# Presentation: 057616

## Clock Auctions, Proxy Auctions, and Possible Hybrids

**Lawrence M. Ausubel***
**University of Maryland**
**November 2003**

***This is joint research with Peter Cramton and Paul Milgrom. Some of** **the methods discussed are subject to issued patents or pending applications.**

## Clock Auction
Defining characteristic of a clock auction is that the auctioneer names prices, while bidders name only quantities
Auctioneer announces a price vector
Bidders respond by reporting quantity vectors
Price is adjusted according to excess demand
Process is repeated until the market clears
No exposure problem in the clock auction here

**Defining characteristic of a clock auction is that the auctioneer names prices, while bidders name only quantities**
**Auctioneer announces a price vector**
**Bidders**** respond by reporting quantity vectors**
**Price is adjusted according to excess demand**
**Process is repeated until the market clears**
**No exposure problem in the clock auction here**

**Introduction**

## Proxy Auction
A particular procedure for package bidding, which exhibits desirable properties
Bidders input their values into “proxy agents”
The proxy agents iteratively submit package bids, selecting the best profit opportunity according to the inputted values
Auctioneer selects provisionally-winning bids according to revenue maximization
Process continues until the proxy agents have no new bids to submit

**A particular procedure for package bidding, which exhibits desirable properties**
**Bidders input their values into “proxy agents”**
**The proxy agents iteratively submit package bids, selecting the best profit opportunity according to the inputted values**
**Auctioneer selects provisionally-winning bids according to revenue maximization**
**Process continues until the proxy agents have no new bids to submit**

**Introduction**

## Hybrid Clock / Proxy Auction
A clock auction, followed by a “final round” consisting of a proxy auction
Bidders directly submit bids in a simultaneous clock auction phase
When the clock phase concludes, bidders have a single opportunity to input proxy values for a proxy phase
The proxy phase concludes the auction

**A clock auction, followed by a “final round” consisting of a proxy auction**
**Bidders directly submit bids in a simultaneous clock auction phase**
**When the clock phase concludes, bidders have a single opportunity to input proxy values for a proxy phase**
**The proxy phase concludes the auction**

**Introduction**

## Hybrid Clock / Proxy Auction
Rules maintained throughout
All bids are kept “live” throughout the auction (i.e., no bid withdrawals)
All bids are treated as mutually exclusive (XOR)
The bids from the clock phase are also treated as package bids in the proxy phase
Activity rules are maintained within the clock phase and between the clock and proxy phases

**Rules maintained throughout**
**All bids are kept “live” throughout the auction (i.e., no bid withdrawals)**
**All bids are treated as mutually exclusive (XOR)**
**The bids from the clock phase are also treated as package bids in the proxy phase**
**Activity rules are maintained within the clock phase and between the clock and proxy phases**

**Introduction**

## Advantages of Clock-Proxy Auction
The clock phase is simple for bidders, and provides essential price discovery
The proxy phase should be expected to yield efficient allocations and competitive revenues, while minimizing the opportunities for collusion

**The clock phase is simple for bidders, and provides essential price discovery**
**The proxy phase should be expected to yield efficient allocations and competitive revenues, while minimizing the opportunities for collusion**

**Introduction**

## Part I: Clock Auctions

** **

## Simultaneous Clock Auction
Practical implementation of the fictitious “Walrasian auctioneer”
Auctioneer announces a price vector
Bidders respond by reporting quantity vectors
Price is adjusted according to excess demand
Process is repeated until the market clears

**Practical implementation of the fictitious “Walrasian auctioneer”**
**Auctioneer announces a price vector**
**Bidders**** respond by reporting quantity vectors**
**Price is adjusted according to excess demand**
**Process is repeated until the market clears**

**Simultaneous Clock Auctions**

## Simultaneous Clock Auction
Strengths
Relatively simple for bidders
Provides highly-usable price discovery
Yields similar outcome as current FCC format, but faster and fewer collusive opportunities
Weaknesses
Limits prices to being linear
Therefore should not yield efficient outcomes

