1 Introduction Auction experiments with Jasa Jinzhong Niu Department of Computer Science, Graduate Center, City University of New York, 365 Fifth Avenue, New York, NY 10016, USA June 3, 2005 An auction is the process of buying and selling things by offering them up for bid, taking bids, and then selling the item to the highest bidder. In economic theory an auction is a method for determining the value of a commodity that has an undetermined or variable price. Recently auctions have interested computer scientists partly because auction mechanisms can help allocate resources among multiple entities and maximize utility, e.g. solving resource allocation problems 1. Where an auction is different from traditional solutions to resource allocation problems is its characteristics of global optimization despite that knowledge is distributed. In auctions, knowledge first refers to the private values traders have in their mind for goods. By bidding and asking, traders somehow make deals with each other and leads to reallocating goods. Overall profit is one of the measurements to evaluate the new distribution of goods, which is the sum of profits all the sellers and buyers obtain through the auction. For a seller, the profit is the difference between the cost of the commodity he sells and the price at which it is sold; and for a buyer, it is the difference between the price at which he buys a commodity and how much he believes it is worth. To better compare overall profits from different auctions, relative overall profit or overall efficiency is used instead, which is overall profit divided by theoretical overall profit. The latter refers to the overall surplus when the market is cleared at the equilibrium 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 making deals and neither can be higher. 1 Other computer science research on auctions aims to automate commodity exchange, explore experimental economics with the aid of computers, etc.. DRAFT 1
As V. Smith unveiled in 1962 [8], auctions 2 of even a small numberof buyers and sellers can lead to high overall efficiency. He however focused on how transaction prices converge to the equilibrium price in different scenarios rather than why this leads to high efficiency. The latter question is unfortunately one computer scientists 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 solving problems 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 are intelligent creatures, but programs are not, at least in the near future. Is it intelligence that contributes to the high efficiency? Gode and Sunder claimed in 1993 that no intelligence is necessary for this goal [3]. They introduced two trading 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-negative profit, performs well, while ZI-U, the more naive version, which shouts an offer at a random price without considering whether it is losing money or not, performs poorly as expected. Cliff however did not think Gode and Sunder s conclusion is correct because the scenarios considered are not as comprehensive as in Smith s experiments, and the results are not statistical, meaning more execution of auctions should be done to obtain reliable results [1]. Cliff further designed a trading strategy called zero intelligence plus (ZIP) and showed ZIP does work better than ZI-C. More trading strategies have been introduced since then to further increase the amount of intelligence in computer traders and result in even better performance 3. Despite many articles have been produced introducing new trading strategies and describe how well they work in some auction setting, most of their auction configurations are not fully clear, which somehow make it nonsense to compare their results. So it is worthwhile to try to replicate them on an open platform and do comparison, which might help suggest in which direction research in this field should go. Briefly, this report aims to summarize results of auction experiments conducted on Jasa 4 and record all other related issues. 1.1 The goal of experiments Experiments are conducted to draw a landscape of how auction mechanisms, or double auctions more specifically, and trading strategies perform in different scenarios. In details, we are trying to Replicate the results regarding various auction mechanisms and trading strategies, including overal efficiency, profit distribution, and speed 2 These 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. 3 All the well-known strategies in literature will be discussed in detail in Section 3.1. 4 An auction simulation tool. More details is in Section 1.2 2
