CAT 2008 Post-Tournament Evaluation: The Mertacor's Perspective
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Presentation given at Trading Agent Design and Analysis workshop 2009 (TADA'09) on Mertacor agent's strategies for TAC Market Design (CAT) 2008
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CAT 2008 Post-Tournament Evaluation: The Mertacor's Perspective
- 1. Lampros C. Stavrogiannis and Pericles A. Mitkas Electrical and Computer Engineering Dept., Aristotle University of Thessaloniki, Greece TADA-09, Pasadena, California, USA, July 13, 2009
- 2. CAT 2008 The Global CE Mertacor Specialist Evaluation Conclusions 9 Pericles A. Mitkas 2
- 3. 500 trading days, 10 trading rounds Multiple markets (specialists) Trading agents Trading strategy (ZI-C, ZIP, RE, GD) Market selection strategy Endowment (private value + entitlement) Single-unit, persistent shouts (bids, asks) 9 Pericles A. Mitkas 3
- 4. 9 Pericles A. Mitkas 4
- 5. Global CE NYSE LSE ASE Global Market 9 Pericles A. Mitkas 5
- 6. Estimation Observations Constant private values Buyers underbid almost as much as sellers overbid Real and reported global CE almost coincide 9 Pericles A. Mitkas 6
- 7. Estimation Record Traders’ highest bids and lowest asks Traders’ number of goods traded Subscribe to opponent specialists Construct global aggregate demand and supply ≥ 80% of traders’ population 4-heap algorithm 009 Pericles A. Mitkas 7
- 8. Estimation Sellers Traders Buyers Games 2008 Mean expected APE = 0.9% - Mean APE smaller Mean first trading day = 6 - 4 different opponents each day 9 Pericles A. Mitkas 8
- 9. 9 Pericles A. Mitkas 9
- 10. Accept shouts Quote-Accepting Policy Match shouts Matching Policy Transactions time Clearing Policy Transactions price Pricing Policy Specialist’s profit Charging Policy 9 Pericles A. Mitkas 10
- 11. Beat global CE price 4-heap algorithm Highest bids <-> Lowest asks Transactions cleared at the First rounds end of each round of each day (CH phase) Global CE price 9 Pericles A. Mitkas 11
- 12. Beat the quote NYSE rule 4-heap algorithm Continuous clearing Remaining rounds (CDA phase) Modified side-biased pricing Balance buyers and sellers More profit to the globally intra-marginal traders 9 Pericles A. Mitkas 12
- 13. Limited Score-Based Charging Profit fee - Discriminatory charging - [0.1, 0.3] Beat opponents with higher cumulative scores in time intervals proportional to score differences - Pay attention to lower opponents with higher daily scores 9 Pericles A. Mitkas 13
- 14. Heterogeneous Populations 1-1 1-N - 1 Mertacor against 5 opponents - 1 opponent against 5 Mertacor specialists Traders’ strategy mix identical to that of the final games for 2008 Homogeneous Populations 6 specialists ZI-C trading agents worst case analysis 9 Pericles A. Mitkas 14
- 15. 1-1 Profit-share Market-share Score TSR 9 Pericles A. Mitkas 15
- 16. 1-1 Daily Results Convergence for MANX and jackaroo Mertacor vs. MANX Mertacor vs. jackaroo 9 Pericles A. Mitkas 16
- 17. 1-N 1 Opponent vs. 5 Mertacors 1 Mertacor vs. 5 Opponents 9 Pericles A. Mitkas 17
- 18. Homogeneous Populations 9 Pericles A. Mitkas 18
- 19. Homogeneous Populations 9 Pericles A. Mitkas 19
- 20. Novel estimation of the global CE Accurate Rapid Independent of pricing policies Further modification for more dynamic environments Results in accordance to CAT 2008 Mertacor Second most profitable specialist Problems with TSR 009 η, Απρίλιος 2009 3οPericles A. Mitkas ΣΦΗΜΜΥ 25 20
- 21. Thank you!
