45 Asymmetric information and the curse of knowledge
We saw earlier in our examination of the market for lemons and the winner’s curse that asymmetric information can cause market failures even if agents are fully rational. However, the rational agents account for the information and behaviour of others and as a result, behave optimally despite that market imperfection.
There is substantial empirical evidence that people do not behave in this way.
For example, people tend to underestimate the extent to which informational differences drive others’ behaviour. They often act as if others have the same information set that they do. Where an agent has information that another doesn’t, this phenomenon is known as the curse of knowledge.
Further, better-informed agents often fail to take advantage of their informational advantage against less-informed agents because they don’t understand the link between information and behaviour.
45.1 The curse of knowledge
The idea behind the curse of knowledge is that better-informed agents should ignore the additional information they hold when predicting the actions of less-informed agents. Experimental evidence shows that people are unable to ignore their private information even when it is in their interests to do so.
For example, Newton (1990) had students participate in an experiment in one of two roles: “Tapper” and “Listener”.
Tappers received a list of 25 well-known songs and were asked to “tap out” the rhythm of one of the songs.
Listeners tried to identify the song based solely on the taps.
Tappers predicted that listeners would identify 50% of the songs.
Listeners only identified 3 of 120 songs correctly (a rate of about 2.5%).
45.2 The market for lemons
While that experiment involved agents who had more information than the other players - they knew the song - we also see failures where the other player has additional information but the agent does not account for that fact.
We can explore this idea in the market for lemons.
Recall our earlier example in Section 41.1 involving the purchase of a used car.
There are two types of cars, good cars and lemons, and only the seller knows the type. The buyer knows that the seller has this information.
A car is good with probability q and a lemon with probability 1−q. To the seller, good cars are worth $10,000 and lemons $5,000. To potential buyers, good cars are worth $15,000 and lemons $7,500.
A “cursed” buyer doesn’t think that the seller’s decision whether to trade depends on the seller’s knowledge of the car.
Suppose that q=0.2. That is, only 20% of the cars are good.
Suppose the cursed buyer believes that cars are sold with equal probability regardless of type.
In that case, the expected value of a car to a buyer is:
\begin{align*} \hat {\text{E}}&=0.2\times 15000+0.8\times 7500 \\[6pt] &=9000 \end{align*}
A buyer would be willing to pay up to $9000 for a car.
At that price, however, the seller of a good car would not be willing to sell. The market will comprise only lemons, which sellers are more than happy to sell. The buyer will pay $9000 for a car worth only $7500 to them.
45.3 The winner’s curse
We can also explore this phenomenon in the winner’s curse. Recall our example of the winner’s curse in Section 41.2 on bidding for an oil field.
Company 1 and company 2 hire a geologist to estimate the value of an oil field. The honest geologist of each company privately reports their estimated valuation to the company. Company 1 learns v_1 and company 2 learns v_2.
v_1 and v_2 are uniformly distributed between $0 and $100 and independent.
Assume the true value of the oil field is the mean of v_1 and v_2:
V=\frac{v_1+v_2}{2}
The two companies simultaneously bid for the field in a first-price auction. The highest bid wins and pays their bid.
Assume company 1 is cursed and therefore assumes that company 2’s bid is independent of v_2. Company 1 assumes v_2 is on average $50 and that company 2 always bids.
Company 1’s expected profit, if they bid v_1, is:
\begin{align*} \hat {\text{E}}[\pi_1|\text{bid }v_1]&=\frac{1}{2}\pi_1(\text{lose})+\frac{1}{2}\pi_1(\text{win}) \\[12pt] &=\frac{1}{2}\times 0+\frac{1}{2}\bigg(\frac{v_1+50}{2}-v_1\bigg) \\[12pt] &=\frac{1}{4}(50-v_1) \end{align*}
We can see that:
\hat {\text{E}}[\pi_1|\text{bid} v_1]>0 \Leftrightarrow v_1>50
That is, company 1 expects to make a profit if they receive a private valaution of more than $50.
However, as shown in Section 41.2, this bidding approach leads to, on average, a loss. Company 1 under-appreciates that company 2 is more likely not to bid when company 2’s information is bad. Therefore, company 1 under-appreciates the extent to which winning the auction is bad news.
45.4 Example
45.4.1 Acquiring a company
Company A is considering acquiring Company T.
The value of Company T depends on the outcome of an oil exploration project. If the project fails, the company under current management will be worth nothing ($0 per share). If the project succeeds, the value of the company under current management could be as high as $100 per share. All values between $0 and $100 are equally likely.
Company T will be worth 50 per cent more in the hands of Company A than under current management. If the project fails, the company will be worth $0 per share under either management. If the exploration project generates a $50 per share value under current management, the value under Company A will be $75 per share. And so on.
Company A is considering what price per share they should offer. This offer must be made before Company A knows the outcome of the drilling project, but after Company T learns the result. Company T will accept any offer from Company A if it is profitable for them.
a) Show that for any offer above zero Company A expects to lose money.
If Company A offers \$x, Company T will accept x% of the time, whenever the firm is worth between $0 and \$x. Since all those values are equally likely, the firm will be worth on average \$x/2 to company T when they accept. The shares will therefore be worth 1.5\times x/2=3x/4 on average for company A. That gives Company A profit of:
\begin{align*} \pi_A&=\frac{3x}{4}-x \\[6pt] &=-\frac{x}{4} \end{align*}
Any offer above $0 generates a negative expected return, a loss of 25% of the offer.
To give an example, if Company A offered $60, it will be accepted 60% of the time - whenever the firm is worth between $0 and $60 for company T. Since all those values are equally likely, the firm will be worth on average $30 to company T when they accept, meaning it will be worth $45 on average for company A. A $60 offer will result in an average loss of $15.
b) People given this problem tend to bid between $50 and $75 per share. A typical explanation offered by these people is that the average outcome for Company T is $50, making the value for Company A $75. Any offer in the range between these two values would be agreeable to both parties.
Explain why a “cursed” player representing Company A might make a non-zero offer.
A “cursed” player representing company A does not think that company T’s decision to sell depends on company T’s knowledge of the oil exploration. As a result, they are likely to bid based on their unconditional expected value of the field, not the value conditional on acceptance.
This bidding approach leads to, on average, a loss. The cursed player under-appreciates that company T is more likely to accept when company T’s valuation is low.