Find out the weakness of common auction mechanisms and trading strategies, e.g. the GD strategy s relatively poor performance in clearing 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 (http://www.csc.liv. ac.uk/~sphelps/jasa/readme.html). Jasa, or Java Auction Simulator API, is a platform for running experiments in agent-based computational economics. Jasa implements variants of the double-auction market, which is a type of auction that is commonly used to run real world marketplaces such as stock markets and futures markets. It is designed to be highly extensible, so that other types of auctions can easily be implemented. The software also provides base classes for implementing simple adaptive trading agents. More information about Jasa can be found at jasa.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 of potential buyers of that item interact to agree a price. The most common auction form is the ascending bid one, or English auction, in which buyers make increasing bids for the sale item, withdrawing from the process as the price increases, until only one buyer remains) [1]. Since only one type of traders makes offer 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 buyers make 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 determine the market demand curve and asks determine the market supply curve, as shown in Figure 1 [6]; the intersection of the two curves gives the marketclearing (equilibrium) price and all possible trades clear simultaneously at that price. Another type of DAs that has drawn much attention is continuous double auction (CDA), where a group of sellers and a group of buyers simultaneously and asynchronously announce asks and bids, and at any time a trader is free to accept an offer from someone in the opponent group. CDA is practically 5 Shout is also commonly used. 3
Figure 1: Demand and Supply curves in a double auction important because CDA variants have been widely adopted in real-world stock or trading markets. Due to their 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 in experimental economics) [8]. The advancement of computing technology led to simulating auctions by running programs and the process view of auctions [4] make it easy to implement auctions mechanisms in computer software. An auction setting involves many dimensions, some describing characteristics of the aution itself and some others dealing with trading agents in it. A typical DA setting involves the following auction mechanism issues: 1. Traders Traders in an auction are divided into a group of sellers and a group of buyers either randomly 6 or the sizes of two groups specified explicitly. 2. Timing An 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 are initialized in a same way and the auction begins/resumes to run until the day ends. Days in an auction 6 As in Smith s experiments[8]. 7 Called periods by some people. 4
are totally isolated from each other except that knowledge obtained by traders over the previous days may remain. The division of days helps to identify the change of performance caused by the adaptive behavior of traders with the accumulation of knowledge over time. 3. Transaction mechanism Transactions occur when asks and bids cross. When to make transactions and clear the market varies across DA variants. CHs clear the market at the end of each day while CDAs match crossing bids and asks whenever they become available. 4. Pricing policy The prices of transactions may be determined by a discriminatory or a non-discriminatory pricing policy. A discriminatory pricing policy determines a price on a transaction-by-transaction basis, e.g. using the average of the corresponding 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 disclosure Traders in an auction may be notified of various events, e.g. the prices of transactions having taken place and shouts made by others. The amount of information available to traders can affect much or 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 days 8. 3 Trading agents Software agents, similar to humans in traditional auctions, are traders in computational experimental auctions. An agent involves the following parameters: 1. Endowments Each seller/buyer is endowed with the right to sell/buy one or more units of an unspecified commodity 9. The endowment is initialized at the beginning of each day. 2. Value mechanism Each trader is assigned a private value for each commodity it sells or buys. For a seller, a private value is the minimum price at which it is willing to sell a unit, and for a buyer, a private value is the maximum price at which it is willing to buy a unit. 8 As in Gode and Sunder s experiments[3]. 9 According to Gode and Sunder [3], DAs with a single unit per trader yields similar results as in those with multiple units per traders. 5