Editor's Notes
- 12/21/12 02:42 © 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
- We will first remind you of some essential facts concerning the CAT tournament. Afterwards, we will introduce the notion of the global Competitive Equilibrium and our estimation technique for it. Then, we will shortly describe our agent’s strategies. Continually, we will present our experimental results and, finally, we will provide you with the conclusions of our work.
- Each game of CAT consists of 500 virtual days, called trading days, each of which is further divided in 10 trading rounds of fixed duration. In the CAT setting there are multiple double auction markets, which are called specialists, as well as multiple traders or trading agents. Each trader has a trading strategy and a market selection strategy. The former determines their bidding behavior and the latter determines the specialist where they will trade. Each trading agent is endowed with a private value, which is drawn from an unknown distribution at the start of the game and remains constant for the rest of it, as well as with a number of goods to trade (called the entitlement of the trader). Traders are able to submit offers (or shouts). Sellers’ offers are called asks and buyers’ offers are called bids. Traders’ shouts are single-unit, meaning that every shout expresses the desire to trade one unit of the good, and persistent, meaning that, once submitted, these shouts remain active until they result in a transaction or the end of the day is reached. The evaluation of the contestants commences and terminates in randomly selected trading days and their score is the sum of the daily scores across these days. The daily score is the mean value of three metrics: (i) the market-share, which is the percentage of the total traders’ population registered in the market, (ii) the profit-share, which is the ratio of the daily profit a specialist obtains to the profit of all specialists, and, (iii) the transaction success rate (TSR), which is the percentage of the shouts accepted that result in transactions
- According to the theory of microeconomics, the aggregate demand and supply curves of a system are expected to meet at a point (that is a pair of price and quantity), which is called the competitive equilibrium of the market and where the allocative efficiency is maximized, if all of the transactions are cleared at its price.
- In a global economy every stock market has its own CE. The global CE is the CE of the equivalent global market where all the trading agents would trade had it not been their splitting due to the existence of multiple specialists. In a competitive scenario, like CAT, where we have mechanisms with payments, it is important for a competitor to identify this point and coordinate its CE with it in order to be both efficient and profitable.
- Our estimation of this point is based on some observations about the game. The first one is that traders’ private values are constant during each game and secondly that, from our experiments, we have observed that buyers’ and sellers’ mean profit margin are nearly equal. So, as depicted in the figure of the slide, real and reported global CE almost coincide.
- To estimate this point, our specialist traces buyers’ highest bids and sellers’ lowest asks submitted, as well as their entitlement. We are also using the possibility of subscription to some of the opponents, thus gaining information to the shouts submitted in their markets, so as to accelerate our estimation process. When a sufficient number of traders have been explored (80% of the total traders’ population for the games of 2008), we use the 4-heap algorithm to construct the global aggregate demand and supply curves and obtain the estimated global CE.
- You can see in this slide the estimated private value distributions for the sellers, the buyers and all the trading agents, as they were obtained from our record for the first final game of 2008. The form of the pdfs is similar for the rest of the games. As can be seen, our estimated pdf is very close to the real theoretical uniform pdf for this game. The mean expected absolute percentage error for our estimation is 0.9% for the three games and we were able to have our estimated global CE very soon within the game (since the 6 th trading day on the average)
- This is the architecture of our specialist, Mertacor. The Market Client is the communication component of our agent with the server. There is also a registry where recorded information is stored. The auctioneer is responsible for the coordination of the agent’s strategies as well as the communication with the market client and the registry components. Finally, there are five different policies providing solutions to an equal number of problems a specialist faces.
- So, a specialist should first filter the shouts to be placed in its market. This is the task of the quote-accepting policy. After that, the matching policy determines the way that these shouts should be matched for potential transactions. Then, the clearing policy decides when the transactions will be cleared and their price will be determined by the pricing policy. Finally, the charging policy is responsible for the fees a specialist should charge traders for its services. We will now discuss these policies as they were implemented in our market.
- For the first rounds of each day, Mertacor acts like a Clearing-House market. Qualified shouts must beat the estimated global CE price. Then, Mertacor utilizes the 4-heap algorithm for the matching operation, so that highest bids are matched with lowest asks. All of the transactions are cleared at the end of each round and their price is set at the price of the estimated global CE.
