ When is the next auction starting?▶ How high will demand be?


EXAMPLE: EBAY

Buyer also observes competitor behavior:▶ Bid amounts, prices observable.▶ Should incorporate this information into behavior.

Conversely, buyer also concerned with how her bids affects others.▶ May try to strategically alter others’ expectations.▶ Can submit a high bid to try to signal high future competition.▶ Howmuch information should be revealed to current and future opponents?


EXAMPLE: AMAZON.COM

Amazon operates a “cloud computing” business.

A large portion of demand is pre-reserved.

But there is also a lot of excess capacity:▶ Amazon recently introduced “Spot Instances.”▶ Runs an auction every hour for excess capacity.▶ Supply fluctuates hour-to-hour (or even faster).▶ So does demand….

How should spot-market be organized?

What auction format should be used?


QUESTIONS

Twomain questions:1. What outcomes are attainable in markets with dynamic populations of privately

informed buyers?2. Can we achieve these outcomes using natural/simple “real-world” institutions?

Approach:▶ Develop a model of a general dynamic environment.▶ Privately informed buyers arrive at random times.▶ Buyers persist on the market, waiting to transact.▶ Uncertain supply: future object availability is stochastic.


PREVIEW: EFFICIENCY

We can achieve efficient outcomes in this setting.

Dynamic analogue of Vickrey-Clarke-Groves.

Charge buyers prices corresponding to externalities.

Externality price accounts for current and future impact on market.


PREVIEW: AUCTIONS

We can also use a sequence of auctions for efficiency.

But interaction across time generates interdependent values.▶ Need information revelation to achieve efficient outcomes.▶ In contrast to static settings, second-price auctions are not ideal.▶ Second-price auction does not reveal enough information.

Using ascending price auctions doeswork


PREVIEW: INFORMATION RENEWAL

New entrants to the market are asymmetrically informed.

Incentives for information revelation differ across groups of buyers.

“Memoryless” behavior provides correct incentives to all.

We can restore symmetry by throwing away information.

Allows information “renewal”: full revelation of private information in every period.


PREVIEW: REVENUE MAXIMIZATION

Revenue maximization is also possible.

Static intuitions carry through to dynamic setting:▶ Dynamic version of incentive compatibility mirrors static.▶ Revenue Equivalence Theorem continues to hold.▶ Trade-offs between revenue and efficiency same as in static world.

Revenue maximization via “efficient” mechanisms with optimal reserve.


MODEL: BUYERS

Countable set I of risk-neutral buyers.

Each buyer i has single-unit demand.

Value is vi ∈ V.

Flow payoff when paying pi,t in period t:

ui,t =

{vi − pi,t if i receives an object at time t,−pi,t otherwise.

Preferences are quasilinear and time-separable.

Common discount factor δ ∈ (0, 1).

Values are persistent over time.Said (2012): Auctions with Dynamic Populations

MODEL: BUYER ARRIVALS

Buyers arrive stochastically to the market.

In each period t,Nt buyers arrive.

Nt is distributed according to λt.

Denote set of arriving buyers by It.

Buyers remain on market until allocated an object.

at : I → {0, 1} indicates presence at time t:

at(i) =

{1 if i is present,0 otherwise.


MODEL: OBJECTS

Objects are homogeneous and indivisible.

Also arrive randomly to the market.

kt ∈ K := {0, 1, . . . , K} objects arrive in period t.

µt(k) is probability of exactly k ∈ K objects available

Objects are non-storable: unallocated objects cannot be carried over to future periods.


RELATED LITERATURE

Efficient dynamic mechanism design: Athey-Segal (2007); Bergemann-Välimäki (2010);Cavallo-Parkes-Singh (2009); Dolan (1978); Bloch-Houy (2010); Ünver (2010).

Optimal dynamic mechanism design: Baron-Besanko (1984); Battaglini (2005);Board-Skrzypacz (2010); Deb (2009); Pavan-Segal-Toikka (2009).

Dynamic auctions and revenue management: Gershkov-Moldovanu (2009, 2010);Pai-Vohra (2009); Vulcano-van Ryzin-Maglaras (2002).

Sequential auctions: Jeitschko (1998, 1999); Kittsteiner-Nikutta-Winter (2004); Lavi-Nisan(2005), Lavi-Segev (2009); Milgrom-Weber (2000); Said (2011).


EFFICIENT MECHANISMS

Want an efficient mechanism.

Efficiency ⇐⇒ maximize social welfare.

