auction experiments with jasa -...

Auction Experiments With Jasa

May 30, 2005

Jinzhong Niu

Department of Computer Science

The Graduate Center, The City University of New York

Contents

1 Introduction 1

1.1 The goal of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Tools used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Jasa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.2 MatLab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Auction mechanisms 2

3 Trading agents 4

3.1 Trading strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Learning policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Measurement of performance 6

5 Experiment Series 1 7

5.1 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5.2 Experiment settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5.3 Interpretation of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5.3.1 Homogeneous auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5.3.2 Heterogeneous auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6 Experiment series 2 15

6.1 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15



6.3.1 Homogeneous auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6.3.2 Heterogeneous auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6.3.3 Performances of strategies in different auction settings . . . . . . . . . . . . . . . 22

7 Experiment series 3 25

7.1 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25



i

List of Figures

1 Demand and Supply curves in a double auction . . . . . . . . . . . . . . . . . . . . . . . 3

2 Efficiency in homogeneous CHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Efficiency in homogeneous CDAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 Efficiency in heterogeneous CHs against ZI-C . . . . . . . . . . . . . . . . . . . . . . . . 10

5 Efficiency in heterogeneous CDAs against ZI-C . . . . . . . . . . . . . . . . . . . . . . . 10

6 Efficiency in heterogeneous CHs against ZIP . . . . . . . . . . . . . . . . . . . . . . . . . 11

7 Efficiency in heterogeneous CDAs against ZIP . . . . . . . . . . . . . . . . . . . . . . . . 11

8 Efficiency in heterogeneous CHs against TT . . . . . . . . . . . . . . . . . . . . . . . . . 11

9 Efficiency in heterogeneous CDAs against TT . . . . . . . . . . . . . . . . . . . . . . . . 12

10 Efficiency in heterogeneous CHs against PS . . . . . . . . . . . . . . . . . . . . . . . . . 12

11 Efficiency in heterogeneous CDAs against PS . . . . . . . . . . . . . . . . . . . . . . . . 12

12 Efficiency in heterogeneous CHs against Kaplan . . . . . . . . . . . . . . . . . . . . . . . 13

13 Efficiency in heterogeneous CDAs against Kaplan . . . . . . . . . . . . . . . . . . . . . . 13

14 Efficiency in heterogeneous CHs against GD . . . . . . . . . . . . . . . . . . . . . . . . . 13

15 Efficiency in heterogeneous CDAs against GD . . . . . . . . . . . . . . . . . . . . . . . . 14

16 Efficiency in homogeneous CDA-EEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

17 Efficiency in homogeneous PCHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

18 Efficiency in heterogeneous PCHs against ZI-C . . . . . . . . . . . . . . . . . . . . . . . 17

19 Efficiency in heterogeneous CDA-EEs against ZI-C . . . . . . . . . . . . . . . . . . . . . 17

20 Efficiency in heterogeneous PCHs against ZIP . . . . . . . . . . . . . . . . . . . . . . . . 18

21 Efficiency in heterogeneous CDA-EEs against ZIP . . . . . . . . . . . . . . . . . . . . . 18

22 Efficiency in heterogeneous PCHs against TT . . . . . . . . . . . . . . . . . . . . . . . . 18

23 Efficiency in heterogeneous CDA-EEs against TT . . . . . . . . . . . . . . . . . . . . . . 19

24 Efficiency in heterogeneous PCHs against PS . . . . . . . . . . . . . . . . . . . . . . . . 19

25 Efficiency in heterogeneous CDA-EEs against PS . . . . . . . . . . . . . . . . . . . . . . 19

26 Efficiency in heterogeneous PCHs against Kaplan . . . . . . . . . . . . . . . . . . . . . . 20

27 Efficiency in heterogeneous CDA-EEs against Kaplan . . . . . . . . . . . . . . . . . . . . 20

28 Efficiency in heterogeneous PCHs against GD . . . . . . . . . . . . . . . . . . . . . . . . 20

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29 Efficiency in heterogeneous CDA-EEs against GD . . . . . . . . . . . . . . . . . . . . . . 21