- For the remaining rounds, Mertacor acts like a CDA market. So, accepted shouts must beat current quote. The matching policy is the same but a transaction is cleared as soon as there is a matchable pair of bids and asks. For this phase, Mertacor implements a modified version of the side-biased pricing rule, introduced by IAMwildCAT in 2007. The objective of this policy is to balance buyer and seller populations in the market. Our modification lies in the case when a transaction between a globally intra-marginal and a globally extra-marginal trader takes place, where we make sure that the former obtains a greater profit.
- Mertacor charges only a profit fee (percentage of the traders’ profit from a transaction), which is limited in the interval [10%,30%]. We selected this fee for two reasons: the first one is that only profitable traders should pay for our services. Secondly, this is the only type of fees that allows us to implement a discriminatory charging rule, which we believe to be the most fair type of charging. Our charging policy is score-based. More specifically. Mertacor tries to beat opponents with higher cumulative scores in time intervals proportional to their score differences, but also considers opponents with highly daily scores, which might threaten its position in the game.
- We conducted a number of experiments to compare our specialist with the remaining contestants. Our experiments can be distinguished in three types: (i) one-to-one experiments, where one opponent is compared against Mertacor, (ii)one-to-many experiments, where many opponents are compared against one Mertacor, and, conversely, many Mertacor specialists are compared against one opponent, and, finally (iii) experiments with homogeneous populations of specialists where all the markets implement the same strategies. In the first two cases, we have used the same strategy mix for traders as with the games of 2008 and we have assessed the specialists mainly according to their scores. For the homogeneous case, we have made a worst-case analysis, where traders follow the ZI-C strategy, and specialists are assessed according to their global allocative efficiency and global coefficient of convergence. The former is the ratio of the traders’ profit to their maximum profit in the equivalent single global market. The global coefficient of convergence is proportional to the standard deviation of the transaction prices from the global competitive equilibrium price divided by the latter price.
- This slide presents our results for the one-to-one scenario. The polar coordinates of each vertex of the solid-line polygon represent Mertacor’s score, whereas the coordinates of the vertices of the dashed-line polygon represent opponents’ respective scores. As can be seen, Mertacor is beaten by PersianCAT and jackaroo and wins over the other specialists. Although Mertacor is the second most profitable specialist, its TSR is low, resulting in a lower score than these two opponents mentioned before.
- We have also plotted the score results on a daily basis for our experiments. Score differences are constant for the majority of the opponents, except for jackaroo and especially MANX, where we can see a relative convergence.
- These are the results of the one-to-many scenario. We can see that these results are qualitatively similar to the one-to-one case. We can see a significantly higher score for Mertacor, when it faces multiple DOG and IAMwildCAT opponents, but this is mainly due to the differences in their charging policies implemented.
- This slide presents our results for the homogeneous population of specialists, and more specifically, the values of the global allocative efficiency. MANX specialists provide the most efficient results. What’s important is that the values for this metric are greater than 90% for all of the contestants, validating once again the effectiveness of the DA mechanism.
- We can also see the results for the global coefficient of convergence. The smaller the value of this metric, the better for a specialist. It is interesting that MANX specialists have the greatest value for this metric, although being the most globally efficient markets. Our high coefficient of convergence is due to the CDA-like policies implemented during the second phase of our strategy.
- In this presentation, we have introduced a novel estimation technique for the global competitive equilibrium, which is quite accurate and rapid. Most important it is independent of the transaction prices in the market. Trying to estimate the price of this point from the latter highly depends on the pricing policies implemented by the opponent markets, thus the accuracy of this estimation might be poor when some of the opponents are inefficient, or set their transaction prices according to their – unknown to us – various objectives. This technique works very well for the CAT’s current static scenario but we should modify it to work effectively in more dynamic environments, where traders’ private values are not constant. Our experimental results are generally in accordance to the results of 2008. Finally, we have seen that Mertacor is quite effective in its profit-share, being the second most profitable specialist in our experiments, but there are some problems concerning its TSR, mostly because of the CDA-like policies during the last rounds, which kept our specialist in the 5 th position.