The collection of the private values determines the demand and supply curves in an auction, and hence determines the equilibrium price and the equilibrium quantity. Private values of traders may be specified explicitly in advance or generated randomly in run-time out of some distribution. 3. Trading strategy A trading strategy helps an agent to determine a shout price, based on the agent s private value and other information obtained over time from the auction. Different trading strategies have different 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 intelligence and 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 high overall efficiency. 3. Zero-Intelligence Plus strategy (ZIP): Designed by Cliff and Bruten [1] to show software agents with additional intelligence motivation of maximizing profit can lead to higher overall efficiency and fairer profit distribution across homogeneous traders. 4. Truth Telling strategy (TT) : Always uses the private value in the shouts. In a CH with all agents using TT, the actual efficiency is 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 algorithm, to adapt its trading behaviour in successive 6
auction rounds by using the agent s profits in the last round as a reward signal. 7. Kaplan Sniping strategy (Kaplan): Todd Kaplan s sniping strategy, with which agents wait until the last minute before attempting to steal the bid. 8. Gjerstad-Dickhaut strategy (GD): The Gjerstad-Dickhaut strategy [2], with which agents calculate the probability of any shout being accepted 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 extensiveform games [7] 2. Widrow-Hoff policy (WH): Originally designed for neural network to minimize errors [9] 4 Measurement of performance We are interested in performance of auction mechanisms and strategies. Performance can be measured in various ways: 1. (Actual) overall efficiency It is used to measure how much social welfare is obtained through the auction. If the (actual) overall profit of the auction is P a = i p i v i for all agents who trade, where p i is the price of the transaction made by agent i and v i is the private value of agent i and the theoretical or equilibrium efficiency P e = v i p 0 i for all agents whose private value is to the left of the equilibrium point where the supply and demand curves intersect, where p 0 is the equilibrium price, the overall efficiency or simply efficiency is E a = P a P e 7
2. Convergence coefficient It is the α introduced by Smith [8] to measure how far an running auction is away from the equilibrium point. It actually measures the profit distribution across traders relative to the equilibrium price [ (pi p 0 ) α = 2 ]/n 100% p 0 3. Competitivity of strategies This is measured by comparing the cumulative profit of agents using a specific strategy against that that of agents using another strategy. Or even more complicatedly, more than 2 types of agents in terms of strategies taken are run in an auction and their relative profit gains are presented in some intuitive graphical way, e.g. the 3-strategy triangle [5]. 4. Computation Effectiveness It measures how many messages (shouts, etc.) transaction. is needed for making a 5 Experiment Series 1 5.1 Goal This series of experiments aim to replicate results reported in literature regarding trading strategies and compare their performance in various scenarios. 5.2 Experiment settings The experiment enumerately executes an auction for each combination of the values of the following dimensions: 1. Auction mechanism either CDA or CH 2. Timing 100 days with 100 periods 10 each day 3. Trading strategies of agents one of ZI-C, ZIP, TT, PS, SR(RE), Kaplan, and GD All sellers always adopt a same strategy, so are all buyers. The two groups however may or may not use a same strategy, resulting in a homogeneous or heterogeneous market. 4. Unit population of traders one of 2, 5, 7, 10, 15, 20, 25, and 30 10 The 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. 8