30 Efficiency in homogeneous ZI-C auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

31 Efficiency in homogeneous ZIP auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

32 Efficiency in homogeneous TT auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

33 Efficiency in homogeneous PS auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

34 Efficiency in homogeneous Kaplan auctions . . . . . . . . . . . . . . . . . . . . . . . . . 23

35 Efficiency in homogeneous RE auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

36 Efficiency in homogeneous GD auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

37 CH with ZI-C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

38 CDA with ZI-C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

39 CDA-EE with ZI-C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

40 PCH with ZI-C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

41 CH with ZIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

42 CDA with ZIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

43 CDA-EE with ZIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

44 PCH with ZIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

45 CH with TT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

46 CDA with TT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

47 CDA-EE with TT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

48 PCH with TT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

49 CH with PS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

50 CDA with PS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

51 CDA-EE with PS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

52 PCH with PS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

53 CH with Kaplan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

54 CDA with Kaplan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

55 CDA-EE with Kaplan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

56 PCH with Kaplan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

57 CH with RE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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58 CDA with RE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

59 CDA-EE with RE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

60 PCH with RE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

61 CH with GD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

62 CDA with GD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

63 CDA-EE with GD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

64 PCH with GD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

iv

List of Tables

v

1 Introduction

An auction is the process of buying and selling things by offering them up for bid, taking bids, and thenselling the item to the highest bidder. In economic theory an auction is a method for determining thevalue of a commodity that has an undetermined or variable price. Recently auctions have interestedcomputer scientists partly because auction mechanisms can help allocate resources among multipleentities and maximize utility, e.g. solving resource allocation problems 1.

What an auction is different from traditional solutions to resource allocation problems is its character-istics of global optimization despite that knowledge is distributed. In auctions, knowledge first refersto the private values traders have in their mind for goods. By bidding and asking, traders somehowmake deals with each other and leads to reallocating goods. Overall profit is one of the measurementsto evaluate the new distribution of goods, which is the sum of profits all the sellers and buyers obtainthrough the auction. For a seller, the profit is the difference between the cost of the commodity he sellsand the price at which it is sold; and for a buyer, it is the difference between the price at which he buysa commodity and how much he believes it is worth. To better compare overall profits from differentauctions, relative overall profit or overall efficiency is used instead, which is overall profit divided bytheoretical overall profit. The latter refers to the overall surplus when the market is cleared at theequilibrium price. The equilibrium price is determined by the supply and demand curves of an auction,at which the total supply of sellers involved in transactions equals the total demand of buyers makingdeals and neither can be higher.

As V. Smith unveiled in 1962 [8], auctions 2 of even a bunch of buyers and sellers can lead to high overallefficiency. He however focused on how transaction prices converge to the equilibrium price in differentscenarios rather than why this leads to high efficiency. The latter question is unfortunately computerscientists have to answer before they try to implement auction mechanisms in the electronic world.In Smith’s experiments, as in real markets, traders are human beings, but computer programs solvingproblems like resource allocation are supposed to be automatic and work without human involvement.Can the programs still lead to at least the same good result as human traders do? Obviously humans areintelligent creatures, but programs are not, at least in the near future. Is it intelligence that contributesto the high efficiency?

Gode and Sunder claimed in 1993 that no intelligence is necessary for this goal [3]. They introduced twotrading strategies, zero intelligence without constraint (ZI-U) and zero intelligence with constraint (ZI-C) and showed that ZI-C, which lacks motivation of maximizing profit but guarantees a non-negativeprofit, performs well, while ZI-U, the more naive version, which shouts an offer at a random pricewithout considering whether it is losing money or not, performs poorly as expected. Cliff and Brutenhowever did not think Gode and Sunder’s conclusion is correct because the scenarios considered are notas comprehensive as in Smith’s experiments, and the results are not statistical, meaning more executionof auctions should be done to obtain reliable results [1]. Cliff and Bruten further designed a tradingstrategies called zero intelligence plus (ZIP) and showed ZIP does work better than ZI-C. More tradingstrategies have been introduced since then to further increase the amount of intelligence in computertraders and result in even better performance 3.

