"Dual-asymmetric information model"

Link to the on-line simulation:
Link to the work page

-- AkshatSinghal - 22 Dec 2006 -- FadilBayyari - 22 Dec 2006

I. Introduction

Transactions involving asymmetric (or private) information are everywhere. A government selling broadcasting licences does not know what buyers are prepared to pay for them; a lender does not know how likely a borrower is to repay; a used-car seller knows more about the quality of the car being sold than do potential buyers. Such asymmetric information can make it difficult for the two people to do business together, which is why economists, especially those practicing game theory, are interested in it. This kind of asymmetry can distort people's incentives and result in significant inefficiencies.

In order to better grasp the effects of asymmetric information, we tested a series of agent-based models with real-life scenarios in mind. Our attempts at recreating the Akerlof's Nobel prize theory were challenging and at times frustrating, but overall rewarding. In examining Akerlof's thesis in detail, we have decided to experiment with what we refer to as the "dual-asymmetric information model." This model is referred to as "dual-asymmetric" not "asymmetric," because it includes a trading scenario with asymmetric buyers and sellers trading at once, as opposed to testing a single asymmetric buyer or seller scenario. We exhibit a model similar to Akerlof's automobile market example, which contains 100 buyers and 100 sellers of two goods-- used cars and money. In keeping the number of lemon sellers (i.e. sellers who know they are selling a lemon and using that information to earn a profit) fixed at 30, and increasing the number of informed buyers, we try to measure how the efficiency of the market changes. We hypothesize that as the number of informed buyers increase (holding asymmetric sellers constant), the effect of having lemons in the system decreases, and so it leads to a greater market efficiency. Our reason for choosing that hypothesis was that a base of well-informed buyers or sellers, but not both, are generally known to increase market efficiency.

II.Lemons, Cars, and Asymmetric Information

George Akerlof’s theory on “asymmetrical” or “asymmetric” information won him the 2001 Nobel Prize in Economics (along with Michael Spence and Joseph E. Stiglitz). His theory is outlined in his article, “The Market for Lemons: Quality Uncertainty and the Market Mechanism,” published in the 1970 Quarterly Journal of Economics. In formulating his thesis, Akerloff concerned himself with the frequent use of “market statistic[s] to judge the quality of prospective purchases.”[1] What he observed was an overwhelming incentive for sellers to market poor quality merchandise in order to produce positive statistical gains for the individual, rather than market higher quality merchandise that would accrue statistical gains for the seller’s firm (and its guild of sellers). In result, there “tends to be a reduction in the average quality of goods and also in the size of the market.”[2]

In order to help explain this process, Akerlof refers to a model with automobiles that captures the essence of asymmetric information and pinpoints the reality of the problem. With so many used cars to choose from and so many sellers with lots claiming to have the “best prices,” eventually one will have to settle on a decision. Such a decision can be costly, while at the same time it can be rewarding. The risk one takes in making a decision rests solely on the true value of the car considering its repair costs, durability, and longetivity. If known, these variables can influence a buyer’s decision to raise or lower his minimum offer price. If unknown, these variables can lead to misfortune for the buyer, as he or she is unaware of the cars true value. This gap of uncertainty is a problem for several buyers with varying degrees of expected purchase values. The used car salesman in this picture has a different story. After all, why would car dealerships hire so many salesmen and women, offering them high salaries and commissions? Obviously these individuals are trained in the art of selling and bargaining, but it’s more than just this. Salesmen have the capability of valuing a car at its true value, with the aforementioned variables considered. They are aware of the cars problems (if any) and value of repairs (if needed) and thus can better gauge the true value of the cars in their lot. What this means in the larger picture is that used car salesmen will always have the upper hand in the deal and the buyer must be wary of this. There are also cases where the opposite is true—that a buyer in a given situation may be asymmetrically informed.

According to Akerlof, there are four types of cars in the automobile market: new cars, used cars, good cars (“oranges”), and bad cars (“lemons”). The relationship between these four cars is related—new cars can be oranges or lemons, as can used cars. Buyers in this model are unaware of whether or not a new or used automobile is a orange or lemon. With this in mind, the buyer faces a probability of (q) that a car is a orange and a probability (1-q) that it is a lemon.

The seller, on the other hand, is aware of his or her vehicles and can accurately judge its repair costs. In doing so, the seller assigns probabilities to cars in order to determine whether or not it is a lemon, and if not, the speed at which it becomes one. Seller’s exhibit asymmetric information, for it must be true that whether or not a car is a lemon or an orange, it is sold at the same price. Consider the following example using oranges and lemons:

Ex.1: Orange/Lemon Net Valuation

In this example, there are two types of cars—oranges and lemons. The seller knows which car is a lemon and which car is an orange. In other words, the seller can decipher which car accrues the highest cost in repairs, which he then uses to imagine its net valuation. Net valuation is calculated as follows:

Valuation – Repair Cost = Net Value (V – RC = NV)

The seller, in this example, values one car for sale at $500, regardless if the car is a lemon or an orange. This is carried out in order to achieve the greatest profit possible—the advantage of being the asymmetric seller. In selling oranges with a fixed repair cost of $100, the seller can sell a car with a net value of $400. When selling a lemon, the seller gains a net value of $100 ($500-$400).

