1. Introduction of Double Auction

As one of the most popular manner to merchandise. auction has a long history. Harmonizing to the different sorts of market construction. there are two sorts of auction. one-side auction and two-side auction ( i. e. dual auction ) . Compared with one-side auction. the market construction of the dual auction is many-to-many. which means that there are more than one marketer and more than one purchaser. so both the purchasers and Sellerss lose their ain comparative advantage which exists in one-side auction. The relationship between them is a sort of equality between demand and supply.

In recent old ages. with the development of the planetary economic system. there are more challenges for new auction theory and its applications. which are shown in the undermentioned facets. First. with the development of the Internet and communicating engineerings. e-commerce has become a new concern method. At the same clip. cyberspace auction has been widely used in the field of e-commerce. Since auction is widely used in the field of merchandising non-scarcity goods. it changes construction of auction. which used to be based on the buyer’s market or the seller’s market. As dual auction can work out the job of collusion and malignant command. it has become a widely used manner in e-commerce.

For illustration. both NYSE and Chicago Exchange have put different sorts of dual auction into pattern. With the turning of fiscal market and e-commerce. the demand for better auction regulations is certainly increasing. Besides. as endeavor restructuring has become a hot subject. dual auction is found to be a manner to cover with belongings minutess. amalgamations and acquisitions. What’s more. with the ascent of demand construction. the variegation scheme for endeavor concern and influence of the supply concatenation direction. there are diversified production. diversified fabrication and diversified demand. Many celebrated auto companies such as Ford are utilizing combinative dual auction to the sale and purchase of car parts. When auction is used in the above Fieldss with assorted demands. there is a great demand for the development of new auction theoretical account.

Compared with other auction mechanisms. dual auction can non merely work out the job of monopoly. but besides cut down the continuance and costs of trade. However. there are still some jobs about it. such as trading regulations. the manner to let go of information and the formation of dealing monetary value.

Harmonizing to the above grounds. dual auction has attracted much attending. And the nucleus theories about it are Smith’s enigma and Hayek job. which try to explicate how the dual auction can make the equilibrium monetary value and equilibrium measure predicted by the demand-supply theoretical account. under the conditions that there is no complete information and few people in the auction.

2. Design of Experiment

In order to make some farther analysis. we conducted an experiment which simplified existent dual auction state of affairss with the aid of several undergraduate pupils under four premises:

First. rational adult male premise. which means everyone wants to maximise his/her net income. Second. the goods are homogenous. so there is no monopoly. Third. there is no cost of directing or acquiring information. i. e. the dealing cost is zero. Fourth. the participants have no information about the experiment parametric quantity ( the value for purchaser or cost for marketer ) before they join the experiment.

( 2 ) Trading regulations

a. When the trade begins. the purchasers give their quotation marks foremost. Who raises his manus foremost will cite foremost. Then. the Sellerss offer the monetary value they ask. B. Both the Sellerss and the purchasers don’t cognize the information about the other side. c. When citing. the marketer must inquire for a monetary value that is lower than the former marketer. and the purchaser must inquire for a monetary value that is higher than the former purchaser. When the monetary value of the two sides is equal. a dealing is reached. d. The trade for each group is divided into three periods and each period lasts for 5 proceedingss.

( 3 ) Trading stairss

a. Divide all the participants into two groups. purchaser and marketer. and each group has 8 people. B. Zero stage trade. In order to do the participants familiar with the regulations. there is a nothing stage trading. the consequence of which is non included into the concluding consequence. c. Begin functionary trade.

d. End trade and take down all the consequences. including every participant’s ain net income in each period and their entire net incomes.

Double Auction Experiment

1. Concept Definition and Parameter Settings

If we carefully see each citing procedure. we will happen the game procedure in dual auction. There are inside game and outside game in the experiment. First. there is among-group game between purchaser and marketer and they want to drive down or force up monetary values to gain as much net income as possible. And based on the theoretical design. a purchaser and a marketer can be merchandising at least one unit of trade good in one trading period. Experiment shows that each purchaser and marketer by and large trade precisely one time each period.

Second. there is within-group game both among purchasers and among Sellerss. Taking purchaser as an illustration. when the marketer quotes a monetary value. purchaser Ten can take to merchandise or wait. If taking to merchandise. he will likely lose a following lower quoted monetary value although obtaining a certain excess. However. if he chooses to wait. so the other purchasers may step in in dealing. which constitute competition for purchaser X. Each purchaser and marketer should see the competition within group. moving as an person in the game. Meanwhile. they should besides see the competition between groups. moving both as an person and a group in the game.

As can be seen. the nucleus of the complex game procedure is the relationship of individual-collective interaction. By detecting dynamic dealing and competitory procedure among single. between the person and the corporate and between the corporate. we try to happen the reading of some jobs. Therefore. building appropriate parametric quantities. we proceed from rational premise to specify single reason and corporate reason severally.