1Other computer science research on auctions aims to automate commodity exchange, explore experimental economics

with the aid of computers, etc..2These auctions are called double-sided auctions, or double auctions (DA), since they involves both competing sellers

and buyers, different from the most common auction mechanism—English auction—where only buyers bid.3All the well-known strategies in literature will be discussed in detail in Section 3.1.

1

Despite many articles have been produced introducing new trading strategies and describe how well theywork in some auction setting, most of their auction configrations are not fully clear, which somehowmake it nonsense to compare their results. So it is worthwhile to try to replicate them on an openplatform and do comparison, which might help suggest in which direction research in this field shouldgo.

Briefly, this report aims to summarize results of auction experiments conducted on Jasa 4 and recordall other related issues.

1.1 The goal of experiments

Experiments are conducted to draw a landscape of how auction mechanisms, or double auctions morespecifically, and trading strategies perform in different scenarios. In details, we are trying to

• Replicate the results regarding various auction mechanisms and trading strategies, including overalefficiency, profit distribution, and speed

• Find out the weakness of common auction mechanisms and trading strategies, e.g. GD strategy’spoor performance in clearning house auctions

• Introduce new strategies that are more reliable and efficient

1.2 Tools used

1.2.1 Jasa

The auction experiments are conducted by using Jasa . Jasa , or Java Auction Simulator API, is aplatform for running experiments in agent-based computational economics. Jasa implements variantsof the double-auction market, which is a type of auction that is commonly used to run real worldmarketplaces such as stock markets and futures markets. It is designed to be highly extensible, sothat other types of auctions can easily be implemented. The software also provides base classes forimplementing simple adaptive trading agents.

More information about Jasa can be found at sourceforge.com.

1.2.2 MatLab

MatLab is used to plot data collected from the experiments.

2 Auction mechanisms

Colloqially, the word ‘auction’ refers to arrangements where sellers of a commodity and a group ofpotential buyers of that item interact to agree a price. The most common auction form is the ascending

4An auction simulation tool. More details is in Section 1.2

2

Figure 1: Demand and Supply curves in a double auction

bid one, or English auction, in which buyers make increasing bids for the sale item, withdrawing fromthe process as the price increases, until only one buyer remains[1]. Since only one type of traders makesoffer in English auction, it and the like are called one-sided auctions.

Accordingly, there are double-sided auctions, or double auctions (DA), in which both sellers and buyersmake offers. The most simplest form of DAs is clearing house auctions (CH), or call markets. In CHs,a central impartial autioneer collects bids—offers 5 of buyers, and asks—offers of sellers; bids determinethe market demand curve and asks determine the market supply curve, as shown in Figure˜1 [6]; theintersection of the two curves gives the market-clearing (equilibrium) price and all possible trades clearsimultaneously at that price.

Another type of DAs that has drawn much attention is continuous double auction (CDA), where agroup of sellers and a group of buyers simultaneously and asynchronously announce asks and bids, andat any time a trader is free to accept an offer from someone in the opponent group. CDA is practicallyimportant because CDA variants have been widely adopted in real-world stock or trading markets.

Due to its generality and common use, DAs are the focus of our experiments.

Traditionally, small-scale auctions with human traders are used to investigate properties of auctions inexperimental economics[8]. The advancement of computing technology led to simulating auctions byrunning programs and the process view of auctions [4]make it easy to implement auctions mechanismsin computer software.

An auction setting involves many dimensions, some describing characteristics of the aution itself andsome others dealing with trading agents in it. A typical DA setting involves the following auctionmechanism issues:

1. Traders5‘Shout’ is also used commonly.

3

Traders in an auction are divided into a group of sellers and a group of buyers with either ran-domness 6 or the sizes of two groups specified explicitly.

2. TimingAn auction typically includes a specific number of ‘days’ 7 and each day is of a certain length,making sure all possible transactions could take place, . At the beginning of each day, traders areinitialized in a same way and the auction begins/resumes to run until the day ends. Days in anauction are totally isolated from each other except that knowledge obtained by traders over theprevious days may remain.The division of days helps to identify the change of performance caused by the adaptive behaviorof traders with the accumulation of knowledge over time.