Plan:1. Characterize efficient policy.2. Efficient directmechanism.3. Corresponding “real-world” indirectmechanism.


PLANNER'S PROBLEM

Consider a social planner who commits to a feasible mechanismM = {xt, pt}t∈N0 at time 0:▶ xi,t is probability of allocating to i at time t.▶ pi,t is payment made by i at time t.

Goal is to maximize allocative efficiency:

max{xi,t}

{E

[∞∑t=0

∑i∈I

δtxi,tvi

]}s.t.

∑i∈I

xi,t ≤ kt for all t,

∞∑t=0

xi,t ≤ 1 for all i,

xi,t = 0 if at(i) = 0.


EFFICIENT POLICY

Objects perishable =⇒ no benefit to “withholding.”

Buyers’ values persistent =⇒ delay cost increasing in vi.

Efficient policy x∗ is an assortative matching.

In each t, allocate to kt highest-valued buyers present.


VICKREY-CLARKE-GROVES

VCG-like mechanisms:▶ Buyers report value on arrival.▶ Mechanism allocates objects efficiently according to x∗.▶ Charge each buyer a price equal to the externality imposed on the market.▶ Leaves each buyer with net payoff equal to marginal contribution to the social welfare.


MARGINAL CONTRIBUTION

Consider an arbitrary agent i ∈ It.

Social welfare when i arrives:

W (ωt, vt) := E

[∞∑s=t

∑j∈I

δs−tx∗j,s(ωs, vs)vj

].

Social welfare when removing i from the market:

W−i(ω−it , vt) := E

∞∑s=t

∑j∈I\{i}

δs−tx∗j,s(ω−is , vs)vj

.i’s marginal contribution to the social welfare:

wi(ωt, vt) := W (ωt, vt)−W−i(ω−it , vt).Said (2012): Auctions with Dynamic Populations


Suppose a single item is available in each period t.

Efficient policy =⇒ allocate to highest-valued buyer (i).

Thought experiment: remove buyer i frommarket.

Efficient policy =⇒ allocate to 2nd-highest buyer (j).



But xj,t = 1 =⇒ cannot allocate to j in the future:=⇒ Period t+ 1: allocate to 3rd-highest buyer instead of 2nd-highest.=⇒ Period t+ 2: allocate to 4th-highest buyer instead of 3rd-highest.=⇒ Period t+ 3: ….

Allocating to j today =⇒ lose j’s futuremarginal contribution.



i’s marginal contribution can be decomposed into two effects.

Presence of i leads to a gain today:vi − vj > 0.

Presence of i also leads to a gain in future:

δE [wj(ωt+1, vt+1)|·]︸︷︷︸j’s future contribution

> 0.

Marginal contribution of i is then

wi(ωt, vt) = vi − vj︸︷︷︸current period

+ δE [wj(ωt+1, vt+1)|·]︸︷︷︸future periods

.


DYNAMIC PIVOT MECHANISM

Incentives aligned by taking into account anticipated future re-orderings of allocations:

vi − pi,t = wi(ωt, vt).

The dynamic pivot mechanismM∗ := {x∗t , p∗t}t∈N0 is the direct mechanism where1. x∗ is the efficient allocation rule, and2. p∗ is defined by p∗i,t(ωt, vt) := x∗i,t(ωt, vt) (vi − wi(ωt, vt)) .

If i is not among the top kt, then x∗i,t = 0 =⇒ p∗i,t = 0.

M∗ gives each buyer her flowmarginal contribution in each period:

ui,s = wi(ωs, vs)− δE [wi(ωs+1, vs+1)] .


DYNAMIC PIVOT MECHANISM

Theorem (Bergemann and Välimäki 2010)The dynamic pivot mechanismM∗ := {x∗t , p∗t}t∈N0 is periodic ex post incentive compatible andindividually rational.

Truthful reporting is not dominant strategy.▶ Reports are periodic ex post optimal, given expectations about future arrivals/behavior.▶ For any realized values, truthful reporting is a Nash equilibrium of the “complete

information” subgame.▶ Buyers have no regret, regardless of competitors’ valuations.

Expected payoff of i ∈ It: E [wi(ωt, vt)].

Sincewi ≥ 0, participation is optimal.


INDIRECT IMPLEMENTATION

The dynamic pivot mechanism is a directmechanism.

It requires a single report upon buyers’ arrival.

Despite truthful revelation, may not be practical or useful in “real world.”