( 1 ) Constructing quoted monetary value maps of the purchaser and the marketer Firstly. presuming the quoted monetary value map of the purchaser I is bidi = six ( 1-?i ) where bidi denotes the quoted monetary value of purchaser i. six denotes the willing-to-pay of purchaser i. ?i denotes expected rate of return.

Second. presuming the quoted monetary value map of the marketer is: askj = cj ( 1+?j ) where askj denotes the quoted monetary value of marketer j. cj denotes the cost of marketer j. ?j denotes the expected rate of return of marketer J.

( 2 ) Harmonizing to the market parametric quantities and theoretical equilibrium monetary value ( 7. 8 ) of purchaser and marketer. we can cipher the standard rate of return of every purchaser and marketer. ?i* and ?j* . severally.

( 3 ) On this footing. we assume that single reason index is bri=?i/?i* of the purchaser. srj= ?j/?j* of the marketer. The higher the index. the higher is the grade of the purchaser or the seller’s single reason. for it indicates more incentive to maximise their involvements strongly. The standard single reason is 1. indicating that the expected rate of return and the existent rate of return of the purchaser or the seller’s are consistent.

( 4 ) Similarly. we can specify the buyer’s corporate reason index as sbri=?i/?i* . where ?i is the mean expected rate of return of all the purchasers who participate in a dealing. ?i* is the standard mean rate of return of the purchasers. What’s more. we can specify the seller’s corporate reason index as ssrj=?j/?j* . The higher the index. the higher is the grade of corporate reason. because it indicates more strongly motive to maximise their corporate involvements. The standard corporate reason is besides 1. bespeaking that the expected corporate rate of return and the existent corporate rate of return of the purchaser or the seller’s are consistent.

2. Analysis of Parameters

In order to analyze the market inefficiency of the 2nd group. we selected two sets of informations as a typical illustration. Group # 1’s dealing monetary value is equal to the theoretical equilibrium monetary value ( 7. 8 ) . while Group # 2’s dealing monetary value is far from the theoretical equilibrium monetary value. merely 6. 3.

Let’s observe the quoted monetary value of the purchasers and the Sellerss in the first group.

We find that in the 2nd offer. S2’s quoted monetary value fell straight from 10 to 7. 5. its monetary value is less than the theoretical equilibrium monetary value 7. 8. which makes the seller’s quoted monetary value become farther and farther off from the equilibrium monetary value. Alternatively. the buyer’s offer is steadily lifting with smaller fluctuation. which makes the purchasers successfully lower monetary value.

Let’s move to the quotation marks of the purchasers and Sellerss from Group # 2.

Obviously. the quote fluctuations of both sides are smaller and the concluding equilibrium monetary value ( Pe ) is closer to the ideal value. Therefore. we may deduce that in the dual auctions where the figure of citations reaches a certain degree. if we want the concluding dealing monetary value to be near to the theoretical equilibrium monetary value. fluctuations in both citations can non be excessively great. otherwise it will be really easy to divert from Pe. accordingly doing either purchaser side or seller side additions excessively much excess.

The ground why we emphasize a certain degree of the figure of citations is that if either one side of the bidders or the inquirers offers a monetary value that is rather close to the expected 1. a trade is really likely to be made. Actually. we do see tonss of speedy minutess in the experiment. particularly the 2nd unit of ammunition of Group # 1. where there would be expected to be fluctuation.

But that speedy trade is based on that either purchaser or marketer or both of them have an intuition about Pe or are merely informed of that monetary value. If the information for both sides is so unequal or even zero. so it will look rather of import to gauge Pe by monetary value fluctuation during the first several quotation marks. On the other manus. nevertheless. significant quote fluctuations will non merely compact the quote infinite afterwards. but besides impair one’s ain market power. while increasing the other side’s market power and excess.

Let’s now look at the alterations in single rate of return and single reason index of Group # 1 and # 2.

Group # 1

A. Expected Rate of Return

The fluctuation of expected rate of return is distinguishable around the marketer S2. where the expected rate of return of purchasers is far higher than that of the Sellerss.

B. Individual Rationality

As can be seen. buyers’ single reason fluctuates more than the sellers’ . while the grade of buyers’ single reason ( & gt ; 1. since unit of ammunition 2 ) is much higher than that of sellers’ ( & lt ; 1. and diminishing since unit of ammunition 2 ) . Therefore. we can presume that there is a corporate irrational phenomenon among the Sellerss.

Normally. both purchaser and marketer will trust to have higher excess and attempt to do the monetary value more good to themselves. So it’s sensible to see that single reason index fluctuates a spot around the standard line or even higher than it. merely to do the concluding dealing monetary value and excess closer to the theoretical 1s.

But in this instance. marketer S2 all of a sudden lowers his expected rate of return ( from the normal 2. 22 to 0. 86 ) . likely because he underestimates Pe or merely wants to rapidly sell the merchandise. It’s rather hard for the undermentioned Sellerss to make the ideal degree. but can merely cite under 1. giving purchasers more infinite for quotation mark and more power to command the market.