3. Transaction mechanismTransactions occur when asks and bids cross. When to make transactions and clear the marketvaries across DA variants. CHs clear the market at the end of each day while CDAs match crossingbids and asks whenever they become available.

4. Pricing policyThe prices of transaction may be discriminatory or non-discriminatory. A discriminatory pricingpolicy determines a price on a transaction-by-transaction basis, e.g. using the average of thecorresponding bid and ask, while in a non-discriminatory policy all transaction prices are same,e.g. a CH clearing the market at the equilibrium price universally.

5. Information disclosureTraders in an auction may be notified of various events, e.g. prices of transactions having takenplace and shouts made by others. The amount of information available to traders can affect muchor less how they adjust their shouts.

An example of a DA setting is a discriminatory open-cry CDA of 6 buyers and 6 sellers lasting 6 days8.

3 Trading agents

Software agents, similar to humans in traditional auctions, are traders in computational experimentalauctions. An agent involves the following parameters:

1. EndowmentsEach seller/buyer is endowed with the right to sell/buy one or more units of an unspecifiedcommodity 9. The endowment is initialized at the beginning of each day.

6As in Smith’s experiments[8].7Called ‘periods’ by some people.8As in Gode and Sunder’s experiments[3].9According to Gode and Sunder [3], DAs with a single unit per trader yields similar results as in those with multiple

units per traders.

4

2. Value mechanismEach trader is assigned a private value for each commodity it sells or buys. For a seller, a privatevalue is the minimum price at which it is willing to sell a unit, and for a buyer, a private value isthe maximum price at which it is willing to buy a unit.The collection of the private values determines the demand and supply curves in an auction, andhence determines the equilibrium price and the equilibrium quantity.Private values of traders may be specified explicitly in advance or generated randomly in run-timeout of some distribution.

3. Trading strategyA trading strategy helps an agent to determine a shout price, based on the agent’s private valueand other information obtained over time from the auction. Different trading strategies havedifferent requirements on information accessbility.

4. Learning policy

For instance, each seller in an auction is set up to trade one single unit of commodity by using truth-telling strategy with the private values drawn from the uniform distribution [0,200].

3.1 Trading strategies

The following are a list of trading strategies that have been introduced in literature:

1. Zero-Intelligence without Constraint strategy (ZI-U):

Introduced by Gode and Sunder [3] and aimed to be a benchmark to show no human intelligenceand no market discipline result in low overall efficiency.

2. Zero-Intelligence with Constraint strategy (ZI-C):

Introduced by Gode and Sunder [3] and aimed to show market discipline only can guarantee highoverall efficiency.

3. Zero-Intelligence Plus strategy (ZIP):

Designed by Cliff and Bruten [1] to show software agents with additional intelligence—motivationof maximizing profit—can lead to higher overall efficiency and fairer profit distribution acrosshomogeneous traders.

4. Truth Telling strategy (TT) :

Always uses the private value in the shouts. In a CH with all agents using TT, the actual efficiencyis identical to the theoretical one.

5. Pure Simple strategy (PS):

Always shouts with a constant mark-up on the agent’s private value.

6. Stimuli-Response strategy (SR):

A trading strategy that uses a stimuli-response learning algorithm, such as the Roth-Erev algo-rithm, to adapt its trading behaviour in successive auction rounds by using the agent’s profits inthe last round as a reward signal.

5

7. Kaplan Snapping strategy (Kaplan):

Todd Kaplan’s sniping strategy, with which agents wait until the last minute before attemptingto “steal the bid”.

8. Gjerstad-Dickhaut strategy (GD):

The Gjerstad-Dickhaut strategy [2], with which agents calculate the probability of any shout beingaccepted and place an offer to maximize expected profit.

3.2 Learning policies

The learning policies that can be used in SR strategy and are considered in our experiments are:

1. Roth-Erev policy (RE):

Designed by Roth and Erev to mimic human-like behaviors in extensive-form games [7]10.

2. Widrow-Hoff policy (WH):

Originally designed for neural network to minimize errors11.