The buyer, in this example, values the seller’s car for sale at $1,000, despite the fact that he has no knowledge of its internal problems. In doing so, his net value of an orange-level car is $900 ($1000-$100). In this transaction, both the buyer and seller go home satisfied (unless of course the buyer can bargain slightly above the seller’s valuation). A risk that the buyer faces is correlated to the ratio of lemons over oranges. If the lemons/oranges ratio is 50%, than the probability that the buyer will purchase a lemon is also 50%. This means that the buyer has a 50% chance of purchasing a car for $1000 that contains a value of either $600(lemon: $1000-$400) or $900(orange: $1000-$100). In short, the buyer holds a higher risk of purchasing a car with a lower net valuation.

Asymmetric cases like the ones mentioned above are generally more severe in reality. Most cars traded at dealerships are lemons, and in some cases, oranges many never be sold. This is because lemon cars and orange cars are sold at the same price, which in turn drives out orange cars.[3] Let’s imagine for a second that the aforementioned table is an illustration of the buyer and seller net valuation for 20 cars. If 18 of these cars are lemons and 2 of these cars are oranges, than the probability that buyer purchases a lemon car without knowing it is 18/20 or 90%. Furthermore, if an individual decides to buy all twenty cars, than he will surely be at a loss (as displayed below). Ex. 3(also shown below) will reverse the order—18 oranges and 2 lemons with asymmetric information, in order to illustrate the “pushing effect” that lemons have(shown in Ex.2).

Ex.2: 18 Lemons & 2 Oranges

Ex.3: 18 Oranges & 2 Lemons

As you can see from Ex. 2, the total net value for a buyer/seller situation exhibiting the "pushing" out effect is $12,600. The total net value for a buyer/seller situation that does not exhibit the "pushing" out effect is $17,400. The difference in total net value between these two graphs is $4,800. This $4,800 is the loss in value to the buyer, resulting from the seller's asymmetric information. Furthermore, it exemplifies the gain and incentive that sellers have in selling lemons over oranges.

III. Experiment

Buyers and Sellers

The Agent-based computational model used in our experiment is different from the Lemon and Orange example we mention above. (we started with the ZI trader model by Mark E. McBride^? in order to calibrate with an existing model of trading, and if run for just one iteration, the system behaves the same as Mr. McBride^?'s ZI-C trader model ). Instead of testing just how sellers benefit from Asymmetric Information, we're looking at how both buyers and sellers benefit from Asymmetric information. Asymmetrically informed buyers benefit by not paying a high price for a low-qualtiy good, which translates to a used car market as a buyer who " knows her cars " and so makes a good buying decision. This seemed like an interesting twist, considering that in this age "the customer is king", and consumers are more informed and more equipped to be informed than ever before.[4]

Our Lemons and Oranges Buyer/Seller Network

Following Akerlof's examples, our experiment is a model market of used cars, implemented in the NetLogo modeling environment. All used cars in this model are exactly identical, and can only be traded in discrete quantities. There are 100 buyers and 100 sellers, and each buyer gets to buy one car in each round of trading, and a seller can sell one car in each round of trading. Before trading begins, each buyer decides on a maximum value (V_buyer) that she has for a used car. Based on this maximum value (V_buyer), the buyer decides on an intial bid price (bidPrice), which she uses in the first round of bidding. In successive rounds of bidding, she would decrease her bid price by $100 in each round that her benefits from the trade increase. We can imagine a buyer to be, say, someone who buys a fleet of used cars for a taxi company and goes to the market with the idea of a maximum amount of money he would pay for a used car.

The seller, similarly, starts off with a cost (C_seller) that he incurred for getting one used car, and based on this cost he comes up with an ask price (askPrice) for the car which is higher than the cost (C_seller). He uses this price the first time he trades. In successive rounds, if the profit he earns from selling one car in a round is greater than the profit he made in the previous round, he increases his askPrice, and decreases it if he makes a smaller profit. In our experiment, V_buyer can have a maximum value of $9000, and C_seller can have a maximum value of $8000.

So, buyers and sellers in this system are Derivative Learners/Followers : they increase or decrease their prices as their benefits change.

Also of note is the fact that sellers and buyers assume that if a seller is selling a used car for a bidPrice, that price includes deductions for all repairs and is a good, honest price . The Lemon sellers here are using asymmetric information because they are selling used cars that have a hidden repair cost in this market where honesty is assumed.