If the Sellerss following S2 used to hold higher outlook than 1. so a phenomenon called incompatibility of corporate reason occurs by the influence of incompatibility of single reason. When it happens. the irrational collectivity’s power is impaired and Pe and excess will stop up more good to the other collectivity. As can be seen from the experiment consequences. the corporate reason index of purchasers is 2. 793. which is much higher than that of Sellerss. 0. 808.

Group # 2
A. Expected Rate of Return

The expected rate of return fluctuates more. relatively. What’s more of import. the values of both sides are rather near.

B. Individual Rationality

This corresponds to our old analysis. The single reason index of both purchasers and Sellerss is ever larger and really near to Group # 1. The single reason peers to the standard single reason when the concluding trade is made. In this state of affairs. the quotation mark scope and market power for both sides are similar without any uncertainty. The monetary value at equilibrium and the excess are close to the theoretical value. Therefore. we can believe that there is no perturbation of single reason to corporate reason for both sides. From the position of corporate reason index. sbri=1. 879,ssrj=1. 692,the difference is comparatively little and both values are larger than 1.

From the analysis above. the followers could be inferred. In certain times of quotation mark. if the market’s dealing monetary value and excess diverge from the theoretical Pe and excess. there must be a negative perturbation of single reason to corporate reason for one side which enables the other side to hold dominant power of quotation mark. In another manner. if the market’s dealing monetary value and excess are close to theoretical values. there is traveling to look two instances.

First. single reason and corporate reason are in conformity with each other for both sides and both have the similar market power which consequences in common hostility ; 2nd. perturbations for both sides may be really big and the reason values are non near at all. which does non demo in all the experimental informations while it could be thought to be theoretically. The values are close merely at the dealing monetary value and it is based on an obvious premiss that the values are larger than 1. since every bit long as one value is less than 1. it is really easy ( non needfully ) to fall to a weak place ( which normally happens in the first unit of ammunition of Group # 2 ) . The manner to analyse these three state of affairss is pretty similar to the one analyzing monopoly and competitory markets. The cardinal component is the consequence of the relation between single reason and corporate reason to market power.

Decision

From the analysis above. we can make a primary decision that the quotation mark from a individual marketer or purchaser can impact the formation and the consequence of market equilibrium. We can utilize individual-collective reason theoretical account to explicate the procedure. Individual reason can do a destabilization to corporate reason ( ensuing in singular fluctuation ) . when the destabilization is little. which means that the single reason that causes it is non less than one. the corporate reason still tends to be consistent and this will non hold a important consequence on the market power of both sides.

But when the destabilization is big. which means that the single reason that causes it is less than one. there will be a important consequence on the consistence of the corporate reason. so there will be a alteration of the two sides’ market power. Then. the equilibrium monetary value and the excess of both sides besides change. So. there is a sort of tenseness between single desirableness and corporate desirableness.

There are some points that we need to pay attending to. First. this sort of relationship becomes more obvious with the increasing of citation times during one period. The deeper ground for this is the deficiency of information and each side has to continuously investigation and attempts to let go of every bit much information. which can maximise his net income. as possible. no affair whether the information is true. If the trade can be reached within one or two times. there will be no such complex game about the info releasing and collection. Second. in world. the destabilization is ever negative ( i. e. a sudden lessening in command or expected return ) . which indicates the delimited reason. We don’t need to take positive destabilization into history.

So. how can we utilize this theoretical account to explicate the non efficiency phenomenon of market in dual auction? There are two facets that we need to pay attending to. First. the relationship of single reason and corporate reason has an consequence on the market power. and so affects the equilibrium monetary value and the ratio of the excess of both sides ; the monetary value either has a bad consequence on the Sellerss or the purchasers ( In our experiment. it is the Sellerss that lose ) .

Therefore. some purchasers or Sellerss that could hold entered the trade are kicked off now. which leads to some deadweight loss. Second. when the market power is out of balance. the figure of games between purchasers and Sellerss will increase. Let’s take the 3rd group ( whose dealing monetary value is averagely 10 % less than theoretical Pe ) as an illustration. When the purchasers realize their power and advantage. they will wait the Sellerss to diminish the monetary value. At that clip. from the position of purchasers. the net incomes of waiting is larger than the hazard. The Sellerss are forced to diminish the monetary value. but merely for a small each clip to avoid a worse monetary value. As a consequence. during the limited trading times. the figure of minutess lessenings. which leads to farther deadweight loss.

Mentions

1. JAVIER GIL-BAZO. DAVID MORENO. AND MIKEL TAPIA. “Price Dynamics. Informational Efficiency. And Wealth Distribution in Continuous Double-Auction Markets” . Computational Intelligence. Volume 23. Number 2. 2007 2. Charles A. Holt. Loren W. Langan. Anne P. Villamil. “Market power in unwritten dual auctions” Economic Inquiry. 24:1 ( 1986: Jan. ) p. 107

3. Juliette Rouchier. Stephane Robin. “Simulation & A ; Gaming” 4. Darren Duxbury. “Experimental Evidence on Trading Behavior. Market Efficiency and Price Formation in Double Auctions with Unknown Trading Duration”