5. Ratio between the population of sellers and of buyers one of 4:1, 2:1, 1:1, 1:2, and 1:4 If the ratio is 8:1 and the unit population of traders is 5, then the auction will involve 40 sellers and 5 buyers. 6. Value mechanism The group of buyers and the group of sellers separately draw from the uniform distribution [0,200]. 7. Endowment A 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 the values of all the other parameters and run with the same setting at least 100 times so as to get reliable data. 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 are ploted with JFreeChart or MatLab. 100 Homogeneous CH ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 20 10 0 Figure 2: Efficiency in homogeneous CHs 9
100 Homogeneous CDA ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 20 10 Figure 3: Efficiency in homogeneous CDAs 100 Heterogeneous CH with ZI C ZI C ZIP TT PS Kaplan RE GD 60 50 40 Figure 4: Efficiency in heterogeneous CHs against ZI-C 10
100 Heterogeneous CDA with ZI C ZI C ZIP TT PS Kaplan RE GD 60 50 40 Figure 5: Efficiency in heterogeneous CDAs against ZI-C 100 95 Heterogeneous CH with ZIP ZI C ZIP TT PS Kaplan RE GD 85 75 Figure 6: Efficiency in heterogeneous CHs against ZIP 11
95 Heterogeneous CDA with ZIP ZI C ZIP TT PS Kaplan RE GD 85 75 65 Figure 7: Efficiency in heterogeneous CDAs against ZIP 100 95 Heterogeneous CH with TT ZI C ZIP TT PS Kaplan RE GD 85 75 Figure 8: Efficiency in heterogeneous CHs against TT 12
95 Heterogeneous CDA with TT ZI C ZIP TT PS Kaplan RE GD 85 75 65 Figure 9: Efficiency in heterogeneous CDAs against TT 100 95 Heterogeneous CH with PS ZI C ZIP TT PS Kaplan RE GD 85 75 65 60 55 Figure 10: Efficiency in heterogeneous CHs against PS 13
100 95 Heterogeneous CDA with PS ZI C ZIP TT PS Kaplan RE GD 85 75 65 60 55 Figure 11: Efficiency in heterogeneous CDAs against PS 100 95 Heterogeneous CH with Kaplan ZI C ZIP TT PS Kaplan RE GD 85 75 centering 65 Figure 12: Efficiency in heterogeneous CHs against Kaplan 14
100 95 Heterogeneous CDA with Kaplan ZI C ZIP TT PS Kaplan RE GD 85 75 65 Figure 13: Efficiency in heterogeneous CDAs against Kaplan 100 Heterogeneous CH with GD ZI C ZIP TT PS Kaplan RE GD 60 50 40 Figure 14: Efficiency in heterogeneous CHs against GD 15
100 95 85 Heterogeneous CDA with GD ZI C ZIP TT PS Kaplan RE GD 75 65 60 55 50 Figure 15: Efficiency in heterogeneous CDAs against GD 16
6 Experiment series 2 6.1 Goal By examining the results we obtained from experiments with CDA and CH, Professor Parsons suggested some new form of auction mechanism can be designed and the following two modified versions of respectively 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 avoid less competitive asks and bids (more specifically those asks higher than and those bids lower than 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 those transactions. The estimation can be made by using the last transaction price, thus the estimation theoretically may converge to the exact equilibrium point eventually. If the estimation of equilibrium price is absolutely accurate, then CDA-EE can theoretically result in the same efficiency as in CH while maintaining the throughput of a CDA. 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 opposite group 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 the granularity of the PCH is, it is expected to exhibit more or less similiar properties to a CH; however obviously transactions in a PCH can be made time to time as in a CDA rather than in a CH have to wait until the end of the auction. 6.2 Experiment settings The same settings were used as for the previous set of experiments. 6.3 Interpretation of results Again, only the overall efficiency is recorded in different scenarios and its changes along some dimension are ploted with JFreeChart or MatLab. 17
100 Homogeneous CDA EE ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 20 10 0 Figure 16: Efficiency in homogeneous CDA-EEs 100 Homogeneous PCH ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 20 10 0 Figure 17: Efficiency in homogeneous PCHs 18
100 Heterogeneous PCH with ZI C ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 Figure 18: Efficiency in heterogeneous PCHs against ZI-C Heterogeneous CDA EE with ZI C ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 20 10 0 Figure 19: Efficiency in heterogeneous CDA-EEs against ZI-C 19