(rand_num = a random number between 0 and 1)

For a buyer k, V_buyer(k) = rand_num * 9000 bidPrice = rand_num * V_buyer(k) Update rule: if profit(t) > profit(t-1) , then bidPrice = bidPrice - 100 (where profit = transactionPrice - V_buyer(k) )

For a seller j, C_seller(j) = rand_num * 8000 askPrice = rand_num * C_seller(j) Update rule: if profit(t) > profit(t-1) , then askPrice = askPrice + 100 if profit(t) > profit(t-1), askPrice = askPrice - 100 (where profit = C_seller(j) - transactionPrice)

Asymmetric Information

Some of these buyers and sellers can have asymmteric information : sellers with asymmetric information are the ones selling lemons, i.e. cars that have a hidden repair cost that they do not tell the buyer about, and buyers with asymmetric information are smart buyers who can differentiate between such lemons sellers and honest sellers of oranges. The asymmetrically informed buyer is a smart consumer, who chooses not to buy from a lemon seller. This can be thought of as the parnoid auto expert - someone who would not buy a car if it seems like it would have major hidden repair costs.

Trading

In each round of trading, a buyer k and a seller j are selected at random, and if the bidPrice(k) of buyer k is greater than the askPrice(j) of seller j, they trade for a transcation price (transactionPrice) that is set randomly between the bidPrice and askPrice. Buyer k and seller j cannot trade again in that round, neither with each other, nor with any other traders.

If the buyer is an asymmetrically informed buyer, and the seller is selling a lemon, the transaction will not happen, and this rule, in essence makes the asymmetric information count

transactionPrice = rand_num[bidPrice,askPrice] (rand_num[bidPrice,askPrice] = a randomly chosen number between bidPrice and askPrice ) ( if the car sold was a lemon, the hidden repair cost (repairCost=$3000) is removed from the buyer's surplus. )

Results

Experiment: Varying number of asymmetric buyers, ceteris paribus

(with number of lemon sellers = 30)

In this experiment, we kept the following variables in the system constant:

number of asymmetrically informed buyers: varied

maximum selling price for a used car: $8000 maximum buying price for a used car: $9000 minimum selling/buying price for a used car: $2000 number of lemon sellers: 30 number of sellers: 100 (this includes lemon sellers) number of buyers: 100 rounds of trading in each iteration: 2000 number of iterations per run: 10 number of runs: 6 (starting from 0 to 100 informed buyers, increasing by 20) hidden repair cost (applies to lemon sellers' cars only): $3000

After running the tests (twice, to account for randomness) we got the following results :

• Table 1: varying number of asymmetrically informed buyers:
  

• Chart 1: varying number of asymmetrically informed buyers:
  

• Table 2: varying number of asymmetrically informed buyers:
  

• Chart 2: varying number of asymmetrically informed buyers:
  

• Dissatisfied with the quality of the above results, we tried two more tests:

• Table 3: varying number of asymmetrically informed buyers by 5, on range [0,100]:
  

• Chart 3: varying number of asymmetrically informed buyers by 5, on range [0,100]:
  

• Table 4: varying number of asymmetrically informed buyers and the number of lemon sellers, in increments of 20 on range [0,100]:
  

• Chart 4: The market efficiency surface on a changing number of lemon sellers and lemon buyers:
  

• Excel sheet for our data: Dual_asymmetry_results.xls: Final results of experiment

Conclusion

The model shows that as the number of asymmetrically informed buyers increases in our model, the market efficiency actually decreases, instead of increasing, as we hypothesized. Whoever said "ignorance is bliss" has been proved correct right now, for a very specific case, using an Agent-based model! Our conjecture is that because there are lemon sellers in the system, as we increase the number of informed buyers, the chances of a lemon seller actually making a sale get lower, and so in the extreme case of a 100% informed consumer population, none of the lemons are sold. So, since these lemon sellers are never making a sale because the informed consumers don't buy from them, they are a loss to society, a.k.a. potential surplus in the market that never gets used. So, here's our lesson of the day:

" If there are sellers with lemons in a market where buyers are fully informed and can discern between a lemon and a cherry, the value of the lemons is a cost to society"

Indeed, looking at the Market efficiency surface chart (which, by the way is not as easy as it looks), we can see how asymmetric information in our used car market affects the overall efficiency.

Bibliography

1. George A. Akerlof, Mani Maun (Aug. 1970). "The Market for 'Lemons': Quality Uncertainty and the Market Mechanism". Quarterly Journal of Economics 84 (3): p. 488.
2. Ibid, 488.
3. Ibid, 489.
4. The Concept of Consumers' Sovereignty, W. H. Hutt, The Economic Journal, Vol. 50, No. 197. (Mar., 1940), pp. 66-77. http://links.jstor.org/sici?sici=0013-0133%28194003%2950%3A197%3C66%3ATCOCS%3E2.0.CO%3B2-T
5. Mark E. McBride^?, 'ZI Trade NetLogo Model' , http://mcbridme.sba.muohio.edu/ace/labs/zitrade/zitradenetlogo.html