Transparency of the mechanism is important.



Banks, Ledyard, and Porter (1989):The transparency of amechanism—the easewithwhich anagent is able to anticipate theresults of any particular strategy—is important in achieving more efficient allocations.

Nalebuff and Bulow (1993):Even Ph.D. students have trouble understanding the [multi-unit Vickrey auction]….The problem is that if people do not understand the payment rules of the auction thenwe do not have confidence that the end result will be efficient.

Ausubel (2004):Many [economists] believe it is too complicated for practitioners to understand.

Is there a natural indirectmechanism for dynamic VCG?


SEQUENTIAL AUCTIONS

Yes: sequential auctions.

But what auction format?

“Standard” analogue of VCG in static settings is the second-price sealed-bid auction.

Sequential second-price sealed-bid auction does not correspond to dynamic VCG.


OPTIONS

Buyers in sequential auctions have an option: lose today and participate in future auctions.

Value of future participation: δV .

Rational bidding: shade bids by option value:

maxbi

{Pr (win)E

[vi −max

j ̸=i{bj}

]+ Pr (lose) δV

}⇐⇒ max

bi

{Pr (win)E

[(vi − δV )−max

j ̸=i{bj}

]}+ δV

=⇒ b∗i = vi − δV .


INTERDEPENDENCE

But value of option depends on expected prices.

Future prices determined by competitors’ values

=⇒ V = V (vi, v−i).

Despite independent private values, market dynamics generate interdependence.

Buyers must learn competitors’ values in order to correctly price options.


SECOND-PRICE AUCTION

Second-price sealed-bid auction does not reveal enough information

=⇒ b∗i = vi − δE [V (vi, v−i)] .

Bidders arriving at different times have different beliefs:=⇒ Asymmetry in expectations.=⇒ Asymmetry in bids.=⇒ Inefficient outcomes.


REVEALING BIDS

Second-price auction with revealed bids?

Any period with new entrants =⇒ uninformed buyers.

Revealing bids after submission is too late.

Can’t make use of information until next period.

Information revelation too “slow” to be useful.


ASCENDING AUCTION

Need an open auction format =⇒ ascending auction.

Price clock rises continuously.

Buyers observe competitors’ exits from auction.

Can infer competitors’ valuations.

Can incorporate information into current-period bidding:

=⇒ b∗i = vi − δV (vi, v−i).


ASCENDING AUCTION

Use a multi-unit, uniform-price version of the Milgrom andWeber (1982) “button” auction.

Sell all kt units at same price to highest kt bidders.

In each period t:▶ Price clock starts at zero, rises continuously.▶ Number of active participants public.▶ Exits publicly observable and irreversible.▶ Auction ends when at most kt buyers remain active.▶ Price paid is price of final exit.

But this generates an additional asymmetry…


MORE ASYMMETRY

Consider losing buyers in period t.

Observe each others’ exit points =⇒ infer values.

At beginning of period t+ 1: perfectly informed.

But new entrants also arrive in period t+ 1.

Buyers are now asymmetrically informed.

Want new entrants to reveal private information.

How do we provide incentives to new buyers?


RESTORING SYMMETRY

Solution: information renewal.

Full revelation of private information in every period.

Achieved by using “memoryless” strategies.

Incumbents disregard past observations, behave as though uninformed:▶ Allows all buyers to behave symmetrically.▶ Provides appropriate incentives for entrants to reveal private information.


RESTORING SYMMETRY

Note: equilibrium behavior, not a restriction on strategies.

Why is it rational to throw away information?

Buyers engage in information revelation in every period.

Buyers expect information to be revealed again.

No need to condition on past history if information will be disclosed anew.


BIDDING STRATEGIES

Let nt be number of buyers present.

Let ym denotem-th highest value.

Buyers stay in auction until indifferent between winning today and participating tomorrow.

Buyers expect to pay prices equal to the externality they impose.▶ Equivalently, option value equals expected marginal contribution to social welfare:

V (vi, v−i) = E [wi(ωt+1, vt+1)|vt = (vi, v−i)] .


BIDDING STRATEGIES

Bid up to price at which indifferent between winning now and receiving marginalcontribution in future:

vi − p︸︷︷︸win now

= δE [wi(ωt+1, vt+1)|vt = (vi, . . . , vi)]︸︷︷︸future marginal contribution

.

Marginal contribution is increasing, but slower than value.=⇒ Buyer with lowest value will be first to drop out.