**Strengths**
**Relatively simple for bidders**
**Provides highly-usable price discovery**
**Yields similar outcome as current FCC format, but faster and fewer collusive opportunities**
**Weaknesses**
**Limits prices to being linear**
**Therefore should not yield efficient outcomes**

**Simultaneous Clock Auctions**

## Issue 1: Treatment of bids which, if accepted, would make aggregate demand < supply
Example: For a particular item, demand = supply, but the price of a complementary item increases. A bidder wishes to reduce his demand
Naive approach: Prevent the reduction
Example: For a particular item, demand > supply, but two bidders simultaneously attempt to reduce their demands
Naive approach: Ration the bidders

**Example: For a particular item, demand = supply, but the price of a complementary item increases. A bidder wishes to reduce his demand**
**Naive approach: Prevent the reduction**
**Example: For a particular item, demand > supply, but two bidders simultaneously attempt to reduce their demands**
**Naive approach: Ration the bidders**

**Simultaneous Clock Auctions**

## Issue 1: Treatment of bids which, if accepted, would make aggregate demand < supply
Example: For a particular item, demand = supply, but the price of a complementary item increases. A bidder wishes to reduce his demand
Difficulty: Creates an exposure problem
Example: For a particular item, demand > supply, but two bidders simultaneously attempt to reduce their demands
Difficulty: Creates an exposure problem

**Example: For a particular item, demand = supply, but the price of a complementary item increases. A bidder wishes to reduce his demand**
**Difficulty: Creates an exposure problem**
**Example: For a particular item, demand > supply, but two bidders simultaneously attempt to reduce their demands**
**Difficulty: Creates an exposure problem**

**Simultaneous Clock Auctions**

## Issue 1: Treatment of bids which, if accepted, would make aggregate demand < supply
Example: For a particular item, demand = supply, but the price of a complementary item increases. A bidder wishes to reduce his demand
Our approach: Allow the reduction
Example: For a particular item, demand > supply, but two bidders simultaneously attempt to reduce their demands
Our approach: No rationing

**Example: For a particular item, demand = supply, but the price of a complementary item increases. A bidder wishes to reduce his demand**
**Our approach: Allow the reduction**
**Example: For a particular item, demand > supply, but two bidders simultaneously attempt to reduce their demands**
**Our approach: No rationing**

**Simultaneous Clock Auctions**

## Issue 1: Treatment of bids which, if accepted, would make aggregate demand < supply
“Full Flexibility” (used in EDF; advocated here)
After each new price vector, bidders can arbitrarily reduce their previous quantities
(But the bid remains “live” in the proxy auction phase)
Advantage: This effectively makes the clock auction a combinatorial auction. There is no exposure problem!
Disadvantage: There may be significant undersell. This is not a big problem, if there are frequent auctions (EDF) or if it is followed by a proxy auction (this talk)

**“****Full Flexibility” (used in EDF; advocated here)**
**After each new price vector, bidders can arbitrarily reduce their previous quantities**
**(But the bid remains “live” in the proxy auction phase)**
**Advantage: This effectively makes the clock auction a combinatorial auction. There is no exposure problem!**
**Disadvantage: There may be significant undersell. This is not a big problem, if there are frequent auctions (EDF) or if it is followed by a proxy auction (this talk)**

**Simultaneous Clock Auctions**

## Issue 2: Activity rules
The problem is that of a bidder hiding as a “snake in the grass” until near the end of the auction, to conceal its true interests / values from opponents
Standard approaches:
No activity rule (laboratory experiments)
Monotonicity in quantities (clock auctions in practice)
Monotonicity in population units (FCC)

**The problem is that of a bidder hiding as a “snake in the grass” until near the end of the auction, to conceal its true interests / values from opponents**
**Standard approaches:**
**No activity rule (laboratory experiments)**
**Monotonicity in quantities (clock auctions in practice)**
**Monotonicity in population units (FCC)**