4 Measurement of performance

We are interested in performance of auction mechanisms and strategies. Performance can be measuredin various ways:

1. (Actual) overall efficiencyIt is used to measure how much social welfare is obtained through the auction. If the (actual)overall profit of the auction is

Pa =∑

i

|pi − vi|

for all agents who trade, where pi is the price of the transaction made by agent i and vi is theprivate value of agent i and the theoretical or equilibrium efficiency

Pe =∑

i

|vi − p0|

for all agents whose private value is to the left of the equilibrium point where the supply anddemand curves intersect, where p0 is the equilibrium price, the overall efficiency or simply efficiencyis

Ea =Pa

Pe

2. Convergence coefficientIt is the α introduced by Smith [8] to measure how far an running auction is away from the equilib-rium point. It actually measures the profit distribution across traders relative to the equilibriumprice

α =

√[∑

(pi − p0)2]/n

p0× 100%

10ToDo: Give details here.11ToDo: give details here.

6

3. Competitivity of strategiesThis is measured by comparing the cumulative profit of agents using a specific strategy againstthat that of agents using another strategy. Or even more complicatedly, more than 2 types ofagents in terms of strategies taken are run in an auction and their relative profit gains are presentedin some intuitive graphical way, e.g. the 3-strategy triangle [5].

4. Computation EffectivenessIt measures how many messages (shouts, etc.) is needed for making a transaction.

5 Experiment Series 1

5.1 Goal

This series of experiments aim to replicate results reported in literature regarding trading strategiesand compare their performance in various scenarios.

5.2 Experiment settings

The experiment enumerately executes an auction for each combination of the values of the followingdimensions:

1. Auction mechanismeither CDA or CH

2. Timing100 days with 100 periods 12 each day13

3. Trading strategies of agentsone of ZI-C, ZIP, TT, PS, SR(RE), Kaplan, and GDAll sellers always adopt a same strategy, so are all buyers. The two groups however may or maynot use a same strategy, resulting in a homogeneous or heterogeneous market.

4. Unit population of tradersone of 2, 5, 7, 10, 15, 20, 25, and 30

5. Ratio between the population of sellers and of buyersone of 4:1, 2:1, 1:1, 1:2, and 1:4If the ratio is 8:1 and the unit population of traders is 5, then the auction will involve 40 sellersand 5 buyers.

6. Value mechanismThe group of buyers and the group of sellers separately draw from the uniformdistribution [0,200].14

12The term ‘period’ follows the convention of Jasa and is used to specify how long relatively a day is. Each period is a

round-robin query of the auctioneer for new shouts from agents.13ToDo: Later on, try different numbers of periods each day.14ToDo: This leads to symmetric supply/demand curves. Later on try flat supply/demand

schedules.

7

7. EmdowmentA single unit is allowed to trade for each trader.

To investigate how much a parameter may affect the auction’s performance, we vary its value and fix thevalues of all the other parameters and run with the same setting at least 100 times so as to get reliabledata. The bigger population is involved in a setting, the fewer times it is repeated. More specially:

5.3 Interpretation of results

Only the overall efficiency is recorded in different scenarios and its changes along some dimension areploted with JFreeChart or MatLab .

5.3.1 Homogeneous auctions

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100Homogeneous CH

Group Size

Effi

cien

cy (

%)

ZI−CZIPTTPSKaplanREGD

0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Homogeneous CH with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 2: Efficiency in homogeneous CHs

8

0 5 10 15 20 25 3010

20

30

40

50

60

70

80

90

100Homogeneous CDA

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Homogeneous CDA with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 3: Efficiency in homogeneous CDAs

9

5.3.2 Heterogeneous auctions

0 5 10 15 20 25 3040

50

60

70

80

90

100Heterogeneous CH with ZI−C

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous CH with ZI−C with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 4: Efficiency in heterogeneous CHs against ZI-C

0 5 10 15 20 25 3040

50

60

70

80

90

100Heterogeneous CDA with ZI−C

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous CDA with ZI−C with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 5: Efficiency in heterogeneous CDAs against ZI-C