Remaining buyers observe exit price, infer value ynt of lowest buyer.


BIDDING STRATEGIES

Buyers update beliefs about future.


vi − p︸︷︷︸win now

= δE [wi(ωt+1, vt+1)|vt = (vi, . . . , vi, ynt)]︸︷︷︸updated future marginal contribution

.

Again, marginal contribution is increasing, but slower than value.=⇒ Buyer with second-lowest value will drop out next.

Remaining buyers observe exit, infer value ynt−1 of 2nd-lowest buyer.


BIDDING STRATEGIES

Proceeding inductively, buyers continue updating their beliefs as bidders drop out.


βtm,nt(ωt, vi, ym+1, . . . , ynt)

:= vi − δE [wi(ωt+1, vt+1)|vt = (vi, . . . , vi, ym+1, . . . , ynt)] .

Buyer withm-th highest value drops out next; remaining buyers infer ym.


BIDDING STRATEGIES

Auction ends when only top kt buyers remain.

Each pays price determined by buyer with (kt + 1)-th highest value:

βtkt+1,nt(ωt, ykt+1, . . . , ynt).

In following periods:▶ Process repeats from beginning.▶ Starting from βt+1nt+1,nt+1(ωt+1, vi).


EQUILIBRIUM

TheoremBidding according to the strategies βtm,nt in each period t is a perfect Bayesian equilibrium of thesequential ascending auction mechanism.

Suppose buyer iwith value vi > ykt+1 wins.

Pays βtkt+1,nt(ωt, ykt+1, . . . , ynt) =

ykt+1 − δE [wkt+1(ωt+1, vt+1)|vt = (ykt+1, . . . , ykt+1, . . . , ynt)] .

This is exactly the externality imposed by i’s presence on the market.▶ If i is removed, x∗ allocates to (kt + 1)-th highest buyer.▶ The planner realizes a gain equal to that buyer’s value.▶ But the planner forgoes that buyer’s future contributions.


OUTCOME EQUIVALENCE

i’s payoff is then

vi − ykt+1︸︷︷︸current period

+ δE [wkt+1(ωt+1, vt+1)|·]︸︷︷︸future periods

= wi(ωt, vt)︸︷︷︸total contribution

.

TheoremThe equilibrium of the sequential ascending auction mechanism is outcome equivalent to thetruth-telling equilibrium of the dynamic pivot mechanism.

Sequence of allocations is identical =⇒ efficient.

Sequence of payments is identical:▶ Winning buyers pay externality.▶ Losing buyers pay nothing.


RECAP

So far:▶ Efficient policy and dynamic VCG.▶ Indirect implementation via sequential ascending auctions.

What about revenue?▶ What is the revenue-maximizing policy?▶ Can it be implemented via a direct mechanism?▶ Can it be implemented via an indirect mechanism?


MONOPOLIST'S PROBLEM

Consider a monopolist who commits to a feasible mechanismM = {xt, pt}t∈N0 at time 0:▶ xi,t is probability of allocating to i at time t.▶ pi,t is payment made by i at time t.

Goal is to maximize revenue:

max

{E

[∞∑t=0

∑i∈I

δtpi,t

]}.

Seller needs to induce buyers to reveal private information.

How can she provide the correct incentives?


BUYER PAYOFFS

Revelation principle holds =⇒ direct revelation is wlog.

Consider i ∈ It with value vi.

Suppose all other buyers are reporting truthfully.

Then i’s payoff from reporting v′i is

Ui(v′i, vi, ωt) := E

[∞∑s=t

δs−t(xi,s(v

′i, v−i)vi − pi,s(v′i, v−i)

)].


IC AND IR

Incentive compatibility: truthful reporting is a best response.

Individual rationality: participation is optimal.

The mechanismM = {xt, pt}t∈N0 is incentive compatible if, for all t, all i ∈ It, and all ωt,

Ui(vi, vi, ωt) ≥ Ui(v′i, vi, ωt) for all vi, v′i ∈ V.

M is individually rational if, for all t, all i ∈ It, and all ωt,

Ui(vi, vi, ωt) ≥ 0 for all vi ∈ V.


REDUCING DIMENSION

Incentive problem simplified by reduction to a single-dimensional allocation problem

Expected discounted probability of allocation:

qi(v′i, ωt) := E

[∞∑s=t

δs−txi,s(v′i, v−i)

].

Expected discounted payment:

mi(v′i, ωt) := E

[∞∑s=t

δs−tpi,s(v′i, v−i)

].