**Simultaneous Clock Auctions**

## Issue 2: Activity rules
Revealed-preference activity rules (advocated here)
Based on standard analysis in consumer theory. Compare times s and t (s < t). Let associated prices be ps, pt and let associated demands be xs, xt. Note:
	and:
	Adding the inequalities yields the RP activity rule:		

**Revealed-preference activity rules (advocated here)**
**Based on standard analysis in consumer theory. Compare times *****s***** and *****t***** (*****s***** < *****t*****). Let associated prices be *****p******s*****, *****p******t*** **and let associated demands be *****x******s*****, *****x******t*****. Note:**
**	****and:**
**	****Adding the inequalities yields the RP activity rule:****	****	**

**Simultaneous Clock Auctions**

## Issue 2: Activity rules
Revealed-preference activity rules (advocated here)
The bid placed by a bidder at time t must satisfy the RPAR inequality with respect to its prior bids at all prior times s (s < t):

One can also apply a “relaxed” RPAR in the proxy phase (with respect to bids in the clock phase):

**Revealed-preference activity rules (advocated here)**
**The bid placed by a bidder at time *****t***** must satisfy the RPAR inequality with respect to its prior bids at all prior times *****s***** (*****s***** < *****t*****):**
**One can also apply a “relaxed” RPAR in the proxy phase (with respect to bids in the clock phase):**

**Simultaneous Clock Auctions**

##  EDF Generation Capacity Auction

- MDI
**market design inc.**

##  Product Group A

**2 years**

**3 years**

** ****Product Group A**

**VPP Base-Load Power**

**MW**

**1****/****1**
**04**

**1****/****1**
**05**

**Time**

**3 mo.**

**6 months**

**1 year**

**4****/****1**
**04**

**7****/****1**
**04**

**1000 MW**

##  Product Group B

**2 years**

**3 years**

** ****Product Group B**

**VPP Peak-Load Power**

**MW**

**1****/****1**
**04**

**1****/****1**
**05**

**Time**

**3 mo.**

**6 months**

**1 year**

**4****/****1**
**04**

**7****/****1**
**04**

**250 MW**

## Part II: Proxy Auctions

** **

##  Package Bidding

**Past FCC auctions (simultaneous ascending auction):**
**Independent bids**
**Approximately-uniform pricing**
**Bidder cannot make bid on B conditional on winning A**
**Package bidding often motivated by complements**
**Even without complements, package bidding may improve outcome by eliminating “demand reduction”**
**In the traditional FCC auction design, bidders have incentive to reduce their bids on marginal units in order to reduce their payments for inframarginal units**

##  Basic Ascending Package Auction

**A set of items is offered for sale**
**A bid (*****A,b******jA*****) by bidder *****j***** specifies a set of items *****A***** and a corresponding *****bid amount***** (bids are “all or nothing”) **
**Bidding proceeds in a series of rounds**
**After each round, *****provisional winning bids *****— a solution to the problem of maximizing revenues from compatible bids — are determined**
**Auction ends after a round with no new bids**
**All bids are treated as mutually exclusive (XOR)**
**All bids are kept “live” throughout the auction**

##  Ascending Proxy Auction

**Each bidder reports his values (and, in one version, a budget limit) to a “proxy bidder”**
**The proxy bidder bids on behalf of the real bidder — iteratively submitting the allowable bid that, if accepted, would maximize the real bidder’s payoff (evaluated according to his reported values)**
**An ascending package auction is conducted with negligibly small bid increments**
**Bidders may or may not have the opportunity to revise the values reported to their proxy agents**
**Auction ends after a round with no new bids (and no further opportunities to revise values to proxy agents)**