100 95 Heterogeneous PCH with ZIP ZI C ZIP TT PS Kaplan RE GD 85 75 65 Figure 20: Efficiency in heterogeneous PCHs against ZIP 100 Heterogeneous CDA EE with ZIP ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 20 10 0 Figure 21: Efficiency in heterogeneous CDA-EEs against ZIP 20
100 95 Heterogeneous PCH with TT ZI C ZIP TT PS Kaplan RE GD 85 75 65 60 Figure 22: Efficiency in heterogeneous PCHs against TT 100 Heterogeneous CDA EE with TT ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 20 10 0 Figure 23: Efficiency in heterogeneous CDA-EEs against TT 21
100 Heterogeneous PCH with PS ZI C ZIP TT PS Kaplan RE GD 60 50 40 Figure 24: Efficiency in heterogeneous PCHs against PS 100 Heterogeneous CDA EE with PS ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 20 10 0 Figure 25: Efficiency in heterogeneous CDA-EEs against PS 22
100 95 Heterogeneous PCH with Kaplan ZI C ZIP TT PS Kaplan RE GD 85 75 65 60 Figure 26: Efficiency in heterogeneous PCHs against Kaplan 60 50 Heterogeneous CDA EE with Kaplan ZI C ZIP TT PS Kaplan RE GD 40 30 20 10 0 Figure 27: Efficiency in heterogeneous CDA-EEs against Kaplan 23
100 Heterogeneous PCH with GD ZI C ZIP TT PS Kaplan RE GD 60 50 40 Figure 28: Efficiency in heterogeneous PCHs against GD 100 Heterogeneous CDA EE with GD ZI C ZIP TT PS Kaplan RE GD 60 50 40 30 20 10 0 Figure 29: Efficiency in heterogeneous CDA-EEs against GD 24
7 Comparing strategies in different auction settings The above interpretation compares the performance of different strategies, this section takes another approach, comparing the performances of a same strategy in different homogeneous auction settings. 100 95 Homogeneous ZI C Auctions CDA CH CDA EE PCH 85 75 65 60 Figure 30: Efficiency in homogeneous ZI-C auctions 25
100 95 Homogeneous ZIP Auctions CDA CH CDA EE PCH 85 75 Figure 31: Efficiency in homogeneous ZIP auctions 100 95 Homogeneous TT Auctions CDA CH CDA EE PCH 85 75 Figure 32: Efficiency in homogeneous TT auctions 26
100 95 Homogeneous PS Auctions CDA CH CDA EE PCH 85 75 65 Figure 33: Efficiency in homogeneous PS auctions 100 Homogeneous Kaplan Auctions CDA CH CDA EE PCH 60 50 40 30 20 10 0 Figure 34: Efficiency in homogeneous Kaplan auctions 27
55 50 45 Homogeneous RE Auctions CDA CH CDA EE PCH 40 35 30 25 20 15 10 5 Figure 35: Efficiency in homogeneous RE auctions 100 95 Homogeneous GD Auctions CDA CH CDA EE PCH 85 75 Figure 36: Efficiency in homogeneous GD auctions 28
8 Experiment series 3 8.1 Goal The experiments are executed to observe the dynamics of auction settings, instead of cumulative statistics done in the previous auctions. 8.2 Experiment settings The experiment enumerately executes an auction for each combination of the values of the following dimensions: 1. Auction mechanism CDA, CH, CDA-EE, or PCH 2. Timing 50 periods 3. Trading strategies of agents one of ZI-C, ZIP, TT, PS, SR(RE), Kaplan, and GD At this moment, all sellers and buyers always adopt a same strategy. That is only homogeneous auctions considered this time. 4. population of traders 20 sellers and 20 buyers 5. Value mechanism The group of buyers and the group of sellers separately draw from the uniform distribution [,150]. 6. Endowment 10 units are allowed to trade for each trader. 8.3 Interpretation of results Here we plot, for each combination of bidding strategy and auction type, four plots. These show, evolving over time, te coefficient of convergence, the overall profit, the bids and asks, and the price at which transactions are being made. 29
Figure 37: CH with ZI-C 30
Figure 38: CDA with ZI-C 31
Figure 39: CDA-EE with ZI-C 32
Figure 40: PCH with ZI-C 33
Figure 41: CH with ZIP 34
Figure 42: CDA with ZIP 35
Figure 43: CDA-EE with ZIP 36
Figure 44: PCH with ZIP 37
Figure 45: CH with TT 38
Figure 46: CDA with TT 39
Figure 47: CDA-EE with TT 40
Figure 48: PCH with TT 41
Figure 49: CH with PS 42
Figure 50: CDA with PS 43
Figure 51: CDA-EE with PS 44
Figure 52: PCH with PS 45
Figure 53: CH with Kaplan 46
Figure 54: CDA with Kaplan 47
Figure 55: CDA-EE with Kaplan 48
Figure 56: PCH with Kaplan 49
Figure 57: CH with RE 50
Figure 58: CDA with RE 51
Figure 59: CDA-EE with RE 52
Figure 60: PCH with RE 53
Figure 61: CH with GD 54
Figure 62: CDA with GD 55
Figure 63: CDA-EE with GD 56
Figure 64: PCH with GD 57
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