10

0 5 10 15 20 25 3070

75

80

85

90

95

100Heterogeneous CH with ZIP

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 3040

50

60

70

80

90

100

110

120Heterogeneous CH with ZIP with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 6: Efficiency in heterogeneous CHs against ZIP

0 5 10 15 20 25 3065

70

75

80

85

90

95Heterogeneous CDA with ZIP

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110

120Heterogeneous CDA with ZIP with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 7: Efficiency in heterogeneous CDAs against ZIP

0 5 10 15 20 25 3070

75

80

85

90

95

100Heterogeneous CH with TT

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 3040

50

60

70

80

90

100

110

120Heterogeneous CH with TT with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 8: Efficiency in heterogeneous CHs against TT

11

0 5 10 15 20 25 3065

70

75

80

85

90

95Heterogeneous CDA with TT

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110

120Heterogeneous CDA with TT with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 9: Efficiency in heterogeneous CDAs against TT

0 5 10 15 20 25 3055

60

65

70

75

80

85

90

95

100Heterogeneous CH with PS

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous CH with PS with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 10: Efficiency in heterogeneous CHs against PS

0 5 10 15 20 25 3055

60

65

70

75

80

85

90

95

100Heterogeneous CDA with PS

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous CDA with PS with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 11: Efficiency in heterogeneous CDAs against PS

12

0 5 10 15 20 25 3065

70

75

80

85

90

95

100Heterogeneous CH with Kaplan

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110

120Heterogeneous CH with Kaplan with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 12: Efficiency in heterogeneous CHs against Kaplan

0 5 10 15 20 25 3065

70

75

80

85

90

95

100Heterogeneous CDA with Kaplan

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110

120Heterogeneous CDA with Kaplan with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 13: Efficiency in heterogeneous CDAs against Kaplan

0 5 10 15 20 25 3040

50

60

70

80

90

100Heterogeneous CH with GD

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous CH with GD with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 14: Efficiency in heterogeneous CHs against GD

13

0 5 10 15 20 25 3050

55

60

65

70

75

80

85

90

95

100Heterogeneous CDA with GD

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous CDA with GD with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 15: Efficiency in heterogeneous CDAs against GD

14

6 Experiment series 2

6.1 Goal

By examining the results we obtained from experiments with CDA and CH, Professor Parsons suggestedsome new form of auction mechanism can be designed and the following two modified versions ofrespectively CDA and CH are designed:

• CDA with equilibrium estimation (CDA-EE)

CDA-EE, based on CDA, tries to estimate the equilibrium price of the market and use it to avoidless competitive asks and bids (more specifically those asks higher than and those bids lowerthan the equilibrium price) making deals with highly competitive bids and asks respectively.This is expected to increase relatively low overall efficiency in CDA than in CH caused by thosetransactions.

The estimation can be made by using the last transaction price, thus the estimation theoreticallymay converge to the exact equilibrium point eventually. If the estimation of equilibrium price isabsolutely acurate, then CDA-EE can result in the same efficiency as in CH.

• Periodic CH (PCH):

PCH takes another approach to keep those less competitive asks and bids away from transactions.It is based on a simple idea that instead of allowing a trader to accept an offer from the oppositegroup as in CDA, PCH forces it to wait until several more competitors are available so that a‘small’ CH auction can be conducted. So a PCH is actually a series of shorter and smaller CHs.

Depending on how much the granuity in a PCH is, a PCH is expected to exhibit more or lesssimiliar properties as a CH does; however obviously transactions in a PCH can be made time totime as in a CDA rather than in a CH have to wait until the end of the auction.



6.3.1 Homogeneous auctions

15

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100Homogeneous CDA−EE

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Homogeneous CDA−EE with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 16: Efficiency in homogeneous CDA-EEs

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100Homogeneous PCH

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Homogeneous PCH with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 17: Efficiency in homogeneous PCHs

16

6.3.2 Heterogeneous auctions

0 5 10 15 20 25 3030

40

50

60

70

80

90

100Heterogeneous PCH with ZI−C

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous PCH with ZI−C with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 18: Efficiency in heterogeneous PCHs against ZI-C

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90Heterogeneous CDA−EE with ZI−C