##  Example: Ascending Proxy Auction

**Two items, A and B; bids must be integers**
**Bidder reports values of v(A) = 10, v(B) = 5, v(A,B) = 20**
**Past high bids by this bidder (all “losing”) were:**
**b(A) = 4, b(B) = 3, b(A,B) = 15**
**Next allowable bids are:**
**b(A) = 5    Yields profits of ******** = v(A) – b(A) = 10 – 5 = 5**
**b(B) = 4    Yields profits of ******** = v(B) – b(B) = 5 – 4 = 1**
**b(A,B) = 16  Yields profits of ******** = v(A,B) – b(A,B) = 20 – 16 = 4**
**So the proxy bidder next places a bid of 5 on A**

##  Example: Ascending Proxy Auction

**Two items, A and B; bids must be integers**
**Bidder reports values of v(A) = 10, v(B) = 5, v(A,B) = 20**
**Past high bids by this bidder (all “losing”) were:**
**b(A) = 4, b(B) = 3, b(A,B) = 15**
**Next allowable bids are:**
**b(A) = 5    Yields profits of ******** = v(A) – b(A) = 10 – 5 = 5**
**b(B) = 4    Yields profits of ******** = v(B) – b(B) = 5 – 4 = 1**
**b(A,B) = 16  Yields profits of ******** = v(A,B) – b(A,B) = 20 – 16 = 4**
**Next allowable bids after that are:**
**b(A) = 6    Yields profits of ******** = v(A) – b(A) = 10 – 6 = 4**
**b(B) = 4    Yields profits of ******** = v(B) – b(B) = 5 – 4 = 1**
**b(A,B) = 16  Yields profits of ******** = v(A,B) – b(A,B) = 20 – 16 = 4**
**So the proxy next bids 6 on A and/or 16 on {A,B}**

## Outcomes in the Core

**The coalitional form game is (*****L*****,*****w*****), where...**
**L denotes the set of players.**
**the seller is *****l *****= 0 **
**the other players are the bidders**
***w*****(*****S*****) denotes the value of coalition *****S*****:**
**If S excludes the seller, let *****w*****(*****S*****)=0**
**If S includes the seller, let **
**The *****Core*****(*****L*****,*****w*****) is the set of all profit allocations that are *****feasible***** for the coalition of the whole and *****cannot be blocked***** by any coalition *****S***

## Outcomes in the Core

_**Theorem (Ausubel and Milgrom, 2002)**_**. The outcome of the ascending proxy auction is a point in *****Core*****(*****L*****,*****w*****) relative to the reported preferences**
**Interpretations:**
**“****Core” outcome assures competitive revenues for the seller**
**“****Core” outcome also assures allocative efficiency, i.e., the** **ascending proxy auction is not subject to the inefficiency of demand reduction**

## Case of Substitutes

**Case of Substitutes**

**If the goods are substitutes, then the Vickrey payoff profile is the bidder-Pareto-optimal point in the core, and the outcome of the ascending proxy auction coincides with the outcome of the Vickrey auction**

- Bidder #1 Payoff

- Bidder #2 Payoff

- Core Payoffs for 1 and 2

- Vickrey Payoff Vector

- v1+v2w(L)-w(L\12)

- w(L)-w(L\1)

- w(L)-w(L\2)

## Case of Non-Substitutes

**Meanwhile, if the goods are not substitutes, then the Vickrey payoff profile is not an element of the core and the ascending proxy auction yields a different outcome from the Vickrey auction (one with higher revenues) **

- Bidder #1 Payoff

- Bidder #2 Payoff

- Core Payoffs for 1 and 2

- Vickrey Payoff Vector

- v1+v2w(L)-w(L\12)

- w(L)-w(L\1)

- w(L)-w(L\2)

- Bidder-Pareto-optimal payoffs

## Outcomes in the Core

_**Theorem (Ausubel and Milgrom, 2002)**_**. If ******** is a bidder-Pareto-optimal point in *****Core*****(*****L*****,*****w*****), then there exists a Nash equilibrium of the ascending proxy auction with associated payoff vector ********.**
**Note 1: This is a complete-information result**
**Note 2: These equilibria may be obtained using strategies of the form: bid your true value minus a nonnegative constant on every package**