IMPLEMENTABLE MECHANISMS

Since buyers are risk-neutral, payoffs are quasilinear, payoff from truthful reporting is

Ûi(vi, ωt) := qi(vi, ωt)vi −mi(vi, ωt).

Immediately yields characterization of IC and IR à la Myerson (1981).

LemmaM = {xt, pt}t∈N0 is incentive compatible and individually rational if, and only if, for all t, alli ∈ It, and all ωt:1. qi(vi, ωt) is nondecreasing in vi;2. Ûi(vi, ωt) = Ûi(0, ωt) +

∫ vi0

qi(v′i, ωt) dv

′i; and

3. Ûi(0, ωt) ≥ 0.


IMPLEMENTABLE ALLOCATIONS

Static settings:▶ Incentive compatibility: higher vi =⇒ higher probability of receiving object.

Here:▶ Incentive compatibility: higher vi =⇒ higher probability of receiving object sooner.▶ Multiple opportunities to receive an object:

qi(v′i, ωt) = E

[∞∑s=t

δs−txi,s(v′i, v−i)

].


REVENUE EQUIVALENCE

Revenue Equivalence Theorem holds in this setting.

Payments pinned down by allocation rule alone.

CorollaryIfM = {xt, pt}t∈N0 is incentive compatible, then for all t ∈ N0, all i ∈ It, and all ωt, theexpected payment of type vi ∈ V of buyer i, conditional on entry, is

mi(vi, ωt) = mi(0, ωt) + qi(vi, ωt)vi −∫ vi0

qi(v′i, ωt) dv

′i.

IfM is also individually rational, thenmi(0, ωt) ≤ 0.


MONOPOLIST'S PROBLEM

Recall monopolist’s optimization problem:

max

{E

[∞∑t=0

∑i∈I

δtpi,t(ωt, v)

]}.

Equivalently:

max

{E

[∞∑t=0

∑i∈It

δtat(i)mi(vi, ωt)

]}.


SOLUTION

Revenue Equivalence =⇒ monopolist’s problem is:

max

{E

[∞∑t=0

∑i∈It

δtat(i)mi(0i, ωt) +∞∑t=0

∑i∈It

δtat(i)qi(vi, ωt)φ(vi)

]},

where virtual value φ is

φ(vi) := vi −1− F (vi)f(vi)

.

Assume wlog φ increasing (otherwise iron).


SOLUTION

Maximize the two pieces separately.

First term: individual rationality ⇐⇒ mi(0, ωt) ≤ 0.▶ So setmi(0, ωt) = 0.

Second term:

E

[∞∑t=0

∑i∈It

δtat(i)qi(vi, ωt)φ(vi)

]= E

[∞∑t=0

∑i∈It

δtxi,t(ωt, v)φ(vi)

].

Same as planner’s problem—but with virtual values.▶ So allocate objects to available buyers with highest (non-negative) virtual values.


OPTIMAL POLICY

Optimal policy x̃ is incentive compatible.

Higher value =⇒ higher virtual value =⇒ greater likelihood of being in top kt.▶ Implies x̃i,t nondecreasing in vi for all t.▶ And also q̃i(ωt, vi) nondecreasing in vi.

What payment rule supports this policy?


MYERSON (1981)

Myerson’s optimal auction can be reinterpreted in terms of VCG.

Instead of maximizing surplus, maximize virtual surplus.▶ Agents report values vi.▶ Mechanism computes virtual values φ(vi).▶ Applies VCG to virtual values.

Optimal mechanism yields allocation and “virtual price.”▶ Virtual price is winner’s marginal contribution to the virtual surplus.▶ Virtual price is inverted into a “standard” price ⇐⇒ lowest winning value.


VIRTUAL SURPLUS

Let r̃ := φ−1(0).

Define virtual surplus:

Π(ωt, vt) := E

[∞∑s=t

∑j∈I

δs−tx̃j,s(ωs, vs) (vj − r̃)

].

Measures contributions beyond the reservation value r̃.

x̃ is efficient for a planner with this payoff function.▶ So run dynamic VCG on virtual surplus.


VIRTUAL VCG

Define

Π−i(ω−it , vt) := E

∞∑s=t

∑j∈I\{i}

δs−tx̃j,s(ω−is , vs) (vj − r̃)

.i’s marginal contribution to the virtual surplus:

w̃i(ωt, vt) := Π(ωt, vt)− Π−i(ω−it , vt).

w̃i is i’s “replacement value” over a buyer with value r̃.