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous CDA−EE with ZI−C with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 19: Efficiency in heterogeneous CDA-EEs against ZI-C

17

0 5 10 15 20 25 3065

70

75

80

85

90

95

100Heterogeneous PCH with ZIP

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110

120Heterogeneous PCH with ZIP with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 20: Efficiency in heterogeneous PCHs against ZIP

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100Heterogeneous CDA−EE with ZIP

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Heterogeneous CDA−EE with ZIP with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 21: Efficiency in heterogeneous CDA-EEs against ZIP

0 5 10 15 20 25 3060

65

70

75

80

85

90

95

100Heterogeneous PCH with TT

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110

120Heterogeneous PCH with TT with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 22: Efficiency in heterogeneous PCHs against TT

18

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100Heterogeneous CDA−EE with TT

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Heterogeneous CDA−EE with TT with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 23: Efficiency in heterogeneous CDA-EEs against TT

0 5 10 15 20 25 3040

50

60

70

80

90

100Heterogeneous PCH with PS

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous PCH with PS with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 24: Efficiency in heterogeneous PCHs against PS

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100Heterogeneous CDA−EE with PS

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Heterogeneous CDA−EE with PS with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 25: Efficiency in heterogeneous CDA-EEs against PS

19

0 5 10 15 20 25 3060

65

70

75

80

85

90

95

100Heterogeneous PCH with Kaplan

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110

120Heterogeneous PCH with Kaplan with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 26: Efficiency in heterogeneous PCHs against Kaplan

0 5 10 15 20 25 300

10

20

30

40

50

60

70Heterogeneous CDA−EE with Kaplan

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Heterogeneous CDA−EE with Kaplan with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 27: Efficiency in heterogeneous CDA-EEs against Kaplan

0 5 10 15 20 25 3040

50

60

70

80

90

100Heterogeneous PCH with GD

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 300

20

40

60

80

100

120Heterogeneous PCH with GD with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 28: Efficiency in heterogeneous PCHs against GD

20

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100Heterogeneous CDA−EE with GD

Group Size

Effi

cien

cy (

%)


0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Heterogeneous CDA−EE with GD with Standard Deviation

Group Size

Effi

cien

cy (

%)


Figure 29: Efficiency in heterogeneous CDA-EEs against GD

21

6.3.3 Performances of strategies in different auction settings

The above interpretation compares the performance of different strategies, this section takes anotherapproach, comparing the performances of a same strategy in different homogeneous auction settings.

0 5 10 15 20 25 3060

65

70

75

80

85

90

95

100Homogeneous ZI−C Auctions

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

0 5 10 15 20 25 3020

30

40

50

60

70

80

90

100

110Homogeneous ZI−C Auctions with Standard Deviation

Group SizeE

ffici

ency

(%

)

CDACHCDA−EEPCH

Figure 30: Efficiency in homogeneous ZI-C auctions

0 5 10 15 20 25 3070

75

80

85

90

95

100Homogeneous ZIP Auctions

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

0 5 10 15 20 25 3065

70

75

80

85

90

95

100

105Homogeneous ZIP Auctions with Standard Deviation

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

Figure 31: Efficiency in homogeneous ZIP auctions

22

0 5 10 15 20 25 3070

75

80

85

90

95

100Homogeneous TT Auctions

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

0 5 10 15 20 25 3065

70

75

80

85

90

95

100

105Homogeneous TT Auctions with Standard Deviation

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

Figure 32: Efficiency in homogeneous TT auctions

0 5 10 15 20 25 3065

70

75

80

85

90

95

100Homogeneous PS Auctions

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

0 5 10 15 20 25 3020

30

40

50

60

70

80

90

100

110

120Homogeneous PS Auctions with Standard Deviation

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

Figure 33: Efficiency in homogeneous PS auctions

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100Homogeneous Kaplan Auctions