##  Monotonicity and Revenue Issues

**Example: Two identical items, A and B; three bidders**
**Bidder 1 values the pair only: v****1****(A,B) = $2 billion**
**Bidder 2 wants a single item only: v****2****(A) = $2 billion**
**Bidder 3 wants a single item only: v****3****(B) = $2 billion**
**The Vickrey auction awards each bidder his incremental value:**
**Bidders 2 and 3 each win one item**
**Social value with Bidder 2 = $4 billion; without Bidder 2 = $2 billion**
**Prices in the Vickrey auction equal zero!**
**The problem in this example is a failure of monotonicity:**
**Adding Bidder 3 reduces Vickrey revenues from $2 billion to zero**
**The Vickrey outcome lies outside the core**
**The proxy auction avoids this problem: Revenues = $2 billion**

##  The Loser Collusion Problem

**Example: Two identical items, A and B; three bidders**
**Bidder 1 values the pair only: v****1****(A,B) = $2 billion**
**Bidder 2 wants a single item only: v****2****(A) = ****$0.5 billion**
**Bidder 3 wants a single item only: v****3****(B) = ****$0.5 billion**
**The losing Bidders 2 and 3 have a profitable joint deviation in the Vickrey auction: bidding $2 billion each**
**This converts it into the previous example**
**Bidders 2 and 3 each win one item at prices of zero**
**The Vickrey auction is unique in its vulnerability to collusion even among *****losing***** bidders**
**The proxy auction avoids this problem: Bidders 2 and 3 can overturn the outcome of Bidder 1 winning only by jointly bidding $2 billion**

##  The Shill Bidding Problem

**Example: Two identical items, A and B; ****two**** bidders**
**Bidder 1 values the pair only: v****1****(A,B) = $2 billion**
**Bidder 2 has v****2****(A) = ****$0.5 billion; ****v****2****(A,B) = ****$1 billion**
**The losing Bidder 2 can set up a bidder under a false name (“shill bidder”). Each of Bidder 2 and the shill Bidder 3 can bid $2 billion each**
**This again converts it into the first example**
**Bidder 2 wins two items and pays zero!**
**The Vickrey auction is vulnerable to shill bidding**

## Part III: Hybrid Auctions

** **

## A simultaneous clock auction is conducted, with a revealed-preference activity rule imposed on bidders, until (approximate) clearing is attained
A proxy auction is conducted as a “final round”.
Bids submitted by proxy agents are restricted to satisfy a (relaxed) revealed-preference activity rule ( > 1) relative to all bids submitted in the clock phase. The value of  is chosen based on competitive conditions
The bids from the clock phase are also treated as “live” package bids in the proxy phase
All package bids (clock and proxy) are treated as mutually exclusive, and the auctioneer selects as provisionally-winning the bids that maximize revenues

**A proxy auction is conducted as a “final round”.**
**Bids submitted by proxy agents are restricted to satisfy a (relaxed) revealed-preference activity rule (********** > 1) relative to all bids submitted in the clock phase. The value of ********** is chosen based on competitive conditions**
**The bids from the clock phase are also treated as “live” package bids in the proxy phase**
**All package bids (clock and proxy) are treated as mutually exclusive, and the auctioneer selects as provisionally-winning the bids that maximize revenues**

**Clock-Proxy Auction**

## Clock auction phase yields price discovery
The feedback of linear prices is extremely useful to bidders
The existence of the clock phase makes bidding in the proxy phase vastly simpler
Focus decision on what is relevant
See what you don't need to consider
See what looks like good possibilities

**The feedback of linear prices is extremely useful to bidders**
**The existence of the clock phase makes bidding in the proxy phase vastly simpler**
**Focus decision on what is relevant**
**See what you don't need to consider**
**See what looks like good possibilities**