DYNAMIC VIRTUAL PIVOT MECHANISM

Align incentives by giving each buyer her marginal contribution to the virtual surplus.

Wantvi − pi,t = w̃i(ωt, vt).

The dynamic virtual pivot mechanism M̃ := {x̃t, p̃t}t∈N0 is the dynamic direct mechanismwhere1. x̃ is the optimal allocation rule, and2. p̃ is defined by p̃i,t(ωt, vt) := x̃i(ωt, vt) (vi − w̃i(ωt, vt)) .


DYNAMIC VIRTUAL PIVOT MECHANISM

In each period, give each buyer her flowmarginal contribution:

ui,t = w̃i(ωt, vt)− δE [w̃i(ωt+1, vt+1)] .

i’s expected payoff is then Ûi(ωt, vi) = E [w̃i(ωt, vt)].

TheoremThe dynamic virtual pivot mechanism M̃ := {x̃t, p̃t}t∈N0 is periodic ex post incentivecompatible and individually rational.

M̃ implements revenue-maximizing policy x̃.

M̃ is very closely related to dynamic VCG.▶ Is there an equivalent “natural” indirect mechanism?



“Standard” static private-values setting:▶ Efficiency via VCG

⇐⇒ Second-price auction.▶ Revenue-maximization via Myerson (1981)

⇐⇒ VCGwith a reserve⇐⇒ Second-price auction with a reserve.

By analogy, in this dynamic setting:▶ Efficiency via dynamic VCG

⇐⇒ Sequential ascending auction.▶ Revenue-maximization via M̃

⇐⇒ Dynamic VCGwith a reserve⇐⇒ Sequential ascending auction with a reserve.


SUMMARY

Develop an intuitive indirect mechanism: sequential ascending auctions.▶ Simple institution that yields efficiency.▶ Equilibrium is outcome equivalent to dynamic VCG.

Extend results to revenue-maximization.▶ Optimal mechanism is a pivot mechanism with a reserve.▶ Optimal indirect mechanism is the sequential ascending auction with a reserve.


LESSONS: DYNAMIC ENVIRONMENTS

Many of our intuitions from the static world carry through.

We can use pivot mechanisms to achieve efficiency.

Auctions continue to be effective institutions.

Same trade-offs between efficiency and revenue.


LESSONS: INSTITUTIONAL DESIGN

But…information is more important in dynamic markets.

Even with independent private values, interaction across time creates interdependence.

Need information revelation to attain desirable outcomes.

Must consider dynamic auction formats to generate enough information: second-priceauction not optimal.


LESSONS: DYNAMIC POPULATIONS

Buyer arrivals introduce a new tension.

Information revelation vs. incentive provision.

Revelation creates asymmetry, but asymmetry creates incentive problems across groups ofbuyers.

Information revelation alone is not sufficient =⇒ need information renewal.


LESSONS: SIMPLICITY

Complex setting:▶ Dynamic population of buyers.▶ Stochastic supply.▶ Asymmetric incentive constraints.

Simple solution:▶ Ascending auctions are a natural, intuitive institution.▶ Bidding strategies are memoryless, no history dependence.▶ Able to achieve desirable outcomes.


FUTURE WORK

Interdependent values:▶ Additional complication: history dependence.▶ New buyers interested in values of previous winners.▶ Information transmission becomes more difficult.▶ How to communicate multi-dimensonal information with one-dimensional strategy?

More general arrival processes:▶ Relax assumption of exogenously-driven arrivals.▶ Allow buyers to condition entry on market conditions, seller to adjust supply.▶ Balance motive to induce entry with rent extraction.▶ Building block for competing markets and platforms.


IntroductionMotivationOverview

ModelEnvironmentRelated literature

Efficient mechanismsEfficient policyDynamic VCG

An efficient auctionIndirect mechanismsSequential auctionsSequential ascending auctionEquilibrium

Revenue maximizationIncentives and revenue equivalenceRevenue equivalenceOptimal policyOptimal mechanismsOptimal auction

ConclusionSummaryLessonsFuture work

Documents

AUCTIONSWITHDYNAMICPOPULATIONS: EFFICIENCYANDREVENUEMAXIMIZATION MaherSaid November2012 · 2020. 6. 27. · EXAMPLE:EBAY ConsiderabuyersearchingforaproductoneBay. Buyerarrivesonthemarket