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

0 5 10 15 20 25 30−20

0

20

40

60

80

100

120Homogeneous Kaplan Auctions with Standard Deviation

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

Figure 34: Efficiency in homogeneous Kaplan auctions

23

0 5 10 15 20 25 305

10

15

20

25

30

35

40

45

50

55Homogeneous RE Auctions

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

0 5 10 15 20 25 30−20

−10

0

10

20

30

40

50

60

70Homogeneous RE Auctions with Standard Deviation

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

Figure 35: Efficiency in homogeneous RE auctions

0 5 10 15 20 25 3075

80

85

90

95

100Homogeneous GD Auctions

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

0 5 10 15 20 25 3040

50

60

70

80

90

100

110

120Homogeneous GD Auctions with Standard Deviation

Group Size

Effi

cien

cy (

%)

CDACHCDA−EEPCH

Figure 36: Efficiency in homogeneous GD auctions

24

7 Experiment series 3

7.1 Goal

The experiments are executed to observe the dynamics of auction settings, instead of cumulative statis-tics done in the previous auctions.


The experiment enumerately executes an auction for each combination of the values of the followingdimensions:

1. Auction mechanismCDA, CH, CDA-EE, or PCH

2. Timing50 periods

3. Trading strategies of agentsone of ZI-C, ZIP, TT, PS, SR(RE), Kaplan, and GDAt this moment, all sellers and buyers always adopt a same strategy. That is only homogeneousauctions considered this time.

4. population of traders20 sellers and 20 buyers

5. Value mechanismThe group of buyers and the group of sellers separately draw from the uniformdistribution [80,150].

6. Emdowment10 units are allowed to trade for each trader.


25

Figure 37: CH with ZI-C

26

Figure 38: CDA with ZI-C

27

Figure 39: CDA-EE with ZI-C

28

Figure 40: PCH with ZI-C

29

Figure 41: CH with ZIP

30

Figure 42: CDA with ZIP

31

Figure 43: CDA-EE with ZIP

32

Figure 44: PCH with ZIP

33

Figure 45: CH with TT

34

Figure 46: CDA with TT

35

Figure 47: CDA-EE with TT

36

Figure 48: PCH with TT

37

Figure 49: CH with PS

38

Figure 50: CDA with PS

39

Figure 51: CDA-EE with PS

40

Figure 52: PCH with PS

41

Figure 53: CH with Kaplan

42

Figure 54: CDA with Kaplan

43

Figure 55: CDA-EE with Kaplan

44

Figure 56: PCH with Kaplan

45

Figure 57: CH with RE

46

Figure 58: CDA with RE

47

Figure 59: CDA-EE with RE

48

Figure 60: PCH with RE

49

Figure 61: CH with GD

50

Figure 62: CDA with GD

51

Figure 63: CDA-EE with GD

52

Figure 64: PCH with GD

53

References

[1] Dave Cliff and Janet Bruten. Minimal-intelligence agents for bargaining behaviours in market-basedenvironments. Technical report, Hewlett-Packard Research Laboratories, Bristol, England, 1997.

[2] Steven Gjerstad and John Dickhaut. Price formation in double auctions. Games and EconomicBehavior, 22:1–29, 1998.

[3] Dhananjay K. Gode and Shyam Sunder. Allocative efficiency of markets with zero-intelligencetraders: Market as a partial substitute for individual rationality. Journal of Political Economy,101(1):119–137, 1993.

[4] Mark Klein, Simon Parsons, and Juan Antonio Rodriguez-Aguilar. A bluffer’s guide to auctions.Technical report, Center for Coordination Science, Sloan School of Management, MassachusettsInstitute of Technology, 2003. Research Note.

[5] Steve Phelps, Simon Parsons, Peter McBurney, and Elizabeth Sklar. Co-evolution of auction mech-anisms and trading strategies: towards a novel approach to microeconomic design. In Proceedingsof ECOMAS 2002 workshop, 2002.

[6] Chris Preist and Maarten van Tol. Adaptive agents in a persistent shout double auction. InProceedings of the 1st International Conference on Information and computation economies, pages11–18. ACM Press, 1998.

[7] Alvin E. Roth and Ido Erev. Learning in extensive-form games: Experimental data and simpledynamic models in the intermediate term. Games and Economic Behavior, 8:164–212, 1995.

[8] V. L. Smith. An experimental study of competitive market behaviour. Journal of Political Economy,70(2):111–137, April 1962.

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