**Why Not Use the Proxy Auction Only?**

**Notes:**
Chess analogy: It is easier to play a game of chess, than to describe how to play in all circumstances.

## Proxy auction ends with core outcome
Efficient allocation
Competitive revenues
No demand reduction
Collusion is limited
Relaxed activity rule means allocation still up for grabs in proxy phase

**Efficient allocation**
**Competitive revenues**
**No demand reduction**
**Collusion is limited**
**Relaxed activity rule means allocation still up for grabs in proxy phase**

**Why Not Use the Clock Auction Only?**

**Notes:**
Chess analogy: It is easier to play a game of chess, than to describe how to play in all circumstances.

## The clock auction is a fast and simple process (compared to the simultaneous ascending auction)
Only provide information relevant for price and quantity discovery (excess demand)
Takes advantage of substitutes (one clock for substitute licenses)
Example: 
proposed 90 MHz of 3G spectrum in 5 blocks: 30, 20, 20, 10, 10
clock alternative: 9 or 18 equivalent blocks per region
Fewer rounds
Get increment increase for all items, rather than having to cycle through over many rounds
“Intra-round bids” allow larger increments, but still permit expression of demands along line segment from start-of-round price to end-of-round price

**Only provide information relevant for price and quantity discovery (excess demand)**
**Takes advantage of substitutes (one clock for substitute licenses)**
**Example: **
**proposed 90 MHz of 3G spectrum in 5 blocks: 30, 20, 20, 10, 10**
**clock alternative: 9 or 18 equivalent blocks per region**
**Fewer rounds**
**Get increment increase for all items, rather than having to cycle through over many rounds**
**“****Intra-round bids” allow larger increments, but still permit expression of demands along line segment from start-of-round price to end-of-round price**

**Advantages of the Clock over the SAA**

**Notes:**
Chess analogy: It is easier to play a game of chess, than to describe how to play in all circumstances.

## Clock auction limits collusion (compared to the simultaneous ascending auction)
Signaling how to split up the licenses greatly limited
No retaliation (since no bidder-specific information)
No stopping when obvious split is reached (since no bidder specific information)
Fewer rounds to coordinate on a split

**Signaling how to split up the licenses greatly limited**
**No retaliation (since no bidder-specific information)**
**No stopping when obvious split is reached (since no bidder specific information)**
**Fewer rounds to coordinate on a split**

**Advantages of the Clock over the SAA**

**Notes:**
Chess analogy: It is easier to play a game of chess, than to describe how to play in all circumstances.

## No exposure problem (unlike SAA)
As long as at least one price increases, bidder can drop quantity on other items
Bidder can safely bid for synergistic gains
Bid is binding only as full package
No threshold problem (unlike SAA with package bids)
Clocks controlled by auctioneer: no jump bids; large bidder cannot get ahead
Linear pricing: small bidders just need to meet price on single item

**As long as at least one price increases, bidder can drop quantity on other items**
**Bidder can safely bid for synergistic gains**
**Bid is binding only as full package**
**No threshold problem (unlike SAA with package bids)**
**Clocks controlled by auctioneer: no jump bids; large bidder cannot get ahead**
**Linear pricing: small bidders just need to meet price on single item**

**Advantages of the Clock Phase**

**Notes:**
Chess analogy: It is easier to play a game of chess, than to describe how to play in all circumstances.

## Combines advantages of 
Clock auction
Proxy auction
Excellent price discovery in clock phase simplifies bidder decision problem
Proxy phase enables bidders to fine-tune allocation based on good price information

**Clock auction**
**Proxy auction**
**Excellent price discovery in clock phase simplifies bidder decision problem**
**Proxy phase enables bidders to fine-tune allocation based on good price information**

**Hybrid Clock/Proxy Auction**

**Notes:**
Chess analogy: It is easier to play a game of chess, than to describe how to play in all circumstances.